Correlation And Regression With SPSS Essays Examples

In this paper I would like to test the relationship between the education level of respondent and total family income. That’s why I pick two variables – EDUC and INCOME and test the relationship between them.

Consider the scatterplot:

It seems that there is no significant correlation between the variables. However, we check this with appropriate test.

Null hypothesis: There is no correlation between the variables.

Alternative hypothesis: There is a significant correlation between the variables.
H0: ρ=0Ha: ρ≠0

Set level of significance alpha at 5%:

α=0.05

Test the correlation with SPSS:

CORRELATIONS /VARIABLES=INCOME EDUC /PRINT=TWOTAIL NOSIG /MISSING=PAIRWISE.
Since p-value of the test is less than 0.001 and less than level of significance alpha (0.05), we reject null hypothesis. There is enough evidence to say that there is weak (r=0.255) positive linear association between the variables (at 5% level of significance)
Significance test is based on the assumption that the distribution of the residuals (i.e., deviations of observations from the regression line) for the dependent variable y is normal (with constant variance for all values of the independent variable x)

Now perform regression analysis with EDUC as predictor and INCOME as criterion variable. Consider linear regression equation:

y=a+bx

Formulate hypotheses:

H0: b=0Ha: b≠0
Set level of significance alpha at 5%:
α=0.05

Run regression analysis in SPSS:

REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS CI(95) R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT INCOME /METHOD=ENTER EDUC.
The p-values of each coefficient are significant; hence, we reject the null hypothesis and approve the alternative hypothesis at 5% level of significance. And the regression equation is the following expression:
INCOME=8.091+0.204*EDUC
This equation helps to find approximate value of total family income when the highest year of school completed is known. There is also 95% CI calculated. It shows that we are 95% confident that true value of the coefficient of “EDUC” is between 0.163 and 0.246

References:

Argyrous, G.(1948). Statistics for Research: With a Guide to SPSS, SAGE, London, ISBN 14129-7. p. 101-103
Levesque, R.(2007). SPSS Programming and Data Management: A Guide for SPSS and SAS Users, Fourth Edition, SPSS Inc., Chicago Ill. ISBN 1-56827-390-8. p. 64