Question

Interpret the tables below: R, R square

interpret the regression coefficients, either b or beta.

  

Model Summaryb
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Durbin-Watson
1	.625a	.390	.390	17.5048	1.978
a. Predictors: (Constant), HIGHEST YEAR OF SCHOOL COMPLETED, FAMILY INCOME IN CONSTANT DOLLARS
b. Dependent Variable: R's socioeconomic index (2010)

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.	Collinearity Statistics
		B	Std. Error	Beta			Tolerance	VIF
1	(Constant)	-9.124	1.774		-5.142	.000
	FAMILY INCOME IN CONSTANT DOLLARS	.000	.000	.252	13.859	.000	.829	1.207
	HIGHEST YEAR OF SCHOOL COMPLETED	3.550	.136	.476	26.168	.000	.829	1.207
a. Dependent Variable: R's socioeconomic index (2010)

Answer 1

1) Interpretation of R^2-----

Since, R^2 tells how much variation in dependent variable is explained by Regressors.

it is also known as to check the goodness of fit of the model

here, R^2 = 0.39 which is much less than 1

so the given model is a poor fit of the data.

2) Interpretation of regression coefficients -----

a) intercept term---

estimate = -9.124

and t value is -5.142 i.e is not significant

in this is we accept the null hypothesis i.e there is not sufficient evidence that intercept term is present in the model

b) for b coefficient

For both cases HIGHEST YEAR OF SCHOOL COMPLETED, FAMILY INCOME IN CONSTANT DOLLARS

the value of test statistic t is high.

since, for HIGHEST YEAR OF SCHOOL COMPLETED t value = 26.168

and for   FAMILY INCOME IN CONSTANT DOLLARS t value = 13.859

which is evidence of significance of both parameter.

Thus decision is - There is sufficient evidence in favor of alternative hypothesis