statistics spss project

RELATIONSHIP BETWEEN PER

CAPITA EXPENDITURE AND

ECONOMIC AND DEMOGRAPHIC

VARIABLES USING ADVANCED

DATA ANALYSIS

SUBMITTED TO: SUBMITTED BY:

Dr. SHAILAJA REGO RISHABH SETHI (A049)

HARSHIT JAIN (A024)

RELATIONSHIP BETWEEN PER CAPITA EXPENDITURE AND ECONOMIC AND DEMOGRAPHIC VARIABLES USING ADVANCED DATA ANALYSIS

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1. Abstract

The relation between the per capita expenditure and the three economic and demographic

variables is very interesting. If we observe the factors on which the per capita expenditure

depends, it tells us about what should be done to improve these per capita expenditures.

This study is done to find out the relation between the per capita expenditure, the economic

ability index, the percentage of population in the metropolitan areas, and the percentage

change in population.

2. Problem statement

Firstly we will check whether the variables are normal. Then the shape of the distribution

and scenes will be checked. We will see whether the distribution is shaped with a high peak

or low peak. It will then be the descriptive statistics of all the variables that will tell us about

their means and the standard deviations. We would then estimate the regression line in

which we will take per capita expenditure as dependent variable and the economic ability

index, percentage of population in the metropolitan area and the percentage change in

population as the independent variables. This will tell us if there is any relation between the

selected dependent and independent variables.

Last but not the least, we will perform an ANOVA test to check if the population means of

the independent variables are equal or not.

3. Description

State and Local Per capita public expenditures and associated state demographic and

economic characteristics are available for the year 1960; we have 48 cases in this regard.

The characteristics that are given in the data are related to the economic situation of the

people and their demography. We have to see if the per capita expenditure really does

depend on the variables that we have selected.

Number of cases: 40 Variable Names:

1, EX: Per capita state and local public expenditures (S)

2, ECAB: Economic ability index, in which income, retail sales, and the value of output

(manufactures, mineral, and agricultural) per capita are equally weighted.

3, MET: Percentage of population living in standard metropolitan areas

4, GROW: Percent change in population. 1950-1960


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The data is given in the appendix.

4. Analysis of the Data

4.1 Graphical representation

The histogram shows high rise and low peak. In this scene most of the values are

3500. Very few values are below S180 and the average is 5280 (app).


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Now we see that the distribution is negatively skewed and is low peaked. The mean is 92.9.

Most of the value are above 100 or 85 while only a very few observations give values of 55.

65. and 115.

The above figure shows the percentage of population living in the metropolitan areas. In

most cases 50% of population live in the metropolitan areas and only one case gives a figure

of 0%. The distribution is a little negatively skewed and low peaked

Here the distribution is positively skewed and highly peaked. The percentage change in the

population fluctuates from minimum to -the maximum value. The most observations result

in a percentage figure of 15% and only one observation gives a figure of 30%.

4.2 Descriptive statistics:


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The above table is a result of the processes done through SPSS n some data. We

have taken 40 observations in total.

The per capita expenditure curve is exhibiting positive scenes and low peak. In the

above case most of the observations show a value of S300. Very few observations give

a figure of per capita expenditure of S180 and the average comes out to be S280 app.

In the case of the economic ability index, we can judge that the distribution is

negatively skewed and is low peaked. The mean comes out to be 92.9. Most of

the observations give a value of 100 or 85 while only a very, few observations give

values of55, 65, and 115.

While the percentage of population living in the metropolitan areas in most

observations is 50% and only a single observation gives a figure of 0%. The

distribution is slightly negatively skewed and. low peaked.

The distribution for the percentage change in population is positively skewed and highly

peaked. The percentage change in the population fluctuates from minimum to the

maximum value. The most observations result in a percentage figure of 15% and only one

observation gives a figure of 30%.

4.3 Test for equality of the means of three samples (ANOVA):

Assumptions

For testing the suggested hypothesis following assumptions are made.


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Now in this test we have to check if the means of the three independent variables

that are the economic ability index, the percentage of people ling in the

metropolitan areas and the percentage change in population are equal.

From the above results that have been extracted through SPSS„ we can state a few

conclusions. We can see that the p value comes out to be 0,000 that is less than the

pre- assigned level of significance that was 0.05. This fact suggests that there is a

significant difference prevalent in the selected independent variables,


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Now we can clearly see from the above results that are given in the table that there is a

significant difference existent in all the three selected independent variables. In all the cases

in the table is which the comparisons have been done, the p- values are less than the pre-

assigned value of the level of significance that is 0,05.. The lower and upper bounds of the

distribution have also been given.

4.4 Estimating the Multiple Regression Line:

Here we can conclude that none of the independent variables that have been selected is

dropped and that is because the coefficients of all the -variables are significantly different.


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From the above results shown in the table, we can see that none of the variables has been

dropped. The given regression line explains about 50% variation of the dependent variable.

The estimated regression line from the above given model is valid because the p- value is

less than the pre- assigned level of significance that is 0.05.

Here multicolinearity does not exist because there is no case in which the p- value gets

greater than the pre- assigned level of significance. So it is the best model to be selected.

Here is no dropped and it explains the dependent variable a lot. The significant difference


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between the coefficients of the -variables involved in the model makes it the best option.

So from the above model, the multiple regression line that can be fitted comes out to be.

Y (PCE) = 75.485+2.439X1- 0.948X2— 0.886X3

Where Y= Per capita expenditure

X1= economic ability index

X2— %age of population in 'metropolitan areas

X3=%a.ge change in population

We can conclude that -there is a significant difference in the coefficients of the independent

variables that are involved in this case. This fact makes a case where none of them can be

dropped_ when we are to estimate a perfect regression line. The reason is the same that is

the p value comes out to be lower. So there is a case of no correlation between the three

independent variables that have been selected.


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5. Conclusion

From all the analysis that has been done, we can conclude the following things,

The per capita expenditure curve is exhibiting positive scenes and low peak.

In the case of the economic ability index, we can judge that the distribution is

negatively skewed and is low peaked.

The distribution is slightly negatively skewed and low peaked in the case of

population in the metropolitan areas.

The distribution for the percentage change in population is positively skewed and

highly peaked.

The multiple regression line that can be fitted comes out to be.

Y (PCE) = 75.485+2.439X1- 0.948X2— 0.886X3


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Data:

256.00

275.00

327.00

85.50

94.30

87.00

19.70

17.70

.00

6.90

14.70

3.70 297.00 107.50 85.20 11120

256.00 94.901

86.20 1.00

312.00 121.60 77.60 25.40

374.00 111.50 85.50 12.90

257.00 117 9 0

78.90 25.50

257.00 103.10 77.90 7.80

336.00 116.10 68.80 19.90

269.00 93.40 78.20 31.10

213.00 77.20 50.90 21.90

308.00 108 A 0

73.10 21.10

273.00 111.80 69.50 21.80

256.00 110.80 48.10 18.30

287.00 120 9 0

76.90 15.50

290.00 104 3 0

46.30 14.90

217.00 85.10 30.90 -7.40

198.00 76.80 34.10 .30

217.00 75.10 45.80 8.10 195.00 78.70 24.60 12.40

183.00 65.20 32.20 12.90

222.00 73.00 46.00 14.40

283.00 80.90 65.60 77.20

217.00 69.40 45.60 7.00

231.00 57.40 8,60 .50

329.00 95.70 51.30 14.40

294.00 100.20

33.20 5 3 0

232.00 99.10 57.90 9.80

369,00 93.40 10.60 2.90

302.00 88.20 12.70 4.60


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269.00 99.10 37.60 6.80

291.00 102 2 0

37.40 13.70 323.00 86.00 5.00 21.90

282.00 84.90 43.90 6.40

246.00 98.80 63.40 24.10

309.00 86.20 27.60 39.40

309.00 90.20 71.40 7430

334.00 97.60 22.60 13.40

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