Do dollars decide in Africa whether a child should live or not? Association of health expenditure on health outcomes in Africa Health expenditures have a statistically significant effect, although low, on infant, neonatal and under‐five mortality in Africa. Supervisor: professor Whitehead Author: Soheila Abachi 11/17/2014
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Table of Contents 1. Abstract ................................................................................................................................................ 3
2. Introduction .......................................................................................................................................... 4
3. Methods ................................................................................................................................................ 5
4. Analysis ................................................................................................................................................. 5
4.1. Linear regression .......................................................................................................................... 5
4.1.1. Assumption of the linear regression .................................................................................... 5
4.2. Principal component analysis ...................................................................................................... 6
4.2.1. Assumption of principal component analysis ..................................................................... 6
4.3. Redundancy analysis .................................................................................................................... 7
5. Results................................................................................................................................................... 7
5.1. General linear model .................................................................................................................... 7
5.2. Principal component analysis ...................................................................................................... 8
5.2.1. PCA on all the variables ............................................................................................................ 8
5.2.2. PCA on 2 sets of variables ........................................................................................................ 9
5.3. Redundancy analysis .................................................................................................................. 10
6. Discussion ........................................................................................................................................... 10
7. Acknowledgments .............................................................................................................................. 10
8. References .......................................................................................................................................... 11
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1. Abstract
Health expenditures have a statistically significant effect on infant, neonatal and under‐five mortality. For African countries, our results imply that total health expenditures (as well as the government component) are certainly important contributor to health outcomes in terms of child mortality rates. Per capita government expenditure on health seemed to be more significant on models especially per capita government expenditure on health for the year 1995. Inter correlation of the two sets of variables, health expenditures and mortality rates, are strong but not between the variables. Infant, neonatal and under‐five mortalities are negatively correlated with the health expenditure in the Sub‐Saharan African countries studied. Health care expenditure seems to be only one of the many factors important in improving the health status of a member. The analysis presented in this paper finds evidence of a weak statistically significant relationship between per capita health spending, and health outcomes. Each of the health outcomes can be an indication of the other health outcome. Neonatal mortality rate itself is an indication of how high or low the infant mortality is going to be in a specific year in a country. This may be due to the infection caused death among the under five which accounts for 73% of under 5 death in Africa. In countries with high infant mortality rate, the absence of a strong statistical relationship may be due to model misspecification or may reflect the fact that at high levels of population health, the returns for the increases in health spending are small. For future studies, other variables should be included.
Abbreviations PC95TEXH 1995 Per capita total expenditure on health (PPP int. $) PC05TEXH 2005 Per capita total expenditure on health (PPP int. $) PC95GEXH 1995 Per capita government expenditure on health (PPP int. $) PC05GEXH 2005 Per capita government expenditure on health (PPP int. $) UFD00 2000 Number of under‐five deaths (thousands) UFD10 2010 Number of under‐five deaths (thousands) ID00 2000 Number of infant deaths (thousands), ID10 2010 Number of infant deaths (thousands) ND00 2000 Number of neonatal deaths (thousands) ND10 2010 Number of neonatal deaths (thousands)
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2. Introduction Life expectancy is linked to economic growth and, 10% increase in life expectancy at
birth will increase the economic growth rate by 0.35% a year, according to WHO (world health organization). There is evidence that empowering health will bring significant benefits for the economy (1). Low health status is a heavy financial burden and according to Commission on Macroeconomics and Health (2001) economic growth of wealthy and poor countries is about 50% different due to the life expectancy and health status. Economists consider child health and mortality as important indicators of the success or failure of a government policy especially when studying developing countries (2). Health definitely is linked with sustainable economic growth and development. This could be due to the fact that healthy population is more productive at work, spend more time in the workplace, stay in labor force longer, invest in their own and children’s education leading to the increased productivity and generally earn higher incomes which could potentially be the funds available for investment in the economy (3).
Two‐thirds of deaths occur in just 10 countries. Child mortality in West and Central Africa is the highest. In these regions, more than 150 of every 1,000 children born die under age five in compare to 6 of every 1,000 children born in a wealthy country (North America, Western Europe and Japan) (UNICEF). Health care expenditure per person per year in high‐income countries exceeded US$ 2,000 while in Africa it averaged between US$13‐$21 in 2001 (Commission for Africa, 2004). In sub‐ Saharan Africa the expenditure should rise to US$ 38 by 2015 just to deliver basic treatment and care for the major communicable diseases (HIV/AIDS, TB and malaria), and early childhood and maternal illnesses (Commission for Macroeconomics and Health, 2001). Total spending on health has shown minimal to no impact on child mortality in some of earlier studies(4, 5). These studies have recorded empirical evidence that public spending on health is not the main cause of child mortality outcomes (6). The variation could be very well explained by other factors such as income, income inequality, female education, mother literacy, degree of ethnolinguistic fractionalization and findings show that these all play significant role in child mortality across countries (7‐9). These results mean that reduced poverty, income inequality, and increased female education would reduce child mortality as much than just increasing public spending on health. Despite public belief, study has shown that government health expenditures account for less than one‐seventh of one percent variation in under‐five mortality across countries and the conclusion was drawn that 95% of the variation in under‐5 mortality can be enlightened by factors such as a country’s per capita income, female educational level, resources at hospital, managed care and choice of region (10, 11). The same applies to low‐income countries where no significant relationship between health expenditure spending and infant mortality was found (12). Enhanced sanitation as a public health measure have proved to play a bigger role in improving child health in the past 150 years than even the most advanced personal medical care technologies (13, 14). Therefore, child mortality may be not a good measure of social and economic conditions such as public health, insurance coverage, or economic crises in all countries but certainly is considered good indicator for African countries. In 2000, the United Nations (UN) set eight targets, known as Millennium Development Goals, aiming to promote human development of which four are in direct or indirect relation to child mortality rate. The key targets to be reached by 2015 throughout the world are in the areas of poverty reduction, health improvements, education attainment, gender equality, environmental sustainability, and fostering global partnerships
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(figure 1). The fourth goal to reduce child mortality by two‐thirds requires action on the first goal, halving extreme poverty and hunger, since malnutrition caused by chronic hunger causes the death of more than 5 million children each year globally (15). 3. Methods
The dataset contains 12 continuous variables with the sample size of 45 (45 African countries) which is large and good enough for the central limit theorem (CLT) [approximately normally distributed]. It is hypothesized that child yearly death rate as an indicator of health outcome, depend upon variance in government and total health expenditure (figure 4, 5, 6). In this research, the economical consequences of health spending on child death rate will be studied and results will be reported. The questions to be answered are as below; 1. Neonatal mortality rate 2010 is a response of government and total health expenditure of
1995 and 2005 2. Neonatal mortality rate 2010 is a response of government and total health expenditure
2005 3. Infant mortality rate 2010 is a response of government and total health expenditure of
1995 and 2005 4. Infant mortality rate 2010 is a response of government and total health expenditure 2005 5. Under 5‐mortality rate 2010 is a response of government and total health expenditure of
1995 and 2005 6. Under 5‐mortality rate 2010 is a response of government and total health expenditure
2005 7. Neonatal mortality rate 2000 is a response of government and total health expenditure
1995 8. Infant mortality rate 2000 is a response of government and total health expenditure 1995 9. Under 5‐mortality rate 2000 is a response of government and total health expenditure
1995 4. Analysis
4.1. Linear regression Performing linear regression about child mortality (response) and explanatory variables
(government and total health expenditures) would tell us if there is any relationship between the response and the explanatory variables thus there might be some collinearity or multicollinearity among the independent variables (exact collinearity should be considered because if there is any then the regression coefficient cannot be calculated). Correlations whether positive, negative, and associations whether strong or weak can be determined in this step.
4.1.1. Assumption of the linear regression To check the normality of each variable, Shapiro‐Wilk normality test was performed
and the p‐values were analyzed on both original dataset and the log10 transformed dataset (table 3). For the original data, the p‐values for all the variables are less than alpha so the null hypothesis is rejected in the favor of alternative hypothesis. To make the data of normal distribution log10 transformation was applied to the dataset. P‐values were improved but still most of the variables are of non‐normal distribution. PC95TEXH, PC05GEXH, UFD10 have p‐values above alpha so Ho is accepted and these variables are of normal distribution.
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Transforming improved the normality but not to satisfactory level thus since listwise deletion of outliers has the risk of losing some influential observation then I decided to keep all the data in the analysis. The hypothesis for Shapiro‐Wilk normality test is as follows;
Ho: data is normal Ha: data is non‐normal The null hypothesis for multiple linear regression is that all the slopes are equal to zero
and the alternative hypothesis is that at least one slope does not equal to zero. Ho: β1=β2=β3=β4=βi=0 Ha: at least one βi is different Best fit could be interpreted as “how good is the proposed model (regression
equation)”and if “it could predict the y values reasonably.” In other words how good is the fitted model for describing the relationship between x and y and so for predicting value of y for a given x within the acceptable x range. Goodness of fit could be measured by coefficient of determination (R2). General rule of thumb is that R2 greater than 60% would make a proposed model safe enough for making predictions.
4.2. Principal component analysis Textbooks state that “principal component analysis is performed on a matrix of Pearson
correlation coefficients therefore data should satisfy the assumptions for this statistic”. To extract the important variables out of the 12 variables in the original dataset and
reduce the dimensionality principal component analysis is to be performed. Components are orthogonal to each other (uncorrelated). PCA is more sensible when data are highly correlated (correlation coefficients bigger than 0.3 and smaller than ‐0.3) and even though normality of the dataset is not essential but would be preferred. If all the variables on the same scale, only then the predictions and interpretation would be rational and this could be achieved by standardizing the data and performing transformation.
4.2.1. Assumption of principal component analysis Linearity is preferred and so the relationship between all observed variables should be
linear. Normal distribution of each observed variable is also desirable but not necessary. For the latter reason variables that demonstrate skewness may be transformed to better approximate the normality. One could also assume the normality of the dataset if the sample size is greater than 25 because the Pearson correlation coefficient is robust against violations of the normality assumption. According to Dr. Whitehead if dataset does not contain any zero values then it can be analyzed by principal component analysis. In addition, normality is preferred not essential, and independence is not required.
The dataset contains no missing values but some unusually large or small values are present which maybe outliers contributing to the non‐normal distribution of the dataset. I kept all the units in because these values maybe influential not outliers.
Variables are relatively correlated for example; per capita health expenditure, government and total, are positively related meaning that increase in one would lead in increasing the other (table 2).
Normality of the original dataset was tested but the data were non‐linear therefore, two forms of transformation were performed, square root and log10. Square root transforming of all the variables did not much help the linearity and normality whereas log10 transforming of
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all the variables induced the normality to some degree keeping its original characteristics (Figure 9, 10).
4.3. Redundancy analysis Redundancy analysis is done to show that there is a linear dependence of the child
mortality variables, Y on the health expenditure variables, X. In redundancy analysis linear regression is applied to represent response variable (child mortality) as linear function of explanatory variable (health expenditure) and then to use PCA in order to visualize the result. Among those components of Y which can be linearly explained with X (multivariate linear regression) one could take those components which represent most of the variance. 5. Results
5.1. General linear model Several multiple linear models were tested with the null hypothesis that the slopes are
all equal to zero. All the tested models have p‐values smaller than alpha (0.5) leading to the rejection of null hypothesis in favor of alternative hypothesis meaning that at least one β is different from zero. There is significant relationship between the independent and the response variable and so changes in x would affect the changes in y.
All the possible models were tested. The answers for biological questions are as follows; Biological question 1: Neonatal mortality rate 2010 has association with the government and total health expenditure of 1995 and 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4). Biological question 2: Neonatal mortality rate 2010 has association with the government and total health expenditure 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 2005 government health expenditure (table 4). Biological question 3: Infant mortality rate 2010 has association with the government and total health expenditure of 1995 and 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4). Biological question 4: Infant mortality rate 2010 has association with the government and total health expenditure 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 2005 government health expenditure (table 4). Biological question 5: Under 5‐mortality rate 2010 has association with the government and total health expenditure of 1995 and 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4). Biological question 6: Under 5‐mortality rate 2010 has association with the government and total health expenditure 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 2005 government health expenditure (table 4). Biological question 7: Neonatal mortality rate 2000 has association with the government and total health expenditure 1995 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4). Biological question 8: Infant mortality rate 2000 has association with the government and total health expenditure 1995 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4).
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Biological question 9: Under 5‐mortality rate 2000 has association with the government and total health expenditure 1995 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4).
Testing the dependence of child mortality rate of 2010, neonatal, infant, and under five, the conclusion can be made that all these variables are more dependent on the government expenditure 1995 and 2005. Another interpretation of the models could be that government expenditure of year 1995 had big influence on the child mortality rates of 2010 (table 4).
Also testing for the dependence of child mortality rate of 2000, neonatal, infant, and under five, the conclusion can be made that all these variables are more dependent on the government expenditure of 1995 (table 4).
The overall interpretation could be that child mortality rates are more dependent on the government expenditure rather than on the total health expenditure (table 4).
Quality of fit of the abovementioned models were assessed one by one (figure 13‐19, 34, 35).
To evaluate the quality of fit a model, few assumptions shall be met; • Normality of error terms by Normal Q‐Q plot • Constant variance by plotting residuals vs. fitted values • Independence of error terms by auto‐correlation analysis (time series) • Presence of influential observations by Cook’s D
For example, the quality of fit of the model 6 was evaluated. The plots show no evident pattern to the residuals vs. fitted values plot and give almost an impression of horizontal band confirming that constant variance assumption is met. The Normal Q‐Q plot passes the pen test and so the normality assumption is met. The residuals vs. leverage plot checks out the absence of influential observations as observation 30 (country; Mauritania) that was previously introduced as influential is out of the Cook’s distance range. Therefore, we conclude that all assumptions are met and none is violated. It is interesting to know that Mauritania is classified as low‐income country by World Bank but has relatively high per capita total and government expenditure with significantly low child death rates.
Bonferonni outlier test was done for the models that initially have adjusted r‐squared values of above 90%. According to this test observation 4 and 30 are outliers (table 8).
Reduced models for all the tested models were the best models as they were simple and had lower AIC compare to the full models (table 4).
5.2. Principal component analysis 5.2.1. PCA on all the variables PCA on correlation matrix (Log10 transformed data) revealed two principal components
with Eigen values more than or equal to 1 (pc1: 2.97, pc2: 1.57). These two principal components cumulatively account for 94.4% of the variance in the dataset (table 6).
Loadings for the correlation matrix (Log10 transformed data) analysis are summarized (table 6) and as noted loadings for child death rates are positively loaded on first component. The per capita health expenditure load negatively on the second component therefore 2nd component could explain the variance on the expenditure (table 6). On the first component, decrease in the health expenditure causes increase in the child mortality rate. Below is the formula for the 1st principal component:
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1st pc (Correlation Matrix) = ‐0.27 (PC95TEXH) ‐0.27 (PC05TEXH) ‐0.26 (PC12TEXH) ‐0.29 (PC95GEXH) ‐0.27 (PC05GEXH) ‐0.27 (PC12GEXH) +0.3 (UFD00) +0.3 (UFD10) +0.3 (ID00) +0.29 (ID10) +0.3 (ND00) +0.28 (ND10)
Scree plot can be performed to decide which components to keep for the Varimax rotation analysis. Looking at the plots for PCA on correlation would reveal that only two components are important, as drop is obvious after these two components. For further analysis, only first two components were maintained. This would plot the eigenvalue associated with a principal component versus the number of the component to expose the relative magnitude of eigenvalues (Figure 20).
Looking at the biplot, one can say that death rates whether infant, neonatal or under 5 are highly correlated for 2000 and 2010. Moreover per capita government and total health expenditure are also highly correlated (Figure 21). Both health expenditure and mortality rates load high on the first component and so most of the variance on the 1st component in explained by the two set of variables but in different direction. Their importance on the component are more or less the same because the size of arrows are almost equal.
Examining the scores plot of correlation matrix analysis, prediction can be made that countries relatively spending big on the health and have very low mortality rates have negative scores (Algeria) on the 1st and 2nd component and countries with very low spending and high mortality have positive scores on the 1st component (Nigeria). Seychelles that spend high and have almost to none mortality rate have high negative scores on the 1st and relatively high negative score on the 2nd component (Figure 22).
Varimax plot makes the interpretation easy as it reveals the relationship of each original variable to the factor. This rotation maximizes the high correlations while minimizing the low correlations. Varimax plot for correlation matrix shows that the countries with relatively big health expenditure have negative scores on both the components and in converse countries with low to minimal health expenditure have positive scores on both the components (Figure 23).
5.2.2. PCA on 2 sets of variables Principal component analysis was done on the independent and dependent variable as
two set. Since the measurements are on the same scale, therefore analysis were done with the covariance matrix.
PCA of the child mortality rates revealed all the principal components with Eigen values more than or equal to 1. These two principal components cumulatively account for 99.9% of the variance in the dataset. Below is the formula for the 1st principal component:
1st pc for child mortality rates (covariance matrix) = ‐0.63(UFD00) ‐0.54(UFD10) ‐0.39(ID00) ‐0.30(ID10) ‐0.17(ND00) ‐0.170(ND10)
PCA of the health expenditure revealed all the principal components with Eigen values more than or equal to 1. These two principal components cumulatively account for 97.1% of the variance in the dataset. Scree plots for both set of PCA confirms the importance of the first 2 components (figure 26‐27). Below is the formula for the 1st principal component:
1st pc for health expenditures (covariance matrix) = ‐0.45(PC95TEXH) ‐0.69(PC05TEXH) ‐0.305(PC95GEXH) ‐0.467(PC05GEXH)
Looking at the biplot for the PCA of mortality rates, one can say that death rates of 2000 are highly correlated so are the 2010 death rates. Based on the size of arrows, importance of
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the under five death rate is more significant the neonatal and the infant. Biplot of health expenditures shows that health expenditures of 1995 are correlated and so are the 2005 expenditure thus importance of total expenditure of 2005 is more significant than the others (1995 government expenditure has the least importance) (figure 28‐29).
Looking at score plot of PCA of the mortality rates, all the variables load negatively on the pc1, some high and some low (figure 32). Score plot of PCA of the expenditures shows that all the variables have loaded negatively and relatively high on pc1 (figure 33).
Varimax plot for PCA of mortality rates shows that the countries with high mortality rates load highly negative on both the components such as Nigeria (figure 30).
Varimax plot for PCA of expenditures shows that the countries with both high government and high total health expenditures load negatively high on the first and positively high on the 2nd component such as Seychelles. In converse, countries with high total and relatively lower government health expenditures load highly negative on the first and positively but relatively lower on the 2nd component such as south Africa (figure 31).
5.3. Redundancy analysis For the variable UFD00, a one unit increase in under 5 death leads to a 1.33 decrease (‐
1.33) in the first canonical variate of set 2 when all of the other variables are held constant. Table 7 presents the standardized canonical coefficients for the first two dimensions
across both sets of variables. For the expenditure variables, the first canonical dimension is most strongly influenced by PC05TEXH (0.25) and for the second dimension (1.00).
For the mortality variables, the first dimension was most strongly influenced by UFD00 ‐1.33 and ID00 1.41 and the second dimension the ND00 ‐1.64 was the dominant variable (figure 24‐25). 6. Discussion
The overall picture is that health expenditure has impact on the child mortality rate and the results are relatively statistically significant. This may be because HIV prevalence has been high in the sub‐Saharan Africa in the two past decades (figure 3). This is in accordance to UN report 2000 saying that “trend in HIV infection will have a profound impact on future rates of infant, child and maternal mortality, life expectancy and economic growth.”
Although all the multiple linear regression models tested were accepted in the favor of the alternative hypothesis that there is relationship between mortality rates and health expenditure however the factors of the models usually were not statistically significant except the health mortality rates e.g. dependence of infant mortality rate on neonatal and under 5 mortality rates with low p‐values and high t values (table 5). Negative loadings of the health expenditure leads to positive relatively high loading of the health outcome, represented as child mortality. One could say that health expenditure has some impact even though low on the mortality rates but other variables have to be included in the analysis to decide its significance. Variables that can be included in the study could be the female education, income, access to vaccines, HIV prevalence, number of trained health professionals, hunger, sanitation, etc.
The results of this analysis are confirmatory to the other similar studies that have found little to no impact of the health expenditure on the health outcomes. 7. Acknowledgments
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I would like to acknowledge the use of data from WHO organization. Data were selected individually and then they were combined in one dataset. 8. References 1. Acemoglu, D.; Johnson, S. Disease and development: the effect of life expectancy on economic growth; National Bureau of Economic Research: 2006. 2. Sen, A., Mortality as an indicator of economic success and failure. The Economic Journal 1998, 108, 1‐25. 3. Bloom, D.; Canning, D., The health and poverty of nations: from theory to practice. Journal of Human Development 2003, 4, 47‐71. 4. Sandiford, P.; Cassel, J.; Montenegro, M.; Sanchez, G., The impact of women's literacy on child health and its interaction with access to health services. Population studies 1995, 49, 5‐17. 5. Rutherford, M. E.; Mulholland, K.; Hill, P. C., How access to health care relates to under‐five mortality in sub‐Saharan Africa: systematic review. Tropical Medicine & International Health 2010, 15, 508‐519. 6. Gupta, S.; Verhoeven, M.; Tiongson, E., Does higher government spending buy better results in education and health care? International Monetary Fund: 1999. 7. Black, R. E.; Morris, S. S.; Bryce, J., Where and why are 10 million children dying every year? The Lancet 2003, 361, 2226‐2234. 8. Lawn, J. E.; Cousens, S.; Zupan, J., 4 million neonatal deaths: when? Where? Why? The Lancet 2005, 365, 891‐900. 9. Kiros, G.‐E.; Hogan, D. P., War, famine and excess child mortality in Africa: the role of parental education. International Journal of Epidemiology 2001, 30, 447‐455. 10. Filmer, D.; Pritchett, L., The impact of public spending on health: does money matter? Social science & medicine 1999, 49, 1309‐1323. 11. Filmer, D.; Pritchett, L., Child mortality and public spending on health: how much does money matter? World Bank Publications: 1997; Vol. 1864. 12. Burnside, C.; Dollar, D., Aid, the incentive regime, and poverty reduction. World Bank, Development Research Group, Macroeconomics and Growth: 1998. 13. Preston, S. H., Mortality trends. Annual Review of Sociology 1977, 163‐178. 14. U.N., Common Database. 2005. 15. Human Development Report 2003.
Assignment 2d, Soheila Abachi
Figure 1:
Figure 2:
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Figure 3: adapted from UNAIDS
Figure 4: bar graph of the health expenditures (total and government) for the year 2005 and health outcomes (Infant, neonatal, under 5mortality rates) for the year 2010
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Figure 5: bar graph of health outcomes (Infant, neonatal, under 5mortality rates) for the years 2000 and 2010
Figure 6: bar graph of the health expenditures (total and government) for the year 1995 and health outcomes (Infant, neonatal, under 5mortality rates) for the year 2000
Figure 7: box plot of original dataset
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Figure 8: scatter plot matrix for original dataset
Figure 9: box plot of log10 transformed dataset
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Figure 10: scatter plot matrix for log10 transformed dataset
Figure 11: box plot of square root transformed dataset
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Figure 12: aq .plot of log10 transformed dataset
Figure 13: model 1 basic diagnostic plots
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~ PC05GEXH + PC05TEXH + PC95GEXH + PC
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-1.0
Fitted values
Res
idua
ls Residuals vs Fitted342
36
-2 0 1 2
-22
Theoretical Quantiles
Sta
ndar
dize
d re
sidu
als
Normal Q-Q
25
342
0.5 1.5 2.5
0.0
1.5
Fitted values
Sta
ndar
dize
d re
sidu
als
Scale-Location25342
0.0 0.2 0.4
-22
Leverage
Sta
ndar
dize
d re
sidu
als
Cook's dist10.5
0.51
Residuals vs Leverage
25
40
14
~ PC05GEXH + PC05TEXH + PC95GEXH + P
19
Figure 16: model 5 basic diagnostic plots
Figure 17: model 4 basic diagnostic plots
0.5 1.0 1.5
-1.0
Fitted values
Res
idua
ls Residuals vs Fitted34
2511
-2 0 1 2
-22
Theoretical QuantilesS
tand
ardi
zed
resi
dual
s
Normal Q-Q34
2511
0.5 1.0 1.5
0.0
1.5
Fitted values
Sta
ndar
dize
d re
sidu
als
Scale-Location34 2511
0.00 0.10 0.20
-22
Leverage
Sta
ndar
dize
d re
sidu
als
Cook's dist0.5
0.51Residuals vs Leverage
25
40
15
lm(ND10 ~ PC05TEXH + PC95TEXH)
0.0 1.0 2.0
-1.0
1.5
Fitted values
Res
idua
ls Residuals vs Fitted342
25
-2 0 1 2
-22
Theoretical Quantiles
Sta
ndar
dize
d re
sidu
als
Normal Q-Q
25
342
0.0 1.0 2.0
0.0
1.5
Fitted values
Sta
ndar
dize
d re
sidu
als
Scale-Location25342
0.0 0.2 0.4
-31
Leverage
Sta
ndar
dize
d re
sidu
als
Cook's dist10.5
0.51
Residuals vs Leverage
2515
40
~ PC05GEXH + PC05TEXH + PC95GEXH + PC
20
Figure 18: model 31 basic diagnostic plots
Figure 19: model 13 basic diagnostic plots
0.0 1.0 2.0
-1.0
1.5
Fitted values
Res
idua
ls Residuals vs Fitted342
25
-2 0 1 2
-22
Theoretical QuantilesS
tand
ardi
zed
resi
dual
s
Normal Q-Q
25
342
0.0 1.0 2.0
0.0
1.5
Fitted values
Sta
ndar
dize
d re
sidu
als
Scale-Location25342
0.0 0.2 0.4
-31
Leverage
Sta
ndar
dize
d re
sidu
als
Cook's dist10.5
0.51
Residuals vs Leverage
2515
40
~ PC05GEXH + PC05TEXH + PC95GEXH + PC
0.5 1.5 2.5
-1.0
Fitted values
Res
idua
ls Residuals vs Fitted3440
11
-2 0 1 2
-21
Theoretical Quantiles
Sta
ndar
dize
d re
sidu
als
Normal Q-Q3440
11
0.5 1.5 2.5
0.0
1.5
Fitted values
Sta
ndar
dize
d re
sidu
als
Scale-Location344011
0.0 0.2 0.4
-22
Leverage
Sta
ndar
dize
d re
sidu
als
Cook's dist10.5
0.51
Residuals vs Leverage40
25 14
21
Figure 34: model 14 basic diagnostic plots
Figure 35: model 16 basic diagnostic plots
0.0 1.0 2.0
-1.0
1.5
Fitted values
Res
idua
ls Residuals vs Fitted3440 2
-2 0 1 2
-12
Theoretical QuantilesS
tand
ardi
zed
resi
dual
s
Normal Q-Q34402
0.0 1.0 2.0
0.0
1.5
Fitted values
Sta
ndar
dize
d re
sidu
als
Scale-Location3440 2
0.0 0.2 0.4
-22
Leverage
Sta
ndar
dize
d re
sidu
als
Cook's dist10.5
0.51
Residuals vs Leverage
25
4034
lm(ND00 ~ PC95GEXH + PC95TEXH)
0.0 1.0 2.0
-1.0
1.5
Fitted values
Res
idua
ls Residuals vs Fitted3440 2
-2 0 1 2
-12
Theoretical Quantiles
Sta
ndar
dize
d re
sidu
als
Normal Q-Q34402
0.0 1.0 2.0
0.0
1.5
Fitted values
Sta
ndar
dize
d re
sidu
als
Scale-Location3440 2
0.0 0.2 0.4
-22
Leverage
Sta
ndar
dize
d re
sidu
als
Cook's dist10.5
0.51
Residuals vs Leverage
25
4034
lm(ND00 ~ PC95GEXH + PC95TEXH)
22
Figure 20: scree plot of PCA on correltaion matrix
Figure 21: plot of PCA on correltaion matrix
Comp.1 Comp.4 Comp.7 Comp.10
Scree plot for PCA1In
ertia
02
46
8
-0.4 -0.2 0.0 0.2
-0.4
-0.2
0.0
0.2
Biplot pca1
Comp.1
Com
p.2
1 2
3
45
6
7
8
9
10
11
12
13
14
15
16
1718
19
20
21
22
23
24
25
262728
29
30 3132
33
34
35
36
37
38
39
40
41
42
434445
-8 -6 -4 -2 0 2 4 6
-8-6
-4-2
02
46
PC95TEXHPC05TEXHPC12TEXH
PC95GEXHPC05GEXHPC12GEXH UFD0UFD1ID00ID10ND0ND10
23
Figure 22:
Figure 23:
-5 0 5
-4-2
02
Scores plot pca1
1st principal component
2nd
prin
cipa
l com
pone
nt
AlgeriaAngola
Benin
Botsw anaBurkina Faso
Burundi
Cabo Verde
Cameroon
Central African Republic
Chad
Comoros
Congo
Côte d'Ivoire
Democratic Republic of the Congo
Equatorial Guinea
Eritrea
EthiopiaGabon
Gambia
Ghana
Guinea
Guinea-Bissau
Kenya
Lesotho
Liberia
Madagascar
Malaw iMali
Mauritania
MauritiusMozambique
Namibia
Niger
Nigeria
Rw anda
Sao Tome and Principe
Senegal
Seychelles
Sierra Leone
South Africa
Sw aziland
Togo
UgandaUnited Republic of TanzaniaZambia
-10 -5 0 5 10
-6
-4
-2
0
2
4
Varimax Scores plot(pca1)
1st varimax component
2nd
varim
ax c
ompo
nent
Algeria
Angola
Benin
Botsw ana
Burkina Faso
Burundi
Cabo Verde
Cameroon
Central African Republic
ChadComoros
CongoCôte d'Ivoire
Democratic Republic of the Congo
Equatorial Guinea
Eritrea
Ethiopia
Gabon
GambiaGhana
Guinea
Guinea-Bissau Kenya
Lesotho
Liberia
Madagascar
Malaw iMali
Mauritania
Mauritius
Mozambique
Namibia
Niger
Nigeria
Rw anda
Sao Tome and Principe
Senegal
Seychelles
Sierra Leone
South Africa
Sw aziland
Togo UgandaUnited Republic of Tanzania
ZambiaCountryPC95TEXHPC05TEXHPC12TEXHPC95GEXHPC05GEXHPC12GEXHUFD00UFD10ID00ID10ND00ND10
Child death rates
Health expenditure
24
Figure 24: redundancy analysis plot, child mortality rates vs. health expenditure 2005
Figure 25: redundancy analysis plot, child mortality rates vs. health expenditure 1995
-4 -2 0 2 4
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
RDA1
RD
A2
type2log.PC05TEXHtype2log.PC05GEXH
1
2
34
5
6
7
8
9
10
1112
13
14
15
16
17
18
19
20
2122
23
24
25
26
27
28
29
30
31
32
33
34
35
36
3738
39
40
41
42
43
4445
type2log.UFD00type2log.UFD10type2log.ID00type2log.ID10type2log.ND00
type2log.ND10
-6 -4 -2 0 2 4 6
-3-2
-10
12
RDA1
RD
A2 type2log.PC95TEXH
type2log.PC95GEXH
1
2
3
4
56
7
8
9
10
11
12
13
14
15
16 17
18
19
20
21
22
2324
25
2627
2829
30
31
32
3334
35
3637
38
39
40
41 4243
4445
type2log.UFD00type2log.UFD10
type2log.ID00type2log.ID10
type2log.ND00type2log.ND10
-10
Comp.1 Comp.3 Comp.5
Scree plot for PCA MortRate
Iner
tia
010
000
3000
050
000
Comp.1 Comp.2 Comp.3 Comp.4
Scree plot for PCA Expd
Iner
tia
020
000
4000
060
000
25
Figure 26: Scree plot for covariance matrix of child mortality rates
Figure 27: Scree plot for covariance matrix of health expenditures
Figure 28: Bi plot for covariance matrix of child mortality rates
Figure 29: Bi plot for covariance matrix of health expenditures
Figure 30: Varimax plot for covariance matrix of child mortality rates
Figure 31: Varimax plot for covariance matrix of health expenditures
-0.8 -0.6 -0.4 -0.2 0.0 0.2
-0.8
-0.6
-0.4
-0.2
0.0
0.2
Biplot pca MortRate
Comp.1
Com
p.2
1
2
345678 9
10
111213
14
1516
17
181920212223 24252627
28293031
3233
34
35
3637
3839404142
43
44
45
-1000 -600 -200 0 200
-100
0-6
00-2
000
200
FD00
UFD10
ID00ID10
ND00ND10
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Biplot pca Expd
Comp.1
Com
p.2
12 3
4
5678910
11121314
15
1617
18
19202122232425262728
29
30
3132
3334353637
38
39
40
4142434445
-1000 -500 0 500 1000
-100
0-5
000
500
1000
PC95TEXH
05TEXH
PC95GEXHPC05GEXH
-1000 -600 -200 0 200
-800
-600
-400
-200
0
Varimax Scores plot(pca Mort Rate)
1st varimax component
2nd
varim
ax c
ompo
nent
Algeria
Angola
BeninBotsw ana
Burkina FasoBurundiCabo Verde
CameroonCentral African Rep
ChadComorosCongo
Côte d'Ivoire
Democratic Republic of the Congo
Equatorial GuineEritrea
Ethiopia
GabonGambiaGhanaGuinea
Guinea-Bissau
Kenya
LesothoLiberiaMadagascarMalaw iMali
MauritaniaMauritius
Mozambique
Namibia
Niger
Nigeria
Rw anda
Sao Tome and PrinSenegalSeychelles
Sierra LeoneSouth Africa
Sw azilandTogo
UgandaUnited Republic of Tanzania
ZambiaCountryPC95TEXHPC05TEXHPC12TEXHPC95GEXHPC05GEXHPC12GEXHUFD00UFD10ID00ID10ND00ND10
-800 -600 -400 -200 0 200
0
200
400
600
800
Varimax Scores plot(pca Expd)
1st varimax component
2nd
varim
ax c
ompo
nent
Algeria
AngolaBenin
Botsw ana
Burkina FasoBurundi
Cabo VerdeCameroonCentral African RepublicChadComoros
CongoCôte d'IvoireDemocratic Republic of the Co
Equatorial Guinea
EritreaEthiopia
Gabon
GambiaGhanaGuinea
Guinea-BissauKenyaLesotho
LiberiaMadagascarMalaw iMaliMauritania
Mauritius
Mozambique
Namibia
NigerNigeriaRw anda
Sao Tome and PrincipeSenegal
Seychelles
Sierra Leone
South Africa
Sw aziland
TogoUgandaUnited Republic of TanzaniaZambia
26
Figure 32: Scores plot for covariance matrix of child mortality rates
Figure 33: Scores plot for covariance matrix of health expenditures
Table 2: Correlation coefficients PC95
TEXH PC05 TEXH
PC12 TEXH
PC95 GEXH
PC05GEXH
PC12GEXH UFD00 UFD10 ID00 ID10 ND00 ND10
PC95TEXH 1.00 0.89 0.78 0.92 0.87 0.83 ‐0.21 ‐0.18 ‐0.20 ‐0.18 ‐0.21 ‐0.18PC05TEXH 0.89 1.00 0.91 0.80 0.92 0.87 ‐0.19 ‐0.16 ‐0.19 ‐0.16 ‐0.20 ‐0.17PC12TEXH 0.78 0.91 1.00 0.74 0.86 0.94 ‐0.20 ‐0.18 ‐0.19 ‐0.17 ‐0.20 ‐0.18PC95GEXH 0.92 0.80 0.74 1.00 0.90 0.88 ‐0.20 ‐0.18 ‐0.20 ‐0.17 ‐0.20 ‐0.18PC05GEXH 0.87 0.92 0.86 0.90 1.00 0.93 ‐0.21 ‐0.19 ‐0.21 ‐0.19 ‐0.21 ‐0.19PC12GEXH 0.83 0.87 0.94 0.88 0.93 1.00 ‐0.22 ‐0.20 ‐0.22 ‐0.19 ‐0.22 ‐0.20UFD00 ‐0.21 ‐0.19 ‐0.20 ‐0.20 ‐0.21 ‐0.22 1.00 0.98 0.99 0.98 0.99 0.99UFD10 ‐0.18 ‐0.16 ‐0.18 ‐0.18 ‐0.19 ‐0.20 0.98 1.00 0.98 0.99 0.96 0.99ID00 ‐0.20 ‐0.19 ‐0.19 ‐0.20 ‐0.21 ‐0.22 0.99 0.98 1.00 0.98 0.99 0.99ID10 ‐0.18 ‐0.16 ‐0.17 ‐0.17 ‐0.19 ‐0.19 0.98 0.99 0.98 1.00 0.96 0.99ND00 ‐0.21 ‐0.20 ‐0.20 ‐0.20 ‐0.21 ‐0.22 0.99 0.96 0.99 0.96 1.00 0.98ND10 ‐0.18 ‐0.17 ‐0.18 ‐0.18 ‐0.19 ‐0.20 0.99 0.99 0.99 0.99 0.98 1.00
Table 3: summary of Shapiro‐Wilk normality test‐p values Shapiro‐Wilk normality test‐p values
Original data Log10 transformed data PC95TEXH 2.221e‐09 0.437PC05TEXH 6.416e‐09 0.01336PC12TEXH 3.201e‐09 0.03242PC95GEXH 4.121e‐11 0.08201PC05GEXH 8.008e‐10 0.1731PC12GEXH 9.39e‐10 0.01635UFD00 6.136e‐11 0.03946UFD10 1.899e‐11 0.06938ID00 6.361e‐11 0.0312ID10 1.363e‐11 0.01937ND00 5.93e‐11 0.005314ND10 2.557e‐11 0.01495Original data set including all variables 2.24e‐13
-1000 -500 0
-600
-200
020
060
0
Scores plot pca Mort Rate
1st principal component
2nd
prin
cipa
l com
pone
nt
AlgeriaAngola BeninBotsw aBurkina FasoBurundiCabo VeCameroonCentral African RChadComoroCongoCôte d'IvoireDemocratic Republic of the CongoEquatorial GEritrea
Ethiopia
GabonGambiaGhanaGuineaGuinea-BisKenyaLesothLiberiaMadagascarMalaw iMaliMauritanMauritiuMozambiqueNamibiNigerNigeriaRw anda
Sao Tome andSenegalSeychelSierra LeonSouth AfricaSw azilaTogoUgandaUnited Republic of TanzanZambiaCountryPC95TEXHPC05TEXHPC12TEXHPC95GEXHPC05GEXHPC12GEXHUFD00UFD10ID00ID10ND00ND10
-1000 -600 -200 0 200
-400
020
040
0
Scores plot pca Expd
1st principal component
2nd
prin
cipa
l com
pone
nt
AlgeriaAngolaBenin
Botsw ana
Burkina FasoBurundiCabo VerdeCameroonCentral African ChadComorosCongoCôte d'IvoireDemocratic Republic
Equatorial Guinea
EritreaEthiopiaGabon
GambiaGhanaGuineaGuinea-BissauKenyaLesothoLiberiaMadagascMalaw iMaliMauritania
Mauritius
MozambiquNamibia NigerNigeriaRw andaSao Tome and PrincipeSenegal
ychelles
Sierra Leone
South Africa
Sw azilandTogoUgandaUnited Republic of ZambiaCountryPC95TEXHPC05TEXHPC12TEXHPC95GEXHPC05GEXHPC12GEXHUFD00UFD10ID00ID10ND00ND10
27
Log10 transformed data including all variables 1.79e‐13
Table 4: summary of multiple regression models tested General linear model and
Reduced model with lowest AIC Adjusted R‐squared
p‐value AIC
Reg1ID10 ID10=2.27‐0.74PC05GEXH+0.01PC05TEXH 0.2438 0.001065 ‐41.53 Reduced Reg1ID10
ID10 ~ PC05GEXH ‐43.53
Reg2ID10 ID10=1.77‐0.19PC05GEXH+0.56PC05TEXH‐
0.92PC95GEXH‐0.12PC95TEXH 0.3177 0.0006102 ‐44.35
Reduced Reg2ID10
ID10 ~ PC95GEXH ‐49.57
Reg31ID10 UFD10=2.55‐0.83PC05GEXH+0.06PC05TEXH 0.2578 0.0007182 ‐38.36 Reduced Reg31ID10
UFD10 ~ PC05GEXH ‐40.35
Reg3UFD10 FD10=2.03‐0.27PC05GEXH+0.71PC05TEXH ‐
0.94PC95GEXH‐0.2PC95TEXH 0.3379 0.0003494 ‐41.69
Reduced Reg3UFD10
UFD10 ~ PC95GEXH ‐46.68
Reg5ND10 ND10=2.15+0.21PC05TEXH‐0.93PC05GEXH 0.2226 0.001903 ‐49.83 Reduced Reg5ND10
ND10 ~ PC05GEXH ‐51.65
Reg4ND10 ND10=1.39‐0.14PC05GEXH+0.68PC05TEXH‐
0.82PC95GEXH‐0.25PC95TEXH 0.2808 0.001613 ‐51.53
Reduced Reg4ND10
ND10 ~ PC95TEXH
‐56.12
Reg13ID00 ID00=2.33‐0.87PC95GEXH+0.06PC95TEXH 0.3603 3.168e‐05 ‐46.38 Reduced Reg13ID00
ID00 ~ PC95GEXH
‐48.36
Reg14ND00 ND00=1.94‐0.78PC95GEXH+0.02PC95TEXH 0.3638 2.825e‐05 ‐55.04 Reduced Reg14ND00
ND00 ~ PC95GEXH
‐57.03
Reg16UFD00
UFD00=2.59‐0.96PC95GEXH + 0.08PC95TEXH
0.3856 1.36e‐05 ‐45.19
Reduced Reg16UFD00
UFD00 ~ PC95GEXH ‐45.2
Table 5: summary of the selected models coefficients and p‐values
28
Table 6: summary of loading on the first 2 components of PCA PCA on correlation matrix Comp 1 Comp 2 PC95TEXH ‐0.278 ‐0.263PC05TEXH ‐0.276 ‐0.343PC12TEXH ‐0.268 ‐0.337 PC95GEXH ‐0.294 ‐0.228PC05GEXH ‐0.279 ‐0.310 PC12GEXH ‐0.276 ‐0.302 UFD00 0.303 ‐0.261 UFD10 0.301 ‐0.272ID00 0.300 ‐0.280 ID10 0.299 ‐0.281ND00 0.302 ‐0.270 ND10 0.285 ‐0.296
Table 7: standardized canonical coefficients of the canonical correlation analysis 1 2 First set of variable PC05TEXH 0.25 1.00 PC05GEXH 0.09 ‐0.84 Second set of Variable UFD00 ‐1.33 ‐0.06 UFD10 0.34 0.34 ID00 1. 0.53 ID10 ‐0.16 0.36 type2log.ND00 ‐0.56 ‐1.64 type2log.ND10 0.17 0.47 Table 8: Summary of Bonferonni outlier test on the selected models
Outlier rstudent unadjusted p‐value Bonferonni p Reg6ND10 30 12.34386 1.0987e‐14 4.9442e‐13 Reg7 ID10 30 ‐3.909981 0.00037968 0.017086 Reg8 UFD10 4 3.436218 0.0014719 0.066235 Reg9 ND10 30 13.33186 1.0957e‐16 4.9307e‐15 Reg10 UFD10 4 3.651499 0.00073142 0.032914 Reg11 UFD10 4 3.18752 0.0027092 0.12191 Reg12 ID10 30 ‐4.224568 0.00012999 0.0058494
29
> str(type2) 'data.frame': 45 obs. of 13 variables: $ Country : Factor w/ 45 levels "Algeria","Angola",..: 1 2 3 4 5 6 7 8 9 10 ... $ PC95TEXH: num 164.7 84.2 43.1 249.4 29.4 ... $ PC05TEXH: num 219.5 139 60.6 628.5 73.7 ... $ PC12TEXH: num 439 212.1 69.6 871.8 90.1 ... $ PC95GEXH: num 119 59.5 19.4 130.6 11.4 ... $ PC05GEXH: num 159.6 69.5 30.1 457.2 43.9 ... $ PC12GEXH: num 369.3 131.9 35.8 491.3 49 ... $ UFD00 : num 24 143 41 4 94 40 1 95 24 76 ... $ UFD10 : num 26 162 33 3 72 36 1 79 22 85 ... $ ID00 : num 20 86 26 3 49 25 1 58 16 43 ... $ ID10 : num 23 72 16 1 41 17 1 37 12 44 ... $ ND00 : num 12 36 11 1 20 11 1 23 7 18 ... $ ND10 : num 15 44 10 1 19 13 1 23 7 22 ... > summary(type2) Country PC95TEXH PC05TEXH PC12TEXH Algeria : 1 Min. : 6.50 Min. : 15.6 Min. : 16.5 Angola : 1 1st Qu.: 29.40 1st Qu.: 48.8 1st Qu.: 67.3 Benin : 1 Median : 45.50 Median : 77.1 Median : 107.8 Botswana : 1 Mean : 94.69 Mean :149.5 Mean : 241.4 Burkina Faso: 1 3rd Qu.: 94.40 3rd Qu.:135.9 3rd Qu.: 204.9 Burundi : 1 Max. :629.30 Max. :739.9 Max. :1431.7 (Other) :39 PC95GEXH PC05GEXH PC12GEXH UFD00 Min. : 0.50 Min. : 3.70 Min. : 7.8 Min. : 1.00 1st Qu.: 10.70 1st Qu.: 20.60 1st Qu.: 28.8 1st Qu.: 7.00 Median : 18.10 Median : 30.70 Median : 45.7 Median : 41.00 Mean : 49.37 Mean : 81.88 Mean : 141.1 Mean : 86.02 3rd Qu.: 48.70 3rd Qu.: 69.50 3rd Qu.: 128.8 3rd Qu.: 94.00 Max. :535.90 Max. :640.90 Max. :1116.2 Max. :934.00 UFD10 ID00 ID10 ND00 Min. : 1.00 Min. : 1.00 Min. : 1.0 Min. : 1.00 1st Qu.: 6.00 1st Qu.: 5.00 1st Qu.: 4.0 1st Qu.: 2.00 Median : 33.00 Median : 26.00 Median : 21.0 Median : 12.00 Mean : 68.87 Mean : 53.13 Mean : 38.4 Mean : 23.47 3rd Qu.: 79.00 3rd Qu.: 55.00 3rd Qu.: 44.0 3rd Qu.: 23.00 Max. :830.00 Max. :567.00 Max. :470.0 Max. :245.00 ND10 Min. : 1.00 1st Qu.: 3.00 Median : 13.00 Mean : 22.62 3rd Qu.: 23.00 Max. :257.00 > cor(type2[,2:13]) PC95TEXH PC05TEXH PC12TEXH PC95GEXH PC05GEXH PC12GEXH PC95TEXH 1.0000000 0.8963071 0.7825579 0.9256020 0.8738156 0.8307543 PC05TEXH 0.8963071 1.0000000 0.9181442 0.8042933 0.9218915 0.8758135 PC12TEXH 0.7825579 0.9181442 1.0000000 0.7406167 0.8695250 0.9479927 PC95GEXH 0.9256020 0.8042933 0.7406167 1.0000000 0.9084133 0.8809864 PC05GEXH 0.8738156 0.9218915 0.8695250 0.9084133 1.0000000 0.9342122 PC12GEXH 0.8307543 0.8758135 0.9479927 0.8809864 0.9342122 1.0000000 UFD00 ‐0.2130300 ‐0.1960245 ‐0.2030396 ‐0.2039303 ‐0.2186197 ‐0.2243362 UFD10 ‐0.1859243 ‐0.1695941 ‐0.1813526 ‐0.1812701 ‐0.1978687 ‐0.2039448 ID00 ‐0.2090670 ‐0.1923454 ‐0.1988736 ‐0.2006420 ‐0.2159624 ‐0.2204190 ID10 ‐0.1816682 ‐0.1663914 ‐0.1770696 ‐0.1777267 ‐0.1937291 ‐0.1988588 ND00 ‐0.2149649 ‐0.2016752 ‐0.2051136 ‐0.2016774 ‐0.2182470 ‐0.2224618 ND10 ‐0.1897916 ‐0.1719560 ‐0.1805229 ‐0.1815529 ‐0.1974623 ‐0.2023317 UFD00 UFD10 ID00 ID10 ND00 ND10 PC95TEXH ‐0.2130300 ‐0.1859243 ‐0.2090670 ‐0.1816682 ‐0.2149649 ‐0.1897916 PC05TEXH ‐0.1960245 ‐0.1695941 ‐0.1923454 ‐0.1663914 ‐0.2016752 ‐0.1719560 PC12TEXH ‐0.2030396 ‐0.1813526 ‐0.1988736 ‐0.1770696 ‐0.2051136 ‐0.1805229 PC95GEXH ‐0.2039303 ‐0.1812701 ‐0.2006420 ‐0.1777267 ‐0.2016774 ‐0.1815529
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PC05GEXH ‐0.2186197 ‐0.1978687 ‐0.2159624 ‐0.1937291 ‐0.2182470 ‐0.1974623 PC12GEXH ‐0.2243362 ‐0.2039448 ‐0.2204190 ‐0.1988588 ‐0.2224618 ‐0.2023317 UFD00 1.0000000 0.9837326 0.9986441 0.9841675 0.9950972 0.9917506 UFD10 0.9837326 1.0000000 0.9813491 0.9984373 0.9679026 0.9948934 ID00 0.9986441 0.9813491 1.0000000 0.9829444 0.9966409 0.9915310 ID10 0.9841675 0.9984373 0.9829444 1.0000000 0.9694700 0.9952155 ND00 0.9950972 0.9679026 0.9966409 0.9694700 1.0000000 0.9846367 ND10 0.9917506 0.9948934 0.9915310 0.9952155 0.9846367 1.0000000 Expenditure 2005 > summary(type2log) PC95TEXH PC05TEXH PC12TEXH PC95GEXH Min. :0.8129 Min. :1.193 Min. :1.217 Min. :‐0.301 1st Qu.:1.4683 1st Qu.:1.688 1st Qu.:1.828 1st Qu.: 1.029 Median :1.6580 Median :1.887 Median :2.033 Median : 1.258 Mean :1.7465 Mean :1.954 Mean :2.113 Mean : 1.350 3rd Qu.:1.9750 3rd Qu.:2.133 3rd Qu.:2.312 3rd Qu.: 1.688 Max. :2.7989 Max. :2.869 Max. :3.156 Max. : 2.729 PC05GEXH PC12GEXH UFD00 UFD10 Min. :0.5682 Min. :0.8921 Min. :0.0000 Min. :0.0000 1st Qu.:1.3139 1st Qu.:1.4594 1st Qu.:0.8451 1st Qu.:0.7782 Median :1.4871 Median :1.6599 Median :1.6128 Median :1.5185 Mean :1.5973 Mean :1.7953 Mean :1.4376 Mean :1.3523 3rd Qu.:1.8420 3rd Qu.:2.1099 3rd Qu.:1.9731 3rd Qu.:1.8976 Max. :2.8068 Max. :3.0477 Max. :2.9703 Max. :2.9191 ID00 ID10 ND00 ND10 Min. :0.000 Min. :0.0000 Min. :0.000 Min. :0.0000 1st Qu.:0.699 1st Qu.:0.6021 1st Qu.:0.301 1st Qu.:0.4771 Median :1.415 Median :1.3222 Median :1.079 Median :1.1139 Mean :1.254 Mean :1.1161 Mean :0.938 Mean :0.9479 3rd Qu.:1.740 3rd Qu.:1.6435 3rd Qu.:1.362 3rd Qu.:1.3617 Max. :2.754 Max. :2.6721 Max. :2.389 Max. :2.4099 > expend <‐data.frame(type2log$PC05TEXH, type2log$PC05GEXH) > mort <‐ data.frame (type2log$UFD00, type2log$ UFD10, type2log$ID00, type2log$ID10, type2log$ND00, type2log$ND10) > OK <‐complete.cases(expend,mort) > ccca<‐cancor(expend[OK,],mort[OK,]) > ccca $cor [1] 0.6317665 0.3706533 $xcoef [,1] [,2] type2log.PC05TEXH 0.25222659 1.0012115 type2log.PC05GEXH 0.09470577 ‐0.8434111 $ycoef [,1] [,2] [,3] [,4] [,5] type2log.UFD00 ‐1.3302539 ‐0.06290979 ‐1.94885071 1.25602481 ‐1.0760095 type2log.UFD10 0.3484259 0.34575788 ‐0.04634281 ‐1.48775584 1.6856152 type2log.ID00 1.4100238 0.53170842 2.10010546 ‐1.57746324 ‐0.4809551 type2log.ID10 ‐0.1676133 0.36381980 0.04142259 2.01909388 ‐1.0925449 type2log.ND00 ‐0.5656447 ‐1.64824239 0.08531634 ‐0.32304602 0.8547105 type2log.ND10 0.1705373 0.47222108 ‐0.02619021 0.09337854 0.2456990 [,6] type2log.UFD00 ‐1.7878817 type2log.UFD10 1.2030900 type2log.ID00 0.5829623 type2log.ID10 0.3455343 type2log.ND00 0.5902689 type2log.ND10 ‐0.9375137 $xcenter type2log.PC05TEXH type2log.PC05GEXH 1.953798 1.597318 $ycenter type2log.UFD00 type2log.UFD10 type2log.ID00 type2log.ID10 type2log.ND00 1.4375796 1.3523235 1.2541245 1.1161151 0.9379719 type2log.ND10 0.9478903 > summary(ccca)
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Length Class Mode cor 2 ‐none‐ numeric xcoef 4 ‐none‐ numeric ycoef 36 ‐none‐ numeric xcenter 2 ‐none‐ numeric ycenter 6 ‐none‐ numeric > rdda<‐rda(expend[OK,],mort[OK,]) > rdda Call: rda(X = expend[OK, ], Y = mort[OK, ]) Inertia Proportion Rank Total 0.4292 1.0000 Constrained 0.1667 0.3885 2 Unconstrained 0.2625 0.6115 2 Inertia is variance Eigenvalues for constrained axes: RDA1 RDA2 0.164933 0.001816 Eigenvalues for unconstrained axes: PC1 PC2 0.25120 0.01127 > plot(rdda) Expenditure 2012 > expend12 <‐data.frame(type2log$PC12TEXH, type2log$PC12GEXH) > mort <‐ data.frame (type2log$UFD00, type2log$ UFD10, type2log$ID00, type2log$ID10, type2log$ND00, type2log$ND10) > OK <‐complete.cases(expend12,mort) > ccca12 <‐cancor(expend12[OK,],mort[OK,]) > ccca12 $cor [1] 0.6541995 0.2365056 $xcoef [,1] [,2] type2log.PC12TEXH 0.08656742 1.0774556 type2log.PC12GEXH 0.21318541 ‐0.9196562 $ycoef [,1] [,2] [,3] [,4] [,5] type2log.UFD00 ‐1.2053364 ‐0.6583229 ‐1.3734335 0.7705718 ‐1.2113809 type2log.UFD10 0.1090623 0.4883119 ‐0.5411692 ‐1.1762698 1.5199605 type2log.ID00 1.6458202 1.2901258 1.6781640 ‐1.1449367 ‐0.1223899 type2log.ID10 ‐0.2818023 ‐0.2427037 0.1256273 1.8570530 ‐1.3927446 type2log.ND00 ‐0.5694125 ‐1.4389385 0.4872880 ‐0.5387228 1.0715744 type2log.ND10 0.1623827 0.6458826 ‐0.1969300 0.2275852 0.2744305 [,6] type2log.UFD00 ‐2.38111298 type2log.UFD10 1.58371100 type2log.ID00 1.10708377 type2log.ID10 0.09736615 type2log.ND00 0.39563066 type2log.ND10 ‐0.76899942 $xcenter type2log.PC12TEXH type2log.PC12GEXH 2.112754 1.795255 $ycenter type2log.UFD00 type2log.UFD10 type2log.ID00 type2log.ID10 type2log.ND00 1.4375796 1.3523235 1.2541245 1.1161151 0.9379719 type2log.ND10 0.9478903 > rdda12 <‐rda(expend12[OK,],mort[OK,]) > rdda12 Call: rda(X = expend12[OK, ], Y = mort[OK, ]) Inertia Proportion Rank Total 0.4893 1.0000 Constrained 0.2047 0.4184 2 Unconstrained 0.2846 0.5816 2 Inertia is variance Eigenvalues for constrained axes: RDA1 RDA2
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0.2040830 0.0006333 Eigenvalues for unconstrained axes: PC1 PC2 0.27391 0.01064 > plot(rdda12) > expend95 <‐data.frame(type2log$PC95TEXH, type2log$PC95GEXH) > mort <‐ data.frame (type2log$UFD00, type2log$ UFD10, type2log$ID00, type2log$ID10, type2log$ND00, type2log$ND10) > OK <‐complete.cases(expend95,mort) > ccca<‐cancor(expend95[OK,],mort[OK,]) > ccca $cor [1] 0.6994977 0.3100254 $xcoef [,1] [,2] type2log.PC95TEXH 0.06660944 0.8773772 type2log.PC95GEXH 0.22907259 ‐0.6585852 $ycoef [,1] [,2] [,3] [,4] [,5] type2log.UFD00 ‐1.20708317 ‐0.1060889 ‐2.16784849 1.73946259 ‐0.68511662 type2log.UFD10 0.38616941 0.4910146 0.11621581 ‐2.03093054 1.26932812 type2log.ID00 0.95348626 ‐0.5139874 2.19106357 ‐1.67922471 ‐0.93209836 type2log.ID10 0.04566393 0.9328908 0.06985725 1.88383771 ‐1.00816905 type2log.ND00 ‐0.34496571 ‐0.9789245 ‐0.02747850 0.07542098 1.42980090 type2log.ND10 0.01333914 0.1955510 0.01406220 ‐0.01910233 0.05312349 [,6] type2log.UFD00 ‐1.3566434 type2log.UFD10 0.7782270 type2log.ID00 0.2796347 type2log.ID10 0.3308526 type2log.ND00 1.0484146 type2log.ND10 ‐1.0765585 $xcenter type2log.PC95TEXH type2log.PC95GEXH 1.746545 1.349832 $ycenter type2log.UFD00 type2log.UFD10 type2log.ID00 type2log.ID10 type2log.ND00 1.4375796 1.3523235 1.2541245 1.1161151 0.9379719 type2log.ND10 0.9478903 > rdda31<‐rda(expend95[OK,],mort[OK,]) > rdda31 Call: rda(X = expend95[OK, ], Y = mort[OK, ]) Inertia Proportion Rank Total 0.4778 1.0000 Constrained 0.2253 0.4715 2 Unconstrained 0.2525 0.5285 2 Inertia is variance Eigenvalues for constrained axes: RDA1 RDA2 0.223500 0.001813 Eigenvalues for unconstrained axes: PC1 PC2 0.23563 0.01688 > plot(rdda31) Principal component analysis > pca1 <‐ princomp(type2log, cor=TRUE,scores=TRUE) ######### correlation matrix > summary(pca1) Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Standard deviation 2.9755211 1.5732152 0.54369657 0.36797783 0.302917671 Proportion of Variance 0.7378105 0.2062505 0.02463383 0.01128397 0.007646593 Cumulative Proportion 0.7378105 0.9440610 0.96869480 0.97997877 0.987625368 Comp.6 Comp.7 Comp.8 Comp.9
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Standard deviation 0.26580451 0.200503950 0.12978737 0.0978056623 Proportion of Variance 0.00588767 0.003350153 0.00140373 0.0007971623 Cumulative Proportion 0.99351304 0.996863190 0.99826692 0.9990640827 Comp.10 Comp.11 Comp.12 Standard deviation 0.0734262542 0.0655267695 0.0393171153 Proportion of Variance 0.0004492846 0.0003578131 0.0001288196 Cumulative Proportion 0.9995133672 0.9998711804 1.0000000000 > pca2 <‐ princomp(type2log, cor=FALSE,scores=TRUE) ######### covariance matrix > summary(pca2) Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Standard deviation 1.8398147 0.8387488 0.26442295 0.19669923 0.174423322 Proportion of Variance 0.7926782 0.1647451 0.01637371 0.00906054 0.007124557 Cumulative Proportion 0.7926782 0.9574234 0.97379708 0.98285762 0.989982182 Comp.6 Comp.7 Comp.8 Comp.9 Standard deviation 0.132818086 0.096927625 0.084810118 0.066385757 Proportion of Variance 0.004131076 0.002200108 0.001684396 0.001032045 Cumulative Proportion 0.994113258 0.996313366 0.997997761 0.999029806 Comp.10 Comp.11 Comp.12 Standard deviation 0.047964249 0.031864686 0.0287579929 Proportion of Variance 0.000538746 0.000237776 0.0001936716 Cumulative Proportion 0.999568552 0.999806328 1.0000000000 > screeplot(pca1,main="Scree plot for PCA1") > screeplot(pca2,main="Scree plot for PCA2") > print(loadings(pca1),cutoff=0.00) Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 Comp.10 PC95TEXH ‐0.278 ‐0.263 ‐0.621 0.355 0.021 ‐0.009 ‐0.526 0.162 ‐0.112 ‐0.111 PC05TEXH ‐0.276 ‐0.343 ‐0.058 0.298 ‐0.211 ‐0.411 0.356 ‐0.139 0.031 0.461 PC12TEXH ‐0.268 ‐0.337 0.378 0.456 0.022 0.256 0.335 0.131 0.113 ‐0.422 PC95GEXH ‐0.294 ‐0.228 ‐0.411 ‐0.455 0.286 0.478 0.404 ‐0.062 ‐0.006 0.071 PC05GEXH ‐0.279 ‐0.310 0.102 ‐0.574 ‐0.161 ‐0.544 ‐0.056 0.084 ‐0.001 ‐0.283 PC12GEXH ‐0.276 ‐0.302 0.514 ‐0.133 0.147 0.284 ‐0.546 ‐0.153 ‐0.040 0.265 UFD00 0.303 ‐0.261 0.042 0.042 0.357 ‐0.146 0.061 0.016 ‐0.452 ‐0.014 UFD10 0.301 ‐0.272 ‐0.076 0.046 0.248 ‐0.130 ‐0.024 ‐0.542 0.001 ‐0.462 ID00 0.300 ‐0.280 0.062 0.021 0.260 ‐0.055 0.070 0.228 ‐0.242 0.408 ID10 0.299 ‐0.281 ‐0.100 ‐0.011 0.045 0.006 ‐0.105 ‐0.176 0.764 0.203 ND00 0.302 ‐0.270 0.002 ‐0.110 ‐0.093 0.069 ‐0.018 0.693 0.196 ‐0.145 ND10 0.285 ‐0.296 ‐0.058 ‐0.081 ‐0.747 0.339 ‐0.005 ‐0.214 ‐0.296 0.007 Comp.11 Comp.12 PC95TEXH 0.116 ‐0.014 PC05TEXH ‐0.376 0.021 PC12TEXH 0.277 ‐0.001 PC95GEXH ‐0.064 0.015 PC05GEXH 0.271 ‐0.017 PC12GEXH ‐0.236 0.012 UFD00 0.039 0.691 UFD10 ‐0.330 ‐0.363 ID00 0.386 ‐0.571 ID10 0.302 0.246 ND00 ‐0.520 ‐0.025 ND10 0.115 0.034 Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Proportion Var 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 Cumulative Var 0.083 0.167 0.250 0.333 0.417 0.500 0.583 0.667 0.750 Comp.10 Comp.11 Comp.12 SS loadings 1.000 1.000 1.000 Proportion Var 0.083 0.083 0.083 Cumulative Var 0.833 0.917 1.000 > print(loadings(pca2),cutoff=0.00) Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 Comp.10 PC95TEXH ‐0.163 ‐0.296 ‐0.518 ‐0.152 0.422 ‐0.093 ‐0.434 ‐0.351 0.245 ‐0.006 PC05TEXH ‐0.151 ‐0.347 ‐0.048 ‐0.021 0.339 ‐0.390 0.323 0.126 ‐0.100 ‐0.096
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PC12TEXH ‐0.162 ‐0.377 0.351 ‐0.061 0.451 0.238 0.364 0.046 ‐0.206 0.162 PC95GEXH ‐0.223 ‐0.354 ‐0.511 ‐0.080 ‐0.424 0.524 0.275 0.139 ‐0.026 ‐0.004 PC05GEXH ‐0.190 ‐0.400 0.063 0.166 ‐0.504 ‐0.625 0.023 ‐0.015 0.002 0.004 PC12GEXH ‐0.196 ‐0.407 0.529 0.029 ‐0.139 0.297 ‐0.547 ‐0.014 0.111 ‐0.030 UFD00 0.400 ‐0.176 0.100 ‐0.381 ‐0.071 ‐0.040 0.145 ‐0.004 0.426 ‐0.022 UFD10 0.383 ‐0.183 ‐0.090 ‐0.269 0.013 ‐0.097 ‐0.206 0.548 0.014 0.502 ID00 0.377 ‐0.192 0.116 ‐0.223 ‐0.060 0.054 0.192 ‐0.238 0.156 ‐0.538 ID10 0.366 ‐0.187 ‐0.134 0.006 0.011 0.003 ‐0.287 0.067 ‐0.729 ‐0.343 ND00 0.344 ‐0.162 0.001 0.198 ‐0.109 0.051 0.126 ‐0.649 ‐0.181 0.540 ND10 0.316 ‐0.190 ‐0.107 0.795 0.173 0.113 0.020 0.235 0.324 ‐0.115 Comp.11 Comp.12 PC95TEXH 0.183 ‐0.049 PC05TEXH ‐0.659 0.119 PC12TEXH 0.487 ‐0.058 PC95GEXH ‐0.079 0.031 PC05GEXH 0.350 ‐0.068 PC12GEXH ‐0.302 0.053 UFD00 0.120 0.656 UFD10 ‐0.049 ‐0.363 ID00 ‐0.052 ‐0.585 ID10 0.107 0.257 ND00 ‐0.201 ‐0.006 ND10 0.061 0.031 Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Proportion Var 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 Cumulative Var 0.083 0.167 0.250 0.333 0.417 0.500 0.583 0.667 0.750 Comp.10 Comp.11 Comp.12 SS loadings 1.000 1.000 1.000 Proportion Var 0.083 0.083 0.083 Cumulative Var 0.833 0.917 1.000 > vari1<‐varimax(pca1$loadings[,1:2]) > vari2<‐varimax(pca2$loadings[,1:2]) > vscores1<‐pca1$scores[,1:2]%*%vari1$rotmat > vscores1 [,1] [,2] 1 0.3720739 ‐2.955009293 2 2.4999021 ‐1.327818614 3 0.4105807 0.871136570 4 ‐3.2447201 ‐4.360971822 5 1.5873217 0.733732839 6 0.5429265 2.041756424 7 ‐4.1307077 ‐1.201212581 8 1.7146026 0.586077082 9 ‐0.2334898 2.435015489 10 1.5361068 1.632877897 11 ‐3.8249512 1.084925998 12 ‐1.3626646 ‐0.602673957 13 1.7782585 0.036833366 14 4.0771283 4.664696946 15 ‐3.3567977 ‐3.746702190 16 ‐1.1532265 3.646743265 17 3.8715380 2.858754747 18 ‐3.2885421 ‐3.631301646 19 ‐2.3017920 0.357439459 20 1.4247199 0.051331356 21 0.9978187 2.012574998 22 ‐1.7977978 1.092356120 23 2.3295742 0.864449984 24 ‐1.9668199 ‐0.707810827 25 ‐0.7203986 3.001047761 26 1.2038387 1.876521266 27 1.2986547 0.997999199 28 1.8219064 0.985985871 29 ‐1.1372082 ‐0.302660640 30 ‐3.4512141 ‐3.817948791
35
31 2.2244894 1.635346558 32 ‐3.1002496 ‐3.600526342 33 1.8583462 2.018351870 34 5.3608300 ‐0.006155771 35 0.9581852 1.005744587 36 ‐4.1250968 ‐0.849891763 37 0.7298086 0.346200785 38 ‐4.1852269 ‐5.727464852 39 0.4873818 ‐0.044551489 40 1.3677764 ‐4.611692538 41 ‐3.0836505 ‐3.072763999 42 ‐0.2937982 1.290569526 43 2.5093508 1.129988938 44 2.5854837 1.312551976 45 1.2097482 ‐0.003853761 > vscores2<‐pca2$scores[,1:2]%*%vari2$rotmat > vscores2 [,1] [,2] 1 0.2375530 ‐1.45186294 2 1.7449469 ‐0.66932551 3 0.3057144 0.40091176 4 ‐2.2391976 ‐2.04564423 5 1.1097202 0.33414821 6 0.3780727 0.97078498 7 ‐2.9073978 ‐0.60210840 8 1.1922214 0.32192590 9 ‐0.1393674 1.13741534 10 1.0817394 0.79865695 11 ‐2.6496926 0.49823870 12 ‐0.9124563 ‐0.31943867 13 1.2377169 0.05947280 14 2.8025331 2.26308629 15 ‐2.3479731 ‐1.77521358 16 ‐0.7610612 1.70776094 17 2.6719684 1.31366803 18 ‐2.2608175 ‐1.68149566 19 ‐1.5944909 0.18670145 20 0.9816870 ‐0.00943937 21 0.6992733 1.00629122 22 ‐1.2174828 0.58449939 23 1.6208569 0.39535141 24 ‐1.3651976 ‐0.36977208 25 ‐0.5042434 1.41003043 26 0.8473727 0.87437590 27 0.9084763 0.43657562 28 1.2726480 0.45388477 29 ‐0.7819927 ‐0.17706630 30 ‐2.5399899 ‐1.80113202 31 1.5455099 0.73323205 32 ‐2.1258282 ‐1.70436360 33 1.3104108 0.98380921 34 3.7044953 0.01505979 35 0.6671602 0.44732756 36 ‐2.9044284 ‐0.35850893 37 0.5000609 0.16496364 38 ‐2.9372286 ‐2.74178608 39 0.3441797 0.07836710 40 0.9583286 ‐2.15394289 41 ‐2.1177089 ‐1.46051324 42 ‐0.1986811 0.61900882 43 1.7351108 0.57573466 44 1.7913994 0.58782237 45 0.8560798 ‐0.03749178 plot(vscores1[,1],vscores1[,2],col=type2$Country,asp=1,xlab="1st varimax component",ylab="2nd varimax component",main="Varimax Scores plot(pca1)", las=1) text(vscores1[,1]‐0.1,vscores1[,2]‐0.1,type2$Country,cex=0.7)
36
arrows(0,0,vari1$loadings [,1],vari1$loadings[,2],col="green") text(vari1$loadings[,1],vari1$loadings[,2],names(type2),asp=1,cex=0.7 ,col="blue") plot(vscores2[,1],vscores2[,2],col=type2$Country,asp=1,xlab="1st varimax component",ylab="2nd varimax component",main="Varimax Scores plot(pca2)", las=1) text(vscores2[,1]‐0.1,vscores2[,2]‐0.1,type2$Country,cex=0.7) arrows(0,0,vari2$loadings [,1],vari2$loadings[,2],col="green") text(vari2$loadings[,1],vari2$loadings[,2],names(type2),asp=1,cex=0.7 ,col="blue") plot(pca1$scores[,1],pca1$scores[,2],col=type2$Country,asp=1,xlab="1st principal component",ylab="2nd principal component",main="Scores plot pca1") text(pca1$scores[,1]‐0.1,pca1$scores[,2]‐0.1,type2$Country,cex=0.7) arrows(0,0,pca1$loadings [,1],pca1$loadings[,2],col="red") text(pca1$loadings[,1]‐0.1,pca1$loadings[,2]‐0.1,names(type2),asp=1,cex=0.7 ,col="blue") plot(pca2$scores[,1],pca2$scores[,2],col=type2$Country,asp=1,xlab="1st principal component",ylab="2nd principal component",main="Scores plot pca2") text(pca2$scores[,1]‐0.1,pca2$scores[,2]‐0.1,type2$Country,cex=0.7) arrows(0,0,pca2$loadings [,1],pca2$loadings[,2],col="red") text(pca2$loadings[,1]‐0.1,pca2$loadings[,2]‐0.1,names(type2),asp=1,cex=0.7 ,col="blue") biplot(pca1,main="Biplot pca1") biplot(pca2,main="Biplot pca2") Reg1ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH, data=type2log) Reg2ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log) Reg3UFD10 <‐ lm(UFD10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log) Reg4ND10 <‐ lm(ND10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log) Reg5ND10 <‐ lm(ND10~ PC05TEXH+ PC95TEXH, data=type2log) Reg6ND10 <‐ lm(ND10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ID10+ UFD10, data=type2log) Reg7ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ND10+ UFD10, data=type2log) Reg8UFD10 <‐ lm(UFD10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ID10+ ND10, data=type2log) Reg9ND10 <‐ lm(ND10~ ID10, data=type2log) Reg10UFD10 <‐ lm(UFD10 ~ PC05GEXH +ID10, data=type2log) Reg11UFD10 <‐ lm(UFD10 ~ ID10, data=type2log) Reg12ID10 <‐ lm(ID10~ ND10+ UFD10, data=type2log) summary(Reg1ID10) summary(Reg2ID10) summary(Reg3ID10) summary(Reg4ND10) summary(Reg5ND10) summary(Reg6ND10) summary(Reg7ID10) summary(Reg8UFD10) summary(Reg9ND10) summary(Reg10UFD10) summary(Reg11UFD10) summary(Reg12ID10) > Reg1ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH, data=type2log) > Reg2ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log) > Reg3UFD10 <‐ lm(UFD10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log) > Reg4ND10 <‐ lm(ND10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log) > Reg5ND10 <‐ lm(ND10~ PC05TEXH+ PC95TEXH, data=type2log) > Reg6ND10 <‐ lm(ND10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ID10+ UFD10, data=type2log) > Reg7ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ND10+ UFD10, data=type2log) > Reg8UFD10 <‐ lm(UFD10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ID10+ ND10, data=type2log) > Reg9ND10 <‐ lm(ND10~ ID10, data=type2log) > Reg10UFD10 <‐ lm(UFD10 ~ PC05GEXH +ID10, data=type2log) > Reg11UFD10 <‐ lm(UFD10 ~ ID10, data=type2log) > Reg12ID10 <‐ lm(ID10~ ND10+ UFD10, data=type2log) > summary(Reg1ID10)
37
Call: lm(formula = ID10 ~ PC05GEXH + PC05TEXH, data = type2log) Residuals: Min 1Q Median 3Q Max ‐1.25751 ‐0.36580 0.00243 0.44775 1.50333 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.27288 0.54868 4.142 0.000162 *** PC05GEXH ‐0.74391 0.51809 ‐1.436 0.158444 PC05TEXH 0.01612 0.63028 0.026 0.979715 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.6104 on 42 degrees of freedom Multiple R‐squared: 0.2782, Adjusted R‐squared: 0.2438 F‐statistic: 8.092 on 2 and 42 DF, p‐value: 0.001065 > summary(Reg2ID10) Call: lm(formula = ID10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH, data = type2log) Residuals: Min 1Q Median 3Q Max ‐0.94914 ‐0.34997 0.01544 0.42213 1.34457 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.7753 0.5616 3.161 0.00299 ** PC05GEXH ‐0.1923 0.6205 ‐0.310 0.75822 PC05TEXH 0.5677 0.8621 0.659 0.51397 PC95GEXH ‐0.9201 0.5266 ‐1.747 0.08829 . PC95TEXH ‐0.1256 0.7100 ‐0.177 0.86052 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.5798 on 40 degrees of freedom Multiple R‐squared: 0.3798, Adjusted R‐squared: 0.3177 F‐statistic: 6.123 on 4 and 40 DF, p‐value: 0.0006102 > summary(Reg3ID10) Call: lm(formula = UFD10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH, data = type2log) Residuals: Min 1Q Median 3Q Max ‐1.14798 ‐0.31673 ‐0.03463 0.39619 1.33012 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.0306 0.5784 3.510 0.00112 ** PC05GEXH ‐0.2752 0.6392 ‐0.431 0.66911 PC05TEXH 0.7153 0.8880 0.805 0.42531 PC95GEXH ‐0.9451 0.5424 ‐1.742 0.08915 . PC95TEXH ‐0.2064 0.7314 ‐0.282 0.77925 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.5973 on 40 degrees of freedom Multiple R‐squared: 0.3981, Adjusted R‐squared: 0.3379 F‐statistic: 6.613 on 4 and 40 DF, p‐value: 0.0003494 > summary(Reg4ND10) Call: lm(formula = ND10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH, data = type2log) Residuals: Min 1Q Median 3Q Max ‐0.96955 ‐0.31210 0.01745 0.38764 1.25601 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.3982 0.5185 2.697 0.0102 * PC05GEXH ‐0.1416 0.5729 ‐0.247 0.8060 PC05TEXH 0.6849 0.7960 0.860 0.3947 PC95GEXH ‐0.8242 0.4862 ‐1.695 0.0978 . PC95TEXH ‐0.2575 0.6556 ‐0.393 0.6966 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
38
Residual standard error: 0.5354 on 40 degrees of freedom Multiple R‐squared: 0.3462, Adjusted R‐squared: 0.2808 F‐statistic: 5.296 on 4 and 40 DF, p‐value: 0.001613 > summary(Reg5ND10) Call: lm(formula = ND10 ~ PC05TEXH + PC95TEXH, data = type2log) Residuals: Min 1Q Median 3Q Max ‐1.10455 ‐0.32213 0.06968 0.38158 1.44247 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.1598 0.4062 5.318 3.77e‐06 *** PC05TEXH 0.2124 0.5114 0.415 0.6800 PC95TEXH ‐0.9315 0.4955 ‐1.880 0.0671 . Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.5566 on 42 degrees of freedom Multiple R‐squared: 0.2579, Adjusted R‐squared: 0.2226 F‐statistic: 7.299 on 2 and 42 DF, p‐value: 0.001903 > summary(Reg6ND10) Call: lm(formula = ND10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH + ID10 + UFD10, data = type2log) Residuals: Min 1Q Median 3Q Max ‐0.28540 ‐0.06882 ‐0.01318 0.05960 0.87147 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) ‐0.03657 0.20549 ‐0.178 0.860 PC05GEXH ‐0.01190 0.19457 ‐0.061 0.952 PC05TEXH 0.25679 0.27244 0.943 0.352 PC95GEXH ‐0.03069 0.17001 ‐0.181 0.858 PC95TEXH ‐0.18526 0.22209 ‐0.834 0.409 ID10 1.34080 0.28712 4.670 3.7e‐05 *** UFD10 ‐0.46567 0.27874 ‐1.671 0.103 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.1804 on 38 degrees of freedom Multiple R‐squared: 0.9295, Adjusted R‐squared: 0.9183 F‐statistic: 83.48 on 6 and 38 DF, p‐value: < 2.2e‐16 > summary(Reg7ID10) Call: lm(formula = ID10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH + ND10 + UFD10, data = type2log) Residuals: Min 1Q Median 3Q Max ‐0.206511 ‐0.043103 0.000377 0.055819 0.130839 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) ‐0.096069 0.091262 ‐1.053 0.299 PC05GEXH 0.048276 0.087281 0.553 0.583 PC05TEXH ‐0.143789 0.121913 ‐1.179 0.246 PC95GEXH ‐0.001895 0.076598 ‐0.025 0.980 PC95TEXH 0.096026 0.099726 0.963 0.342 ND10 0.271952 0.058235 4.670 3.7e‐05 *** UFD10 0.734343 0.052201 14.068 < 2e‐16 *** Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.08125 on 38 degrees of freedom Multiple R‐squared: 0.9884, Adjusted R‐squared: 0.9866 F‐statistic: 541.1 on 6 and 38 DF, p‐value: < 2.2e‐16 > summary(Reg8UFD10) Call: lm(formula = UFD10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH + ID10 + ND10, data = type2log) Residuals: Min 1Q Median 3Q Max ‐0.199873 ‐0.061220 0.004548 0.044997 0.277463 Coefficients:
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Estimate Std. Error t value Pr(>|t|) (Intercept) 0.20790 0.11044 1.882 0.0674 . PC05GEXH ‐0.07629 0.10860 ‐0.703 0.4866 PC05TEXH 0.16733 0.15242 1.098 0.2792 PC95GEXH ‐0.01512 0.09551 ‐0.158 0.8751 PC95TEXH ‐0.10078 0.12483 ‐0.807 0.4245 ID10 1.14240 0.08121 14.068 <2e‐16 *** ND10 ‐0.14694 0.08795 ‐1.671 0.1030 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.1013 on 38 degrees of freedom Multiple R‐squared: 0.9835, Adjusted R‐squared: 0.9809 F‐statistic: 378.4 on 6 and 38 DF, p‐value: < 2.2e‐16 > summary(Reg9ND10) Call: lm(formula = ND10 ~ ID10, data = type2log) Residuals: Min 1Q Median 3Q Max ‐0.24440 ‐0.06061 ‐0.01183 0.02462 1.01541 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) ‐0.01541 0.05066 ‐0.304 0.762 ID10 0.86309 0.03854 22.392 <2e‐16 *** Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.1795 on 43 degrees of freedom Multiple R‐squared: 0.921, Adjusted R‐squared: 0.9192 F‐statistic: 501.4 on 1 and 43 DF, p‐value: < 2.2e‐16 > summary(Reg10UFD10) Call: lm(formula = UFD10 ~ PC05GEXH + ID10, data = type2log) Residuals: Min 1Q Median 3Q Max ‐0.200100 ‐0.035128 ‐0.001316 0.035550 0.303160 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.26660 0.07723 3.452 0.00128 ** PC05GEXH ‐0.03483 0.03549 ‐0.981 0.33205 ID10 1.02261 0.02559 39.966 < 2e‐16 *** Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.1012 on 42 degrees of freedom Multiple R‐squared: 0.9818, Adjusted R‐squared: 0.981 F‐statistic: 1136 on 2 and 42 DF, p‐value: < 2.2e‐16 > summary(Reg11UFD10) Call: lm(formula = UFD10 ~ ID10, data = type2log) Residuals: Min 1Q Median 3Q Max ‐0.196194 ‐0.039393 0.002385 0.040477 0.280927 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.19619 0.02856 6.869 1.99e‐08 *** ID10 1.03585 0.02173 47.669 < 2e‐16 *** Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.1012 on 43 degrees of freedom Multiple R‐squared: 0.9814, Adjusted R‐squared: 0.981 F‐statistic: 2272 on 1 and 43 DF, p‐value: < 2.2e‐16 > summary(Reg12ID10) Call: lm(formula = ID10 ~ ND10 + UFD10, data = type2log) Residuals: Min 1Q Median 3Q Max ‐0.223507 ‐0.046779 0.009083 0.038863 0.139237 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) ‐0.12621 0.02625 ‐4.809 1.98e‐05 *** ND10 0.26492 0.05595 4.735 2.51e‐05 *** UFD10 0.73296 0.04813 15.230 < 2e‐16 ***
40
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.07906 on 42 degrees of freedom Multiple R‐squared: 0.9879, Adjusted R‐squared: 0.9873 F‐statistic: 1713 on 2 and 42 DF, p‐value: < 2.2e‐16 > Reg13ID00 <‐ lm(ID00~ PC95GEXH+ PC95TEXH, data=type2log) > summary(Reg13ID00) Call: lm(formula = ID00 ~ PC95GEXH + PC95TEXH, data = type2log) 0.3603 3.168e‐05 Residuals: Min 1Q Median 3Q Max ‐1.16781 ‐0.31009 ‐0.01399 0.41798 1.36909 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.33200 0.45444 5.132 *** PC95GEXH ‐0.87670 0.40332 ‐2.174 0.0354 * PC95TEXH 0.06042 0.50895 0.119 0.9061 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.5784 on 42 degrees of freedom Multiple R‐squared: 0.3894, Adjusted R‐squared: 0.3603 F‐statistic: 13.39 on 2 and 42 DF, p‐value: 3.168e‐05 > step(Reg13ID00) Start: AIC=‐46.38 ID00 ~ PC95GEXH + PC95TEXH Df Sum of Sq RSS AIC ‐ PC95TEXH 1 0.00471 14.056 ‐48.362 <none> 14.052 ‐46.377 ‐ PC95GEXH 1 1.58081 15.632 ‐43.579 Step: AIC=‐48.36 ID00 ~ PC95GEXH Df Sum of Sq RSS AIC <none> 14.056 ‐48.362 ‐ PC95GEXH 1 8.9567 23.013 ‐28.177 Call: lm(formula = ID00 ~ PC95GEXH, data = type2log) Coefficients: (Intercept) PC95GEXH 2.3783 ‐0.8328 > Reg14ND00 <‐ lm(ND00~ PC95GEXH+ PC95TEXH, data=type2log) > summary(Reg14ND00) Call: lm(formula = ND00 ~ PC95GEXH + PC95TEXH, data = type2log) 0.3638 2.825e‐05 Residuals: Min 1Q Median 3Q Max ‐0.8634 ‐0.3571 0.0345 0.3797 1.3348 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.94348 0.41275 4.709 2.73e‐05 *** PC95GEXH ‐0.78351 0.36632 ‐2.139 0.0383 * PC95TEXH 0.02983 0.46226 0.065 0.9489 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.5254 on 42 degrees of freedom
41
Multiple R‐squared: 0.3927, Adjusted R‐squared: F‐statistic: 13.58 on 2 and 42 DF, p‐value: > step(Reg14ND00) Start: AIC=‐55.04 ND00 ~ PC95GEXH + PC95TEXH Df Sum of Sq RSS AIC ‐ PC95TEXH 1 0.00115 11.593 ‐57.032 <none> 11.592 ‐55.037 ‐ PC95GEXH 1 1.26260 12.854 ‐52.384 Step: AIC=‐57.03 ND00 ~ PC95GEXH Df Sum of Sq RSS AIC <none> 11.593 ‐57.032 ‐ PC95GEXH 1 7.4953 19.088 ‐36.592 Call: lm(formula = ND00 ~ PC95GEXH, data = type2log) Coefficients: (Intercept) PC95GEXH 1.9663 ‐0.7618 > Reg16UFD00 <‐ lm(UFD00~ PC95GEXH+ PC95TEXH, data=type2log) > summary(Reg16UFD00) Call: lm(formula = UFD00 ~ PC95GEXH + PC95TEXH, data = type2log) :0.3856 1.36e‐05 Residuals: Min 1Q Median 3Q Max ‐1.22820 ‐0.33891 0.02096 0.41085 1.38918 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.59999 0.47066 5.524 1.91e‐06 *** PC95GEXH ‐0.96519 0.41771 ‐2.311 0.0258 * PC95TEXH 0.08041 0.52711 0.153 0.8795 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.5991 on 42 degrees of freedom Multiple R‐squared: 0.4135, Adjusted R‐squared: 0.3856 F‐statistic: 14.81 on 2 and 42 DF, p‐value: 1.36e‐05 > step(Reg16UFD00) Start: AIC=‐43.22 UFD00 ~ PC95GEXH + PC95TEXH Df Sum of Sq RSS AIC ‐ PC95TEXH 1 0.00835 15.081 ‐45.196 <none> 15.072 ‐43.221 ‐ PC95GEXH 1 1.91604 16.988 ‐39.836 Step: AIC=‐45.2 UFD00 ~ PC95GEXH Df Sum of Sq RSS AIC <none> 15.081 ‐45.196 ‐ PC95GEXH 1 10.618 25.699 ‐23.209 Call: lm(formula = UFD00 ~ PC95GEXH, data = type2log) Coefficients: (Intercept) PC95GEXH 2.6616 ‐0.9068 > Reg31ID10 <‐ lm(UFD10~ PC05GEXH+ PC05TEXH, data=type2log) > summary(Reg31ID10)
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Call: lm(formula = UFD10 ~ PC05GEXH + PC05TEXH, data = type2log) Residuals: Min 1Q Median 3Q Max ‐1.19681 ‐0.34696 ‐0.00033 0.44469 1.50250 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.5550 0.5684 4.495 5.38e‐05 *** PC05GEXH ‐0.8337 0.5367 ‐1.553 0.128 PC05TEXH 0.0660 0.6529 0.101 0.920 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.6323 on 42 degrees of freedom Multiple R‐squared: 0.2916, Adjusted R‐squared: 0.2578 F‐statistic: 8.643 on 2 and 42 DF, p‐value: 0.0007182 > step(Reg31ID10) Start: AIC=‐38.36 UFD10 ~ PC05GEXH + PC05TEXH Df Sum of Sq RSS AIC ‐ PC05TEXH 1 0.00409 16.797 ‐40.346 <none> 16.793 ‐38.356 ‐ PC05GEXH 1 0.96487 17.758 ‐37.842 Step: AIC=‐40.35 UFD10 ~ PC05GEXH Df Sum of Sq RSS AIC <none> 16.797 ‐40.346 ‐ PC05GEXH 1 6.9074 23.704 ‐26.845 Call: lm(formula = UFD10 ~ PC05GEXH, data = type2log) Coefficients: (Intercept) PC05GEXH 2.6028 ‐0.7829 stepwise(Reg22ND10, direction='forward/backward', criterion='AIC') stepwise(Reg21ID10, direction='forward/backward', criterion='AIC') Reg21ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH+ ID00+ ND00+ UFD00+ ND10+ UFD10, data=type2log) Reg22ND10 <‐ lm(ND10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ID10+ ID00+ ND00+ UFD00+ UFD10, data=type2log) Reg3UFD10 <‐ lm(UFD10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log) Reg4ND10 <‐ lm(ND10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log) Reg5ND10 <‐ lm(ND10~ PC05TEXH+ PC95TEXH, data=type2log) Reg6ND10 <‐ lm(ND10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ID10+ UFD10, data=type2log) Reg7ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ND10+ UFD10, data=type2log) Reg8UFD10 <‐ lm(UFD10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ID10+ ND10, data=type2log) Reg9ND10 <‐ lm(ND10~ ID10, data=type2log) Reg10UFD10 <‐ lm(UFD10 ~ PC05GEXH +ID10, data=type2log) Reg11UFD10 <‐ lm(UFD10 ~ ID10, data=type2log) Reg12ID10 <‐ lm(ID10~ ND10+ UFD10, data=type2log) summary(Reg1ID10) summary(Reg2ID10) summary(Reg3ID10) summary(Reg4ND10) summary(Reg5ND10) summary(Reg6ND10) summary(Reg7ID10) summary(Reg8UFD10) summary(Reg9ND10) summary(Reg10UFD10) summary(Reg11UFD10) summary(Reg12ID10) > step(Reg6ND10) Start: AIC=‐147.74 ND10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH + ID10 + UFD10 Df Sum of Sq RSS AIC
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‐ PC05GEXH 1 0.00012 1.2368 ‐149.74 ‐ PC95GEXH 1 0.00106 1.2377 ‐149.70 ‐ PC95TEXH 1 0.02264 1.2593 ‐148.93 ‐ PC05TEXH 1 0.02891 1.2656 ‐148.70 <none> 1.2367 ‐147.74 ‐ UFD10 1 0.09083 1.3275 ‐146.55 ‐ ID10 1 0.70971 1.9464 ‐129.33 Step: AIC=‐149.74 ND10 ~ PC05TEXH + PC95GEXH + PC95TEXH + ID10 + UFD10 Df Sum of Sq RSS AIC ‐ PC95GEXH 1 0.00219 1.2390 ‐151.66 ‐ PC95TEXH 1 0.02744 1.2642 ‐150.75 <none> 1.2368 ‐149.74 ‐ PC05TEXH 1 0.06413 1.3009 ‐149.46 ‐ UFD10 1 0.09127 1.3281 ‐148.53 ‐ ID10 1 0.71560 1.9524 ‐131.19 Step: AIC=‐151.66 ND10 ~ PC05TEXH + PC95TEXH + ID10 + UFD10 Df Sum of Sq RSS AIC ‐ PC95TEXH 1 0.04909 1.2881 ‐151.91 <none> 1.2390 ‐151.66 ‐ PC05TEXH 1 0.06280 1.3018 ‐151.43 ‐ UFD10 1 0.08935 1.3283 ‐150.52 ‐ ID10 1 0.71362 1.9526 ‐133.19 Step: AIC=‐151.91 ND10 ~ PC05TEXH + ID10 + UFD10 Df Sum of Sq RSS AIC ‐ PC05TEXH 1 0.01372 1.3018 ‐153.43 <none> 1.2881 ‐151.91 ‐ UFD10 1 0.07522 1.3633 ‐151.35 ‐ ID10 1 0.68840 1.9765 ‐134.64 Step: AIC=‐153.43 ND10 ~ ID10 + UFD10 Df Sum of Sq RSS AIC <none> 1.3018 ‐153.43 ‐ UFD10 1 0.08328 1.3851 ‐152.64 ‐ ID10 1 0.69483 1.9966 ‐136.18 Call: lm(formula = ND10 ~ ID10 + UFD10, data = type2log) Coefficients: (Intercept) ID10 UFD10 0.06992 1.31361 ‐0.43493 > step(Reg7ID10) Start: AIC=‐219.53 ID10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH + ND10 + UFD10 Df Sum of Sq RSS AIC ‐ PC95GEXH 1 0.00000 0.25083 ‐221.53 ‐ PC05GEXH 1 0.00202 0.25285 ‐221.17 ‐ PC95TEXH 1 0.00612 0.25695 ‐220.45 ‐ PC05TEXH 1 0.00918 0.26001 ‐219.92 <none> 0.25083 ‐219.53 ‐ ND10 1 0.14395 0.39478 ‐201.12 ‐ UFD10 1 1.30630 1.55713 ‐139.37 Step: AIC=‐221.53 ID10 ~ PC05GEXH + PC05TEXH + PC95TEXH + ND10 + UFD10 Df Sum of Sq RSS AIC ‐ PC05GEXH 1 0.00281 0.25364 ‐223.03 ‐ PC05TEXH 1 0.00981 0.26064 ‐221.81 ‐ PC95TEXH 1 0.01006 0.26089 ‐221.76 <none> 0.25083 ‐221.53 ‐ ND10 1 0.14424 0.39507 ‐203.09 ‐ UFD10 1 1.31366 1.56449 ‐141.16 Step: AIC=‐223.03 ID10 ~ PC05TEXH + PC95TEXH + ND10 + UFD10 Df Sum of Sq RSS AIC ‐ PC05TEXH 1 0.00826 0.26190 ‐223.59
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‐ PC95TEXH 1 0.00854 0.26218 ‐223.54 <none> 0.25364 ‐223.03 ‐ ND10 1 0.14609 0.39973 ‐204.56 ‐ UFD10 1 1.32396 1.57761 ‐142.78 Step: AIC=‐223.59 ID10 ~ PC95TEXH + ND10 + UFD10 Df Sum of Sq RSS AIC ‐ PC95TEXH 1 0.00063 0.26254 ‐225.48 <none> 0.26190 ‐223.59 ‐ ND10 1 0.13916 0.40107 ‐206.41 ‐ UFD10 1 1.37377 1.63568 ‐143.16 Step: AIC=‐225.48 ID10 ~ ND10 + UFD10 Df Sum of Sq RSS AIC <none> 0.26254 ‐225.48 ‐ ND10 1 0.14013 0.40267 ‐208.23 ‐ UFD10 1 1.44996 1.71249 ‐143.09 Call: lm(formula = ID10 ~ ND10 + UFD10, data = type2log) Coefficients: (Intercept) ND10 UFD10 ‐0.1262 0.2649 0.7330 > step(Reg8UFD10) Start: AIC=‐199.65 UFD10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH + ID10 + ND10 Df Sum of Sq RSS AIC ‐ PC95GEXH 1 0.00026 0.39047 ‐201.62 ‐ PC05GEXH 1 0.00507 0.39528 ‐201.07 ‐ PC95TEXH 1 0.00669 0.39690 ‐200.88 ‐ PC05TEXH 1 0.01238 0.40259 ‐200.24 <none> 0.39021 ‐199.65 ‐ ND10 1 0.02866 0.41887 ‐198.46 ‐ ID10 1 2.03218 2.42240 ‐119.49 Step: AIC=‐201.62 UFD10 ~ PC05GEXH + PC05TEXH + PC95TEXH + ID10 + ND10 Df Sum of Sq RSS AIC ‐ PC05GEXH 1 0.00951 0.39998 ‐202.53 ‐ PC95TEXH 1 0.01449 0.40495 ‐201.98 ‐ PC05TEXH 1 0.01450 0.40497 ‐201.98 <none> 0.39047 ‐201.62 ‐ ND10 1 0.02855 0.41902 ‐200.44 ‐ ID10 1 2.04494 2.43541 ‐121.25 Step: AIC=‐202.54 UFD10 ~ PC05TEXH + PC95TEXH + ID10 + ND10 Df Sum of Sq RSS AIC ‐ PC05TEXH 1 0.00507 0.40505 ‐203.97 ‐ PC95TEXH 1 0.01113 0.41110 ‐203.30 <none> 0.39998 ‐202.53 ‐ ND10 1 0.02884 0.42882 ‐201.40 ‐ ID10 1 2.08781 2.48778 ‐122.29 Step: AIC=‐203.97 UFD10 ~ PC95TEXH + ID10 + ND10 Df Sum of Sq RSS AIC ‐ PC95TEXH 1 0.00871 0.41376 ‐205.01 <none> 0.40505 ‐203.97 ‐ ND10 1 0.02523 0.43028 ‐203.25 ‐ ID10 1 2.12463 2.52968 ‐123.54 Step: AIC=‐205.01 UFD10 ~ ID10 + ND10 Df Sum of Sq RSS AIC <none> 0.41376 ‐205.01 ‐ ND10 1 0.02647 0.44023 ‐204.22 ‐ ID10 1 2.28516 2.69892 ‐122.62 Call: lm(formula = UFD10 ~ ID10 + ND10, data = type2log) Coefficients:
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(Intercept) ID10 ND10 0.1941 1.1552 ‐0.1382 > step(Reg9ND10) Start: AIC=‐152.64 ND10 ~ ID10 Df Sum of Sq RSS AIC <none> 1.3851 ‐152.641 ‐ ID10 1 16.151 17.5362 ‐40.408 Call: lm(formula = ND10 ~ ID10, data = type2log) Coefficients: (Intercept) ID10 ‐0.01541 0.86309 > step(Reg10UFD10) Start: AIC=‐203.24 UFD10 ~ PC05GEXH + ID10 Df Sum of Sq RSS AIC ‐ PC05GEXH 1 0.0099 0.4402 ‐204.220 <none> 0.4304 ‐203.241 ‐ ID10 1 16.3667 16.7971 ‐40.346 Step: AIC=‐204.22 UFD10 ~ ID10 Df Sum of Sq RSS AIC <none> 0.4402 ‐204.220 ‐ ID10 1 23.264 23.7045 ‐26.845 Call: lm(formula = UFD10 ~ ID10, data = type2log) Coefficients: (Intercept) ID10 0.1962 1.0359 > step(Reg11UFD10) Start: AIC=‐204.22 UFD10 ~ ID10 Df Sum of Sq RSS AIC <none> 0.4402 ‐204.220 ‐ ID10 1 23.264 23.7045 ‐26.845 Call: lm(formula = UFD10 ~ ID10, data = type2log) Coefficients: (Intercept) ID10 0.1962 1.0359 > step(Reg12ID10) Start: AIC=‐225.48 ID10 ~ ND10 + UFD10 Df Sum of Sq RSS AIC <none> 0.26254 ‐225.48 ‐ ND10 1 0.14013 0.40267 ‐208.23 ‐ UFD10 1 1.44996 1.71249 ‐143.09 Call: lm(formula = ID10 ~ ND10 + UFD10, data = type2log) Coefficients: (Intercept) ND10 UFD10 ‐0.1262 0.2649 0.7330 > step(Reg1ID10) Start: AIC=‐41.53 ID10 ~ PC05GEXH + PC05TEXH Df Sum of Sq RSS AIC ‐ PC05TEXH 1 0.00024 15.651 ‐43.526 <none> 15.651 ‐41.526 ‐ PC05GEXH 1 0.76829 16.419 ‐41.370 Step: AIC=‐43.53 ID10 ~ PC05GEXH Df Sum of Sq RSS AIC <none> 15.651 ‐43.526 ‐ PC05GEXH 1 6.0308 21.682 ‐30.859 Call:
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lm(formula = ID10 ~ PC05GEXH, data = type2log) Coefficients: (Intercept) PC05GEXH 2.2846 ‐0.7315 > step(Reg2ID10) Start: AIC=‐44.35 ID10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH Df Sum of Sq RSS AIC ‐ PC95TEXH 1 0.01051 13.459 ‐46.317 ‐ PC05GEXH 1 0.03229 13.480 ‐46.245 ‐ PC05TEXH 1 0.14580 13.594 ‐45.867 <none> 13.448 ‐44.353 ‐ PC95GEXH 1 1.02622 14.474 ‐43.043 Step: AIC=‐46.32 ID10 ~ PC05GEXH + PC05TEXH + PC95GEXH Df Sum of Sq RSS AIC ‐ PC05GEXH 1 0.02216 13.481 ‐48.243 ‐ PC05TEXH 1 0.18486 13.643 ‐47.704 <none> 13.459 ‐46.317 ‐ PC95GEXH 1 2.19234 15.651 ‐41.526 Step: AIC=‐48.24 ID10 ~ PC05TEXH + PC95GEXH Df Sum of Sq RSS AIC ‐ PC05TEXH 1 0.2040 13.685 ‐49.568 <none> 13.481 ‐48.243 ‐ PC95GEXH 1 2.9385 16.419 ‐41.370 Step: AIC=‐49.57 ID10 ~ PC95GEXH Df Sum of Sq RSS AIC <none> 13.685 ‐49.568 ‐ PC95GEXH 1 7.9972 21.682 ‐30.859 Call: lm(formula = ID10 ~ PC95GEXH, data = type2log) Coefficients: (Intercept) PC95GEXH 2.1783 ‐0.7869 > step(Reg3UFD10) Start: AIC=‐41.69 UFD10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH Df Sum of Sq RSS AIC ‐ PC95TEXH 1 0.02841 14.297 ‐43.597 ‐ PC05GEXH 1 0.06612 14.335 ‐43.479 ‐ PC05TEXH 1 0.23143 14.500 ‐42.963 <none> 14.269 ‐41.687 ‐ PC95GEXH 1 1.08281 15.351 ‐40.395 Step: AIC=‐43.6 UFD10 ~ PC05GEXH + PC05TEXH + PC95GEXH Df Sum of Sq RSS AIC ‐ PC05GEXH 1 0.04049 14.338 ‐45.470 ‐ PC05TEXH 1 0.25415 14.551 ‐44.805 <none> 14.297 ‐43.597 ‐ PC95GEXH 1 2.49599 16.793 ‐38.356 Step: AIC=‐45.47 UFD10 ~ PC05TEXH + PC95GEXH Df Sum of Sq RSS AIC ‐ PC05TEXH 1 0.2543 14.592 ‐46.679 <none> 14.338 ‐45.470 ‐ PC95GEXH 1 3.4204 17.758 ‐37.842 Step: AIC=‐46.68 UFD10 ~ PC95GEXH Df Sum of Sq RSS AIC <none> 14.592 ‐46.679 ‐ PC95GEXH 1 9.1128 23.704 ‐26.845 Call: lm(formula = UFD10 ~ PC95GEXH, data = type2log) Coefficients:
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(Intercept) PC95GEXH 2.486 ‐0.840 > step(Reg4ND10) Start: AIC=‐51.53 ND10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH Df Sum of Sq RSS AIC ‐ PC05GEXH 1 0.01751 11.482 ‐53.464 ‐ PC95TEXH 1 0.04422 11.509 ‐53.359 ‐ PC05TEXH 1 0.21221 11.677 ‐52.707 <none> 11.465 ‐51.532 ‐ PC95GEXH 1 0.82354 12.288 ‐50.411 Step: AIC=‐53.46 ND10 ~ PC05TEXH + PC95GEXH + PC95TEXH Df Sum of Sq RSS AIC ‐ PC95TEXH 1 0.02806 11.510 ‐55.354 ‐ PC05TEXH 1 0.31292 11.795 ‐54.254 <none> 11.482 ‐53.464 ‐ PC95GEXH 1 1.53092 13.013 ‐49.832 Step: AIC=‐55.35 ND10 ~ PC05TEXH + PC95GEXH Df Sum of Sq RSS AIC ‐ PC05TEXH 1 0.32103 11.831 ‐56.116 <none> 11.510 ‐55.354 ‐ PC95GEXH 1 2.59769 14.108 ‐48.196 Step: AIC=‐56.12 ND10 ~ PC95GEXH Df Sum of Sq RSS AIC <none> 11.831 ‐56.116 ‐ PC95GEXH 1 5.7049 17.536 ‐40.408 Call: lm(formula = ND10 ~ PC95GEXH, data = type2log) Coefficients: (Intercept) PC95GEXH 1.8451 ‐0.6646 > step(Reg5ND10) Start: AIC=‐49.83 ND10 ~ PC05TEXH + PC95TEXH Df Sum of Sq RSS AIC ‐ PC05TEXH 1 0.05344 13.067 ‐51.647 <none> 13.013 ‐49.832 ‐ PC95TEXH 1 1.09483 14.108 ‐48.196 Step: AIC=‐51.65 ND10 ~ PC95TEXH Df Sum of Sq RSS AIC <none> 13.067 ‐51.647 ‐ PC95TEXH 1 4.4696 17.536 ‐40.408 Call: lm(formula = ND10 ~ PC95TEXH, data = type2log) Coefficients: (Intercept) PC95TEXH 2.2445 ‐0.7424 > MRatelog <‐log10(MRate) > Expdlog <‐log10(Expd) > pca4 <‐ princomp(MRate, cor=FALSE,scores=TRUE) > summary(pca4) Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Standard deviation 240.6712537 21.580593477 4.9164357087 3.3632015124 Proportion of Variance 0.9912823 0.007970319 0.0004136658 0.0001935774 Cumulative Proportion 0.9912823 0.999252652 0.9996663179 0.9998598954 Comp.5 Comp.6 Standard deviation 2.6116759810 1.168652e+00 Proportion of Variance 0.0001167314 2.337328e‐05 Cumulative Proportion 0.9999766267 1.000000e+00 > pca5 <‐ princomp(Expd, cor=FALSE,scores=TRUE) > summary(pca5)
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Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Standard deviation 254.7106243 56.78197841 42.64790519 12.594796486 Proportion of Variance 0.9257744 0.04600787 0.02595413 0.002263567 Cumulative Proportion 0.9257744 0.97178230 0.99773643 1.000000000 > screeplot(pca4,main="Scree plot for PCA MortRate") > screeplot(pca5,main="Scree plot for PCA Expd") > print(loadings(pca4),cutoff=0.00) Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 UFD00 ‐0.635 ‐0.485 0.532 ‐0.161 ‐0.212 0.085 UFD10 ‐0.541 0.675 0.203 0.350 0.274 ‐0.115 ID00 ‐0.390 ‐0.339 ‐0.568 ‐0.053 0.619 0.158 ID10 ‐0.306 0.350 ‐0.378 ‐0.694 ‐0.368 ‐0.154 ND00 ‐0.171 ‐0.259 ‐0.323 0.450 ‐0.329 ‐0.699 ND10 ‐0.170 0.068 ‐0.325 0.406 ‐0.504 0.665 Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 Proportion Var 0.167 0.167 0.167 0.167 0.167 0.167 Cumulative Var 0.167 0.333 0.500 0.667 0.833 1.000 > print(loadings(pca5),cutoff=0.00) Loadings: Comp.1 Comp.2 Comp.3 Comp.4 PC95TEXH ‐0.458 0.457 0.620 0.443 PC05TEXH ‐0.692 ‐0.641 0.166 ‐0.287 PC95GEXH ‐0.305 0.607 ‐0.163 ‐0.715 PC05GEXH ‐0.467 0.104 ‐0.749 0.459 Comp.1 Comp.2 Comp.3 Comp.4 SS loadings 1.00 1.00 1.00 1.00 Proportion Var 0.25 0.25 0.25 0.25 Cumulative Var 0.25 0.50 0.75 1.00 > print(loadings(pca4)) Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 UFD00 ‐0.635 ‐0.485 0.532 ‐0.161 ‐0.212 UFD10 ‐0.541 0.675 0.203 0.350 0.274 ‐0.115 ID00 ‐0.390 ‐0.339 ‐0.568 0.619 0.158 ID10 ‐0.306 0.350 ‐0.378 ‐0.694 ‐0.368 ‐0.154 ND00 ‐0.171 ‐0.259 ‐0.323 0.450 ‐0.329 ‐0.699 ND10 ‐0.170 ‐0.325 0.406 ‐0.504 0.665 Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 Proportion Var 0.167 0.167 0.167 0.167 0.167 0.167 Cumulative Var 0.167 0.333 0.500 0.667 0.833 1.000 > print(loadings(pca5)) Loadings: Comp.1 Comp.2 Comp.3 Comp.4 PC95TEXH ‐0.458 0.457 0.620 0.443 PC05TEXH ‐0.692 ‐0.641 0.166 ‐0.287 PC95GEXH ‐0.305 0.607 ‐0.163 ‐0.715 PC05GEXH ‐0.467 0.104 ‐0.749 0.459 Comp.1 Comp.2 Comp.3 Comp.4 SS loadings 1.00 1.00 1.00 1.00 Proportion Var 0.25 0.25 0.25 0.25 Cumulative Var 0.25 0.50 0.75 1.00 > biplot(pca4,main="Biplot pca MortRate") > biplot(pca5,main="Biplot pca Expd") > vari4<‐varimax(pca4$loadings[,1:2]) > vari5<‐varimax(pca5$loadings[,1:2]) > vscores4<‐pca4$scores[,1:2]%*%vari4$rotmat > vscores4 [,1] [,2] 1 53.316796 64.912832 2 ‐106.580515 ‐55.990154 3 49.083339 49.524650 4 88.101534 90.489376
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5 ‐4.239338 ‐2.435083 6 45.695678 50.980704 7 90.258636 93.675543 8 ‐9.409700 ‐8.452083 9 63.096455 68.202642 10 ‐15.036567 16.786585 11 89.282454 92.992417 12 79.490978 79.240748 13 ‐5.779456 ‐6.747560 14 ‐351.799339 ‐312.518271 15 88.262746 91.794480 16 75.935825 80.359166 17 ‐223.666193 ‐381.648513 18 87.799013 91.832564 19 84.251035 88.932555 20 8.195585 24.997485 21 32.521703 29.872875 22 81.518028 85.410567 23 ‐56.955525 ‐47.045888 24 83.412682 87.081176 25 74.834422 71.158403 26 28.897341 15.030257 27 22.701496 6.013771 28 ‐18.147938 ‐12.828544 29 76.044839 82.385019 30 88.729685 93.049630 31 ‐37.852894 ‐49.059659 32 87.637802 90.527459 33 ‐27.079224 ‐28.741102 34 ‐1002.770754 ‐920.415363 35 48.743973 2.459900 36 90.258636 93.675543 37 47.083716 39.867364 38 90.258636 93.675543 39 43.376478 52.057556 40 9.331468 10.928966 41 87.637802 90.527459 42 64.741107 70.667601 43 ‐63.450987 ‐84.315801 44 ‐58.696739 ‐103.105205 45 20.965282 14.192390 > vscores5<‐pca5$scores[,1:2]%*%vari5$rotmat > vscores5 [,1] [,2] 1 ‐83.610448 116.093367 2 15.748306 ‐4.013455 3 98.216966 ‐66.998114 4 ‐561.051428 264.415911 5 81.557314 ‐76.775757 6 116.467697 ‐91.726375 7 14.919499 ‐4.609611 8 67.946527 ‐71.398202 9 131.770509 ‐88.075596 10 96.143331 ‐77.312612 11 112.407391 ‐62.300983 12 74.519313 ‐16.817326 13 62.695334 ‐36.301423 14 147.838872 ‐107.184373 15 ‐281.058171 61.204423 16 147.881175 ‐92.791330 17 135.545789 ‐101.051462 18 ‐251.289864 290.621319 19 80.171031 ‐59.852772 20 67.327341 ‐55.390535 21 114.417256 ‐87.020544 22 103.433155 ‐21.002997
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23 101.880855 ‐66.216757 24 74.939990 ‐42.931950 25 137.490020 ‐108.032810 26 118.492008 ‐84.384338 27 102.995841 ‐81.143271 28 95.227192 ‐73.320947 29 78.618446 ‐31.030988 30 ‐353.255657 156.994993 31 113.446726 ‐88.913400 32 ‐252.701335 176.220258 33 114.559674 ‐85.085186 34 43.844684 ‐62.864796 35 109.288349 ‐90.400586 36 ‐5.747955 ‐0.235380 37 67.454938 ‐64.933084 38 ‐639.685658 843.277198 39 25.391409 ‐44.755075 40 ‐620.958114 332.761099 41 ‐183.937553 110.883228 42 107.266381 ‐80.795279 43 79.533957 ‐86.111966 44 119.170817 ‐86.789066 45 74.688090 ‐53.903447 plot(vscores4[,1],vscores4[,2],col=type2$Country,asp=1,xlab="1st varimax component",ylab="2nd varimax component",main="Varimax Scores plot(pca Mort Rate)", las=1) text(vscores4[,1]‐0.1,vscores4[,2]‐0.1,type2$Country,cex=0.7) arrows(0,0,vari4$loadings [,1],vari4$loadings[,2],col="green") text(vari4$loadings[,1],vari4$loadings[,2],names(type2),asp=1,cex=0.7 ,col="blue") plot(vscores5[,1],vscores5[,2],col=type2$Country,asp=1,xlab="1st varimax component",ylab="2nd varimax component",main="Varimax Scores plot(pca Expd)", las=1) text(vscores5[,1]‐0.1,vscores5[,2]‐0.1,type2$Country,cex=0.7) arrows(0,0,vari5$loadings [,1],vari5$loadings[,2],col="green") text(vari5$loadings[,1],vari5$loadings[,2],names(type2),asp=1,cex=0.7 ,col="blue") plot(pca4$scores[,1],pca4$scores[,2],col=type2$Country,asp=1,xlab="1st principal component",ylab="2nd principal component",main="Scores plot pca Mort Rate") text(pca4$scores[,1]‐0.1,pca4$scores[,2]‐0.1,type2$Country,cex=0.7) arrows(0,0,pca4$loadings [,1],pca4$loadings[,2],col="red") text(pca4$loadings[,1]‐0.1,pca4$loadings[,2]‐0.1,names(type2),asp=1,cex=0.7 ,col="blue") plot(pca5$scores[,1],pca5$scores[,2],col=type2$Country,asp=1,xlab="1st principal component",ylab="2nd principal component",main="Scores plot pca Expd") text(pca5$scores[,1]‐0.1,pca5$scores[,2]‐0.1,type2$Country,cex=0.7) arrows(0,0,pca5$loadings [,1],pca5$loadings[,2],col="red") text(pca5$loadings[,1]‐0.1,pca5$loadings[,2]‐0.1,names(type2),asp=1,cex=0.7 ,col="blue")