topic17 regression spss

Poverty Estimation, Inequality, Correlation & Regression & Trend Growth Rate:

SPSS/STATA

Srinivasulu RajendranCentre for the Study of Regional Development (CSRD)

Jawaharlal Nehru University (JNU)New Delhi

Indiar.srinivasulu@gmail.com

Objective of the session

To understand How HHsize influences the monthly per

capita total expenditure of the households based

OLS

1. What is the procedure to perform Regression?2. How do we interpret results?4. What are procedure available for estimating poverty line and Poverty rate and how to do with Econometric software

Identify the relationship between variables that we want to perform Scatter plot for outliers and type of relationship

Monthly HH food Expenditure and HHSIZE

Linear Regression Analysis using SPSS

ObjectivesRegression analysis is the next step up after

correlation; it is used when we want to predict the value of a variable based on the value of another variable. In this case, the variable we are using to predict the other variable's value is called the independent variable or sometimes the predictor variable. The variable we are wishing to predict is called the dependent variable or sometimes the outcome variable.

Assumption

Variables are approximately normally distributed (see Testing for Normality guide).

There is a linear relationship between the two variables.

There are classical assumption ……..

Step 1

Procedure1.Click Analyze > Regression > Linear... on the top menu.

You will be presented with the following dialog box:

Step 2

Transfer the independent (predictor) variable, hhsize, into the "Independent(s):" box and the dependent (outcome) variable, mfx, into the "Dependent:" box. You can do this by either drag-and-dropping or by using the buttons.

Click the button.

Dependent Variable

Independent Vari

Step 2

Extra options

Click “Statistics” and it provides Regression coefficients, depends on your analysis you may select your relevant test

Finally click “Continue”

Plot - Options

Click “Plot” and it provides option to plot histogram, normal probability, etc, depends on your analysis you may select your relevant plot

Finally click “Continue”

Click “OK” to get results in the output viewer

Output of Linear Regression Analysis

SPSS will generate quite a few tables in its results section for a linear regression.

In this session, we are going to look at the important tables Model Summary table.

This table provides the R and R2 value. The R value is 0.608, which represents the simple correlation and, therefore, indicates a high degree of correlation. The R2 value indicates how much of the dependent variable, monthly HH food exp, can be explained by the independent variable, hhsize. In this case, 37.0% can be explained.

Model Summary

Model R R SquareAdjusted R

SquareStd. Error of the Estimate

1 .608a .370 .370 2157.08

The next table is the ANOVA table.

This table indicates that the regression model predicts the outcome variable significantly well. How do we know this? Look at the "Regression" row and go to the Sig. column.

This indicates the statistical significance of the regression model that was applied. Here, P < 0.0005 which is less than 0.05 and indicates that, overall, the model applied is significantly good enough in predicting the outcome variable.

ANOVAb

Model Sum of Squares dfMean

Square F Sig.1 Regressio

n3378640742.5 1.0 3378640742

.5726.116 .000a

Residual 5746495913.9 1235.0

4653033.1

Total 9125136656.4 1236.0

The table below, Coefficients, provides us with information on each predictor variable.

This provides us with the information necessary to predict monthly food exp from hhsize. We can see that both the constant and hhsize contribute significantly to the model (by looking at the Sig. column). By looking at the B column under the Unstandardized Coefficients column we can present the regression equation as

mfx = 669.3+ 861.7(hhsize)Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig.B Std. Error Beta1 (Constant) 669.294 151.807

 4.409 .000

Household size 861.655 31.976 .608 26.947 .000

Interpretation If HHSIZE goes up by a member or individual, the

average monthly HH food expenditure (mfx) goes up by about 862 taka. The intercept value of about 669 taka tells us that if hhsize were zero, mfx would be about 669 taka. The r 2 value of 0.37 means approximately 37 percent

of the variation in the mfx is explained by variationin the hhsize.

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig.B Std. Error Beta1 (Constant) 669.294 151.807

 4.409 .000

Household size 861.655 31.976 .608 26.947 .000