Correlation and Regression with SPSS

Statistical assumptions for the study

The difference is zero

The data is normally distributed

The variance of the two variables are equal (homoscedasticity)

The study wishes to analyze the correlation that exists between education and affirmative action. During the study, t-test will be used for hypothesis testing. The independent variable is education while affirmative action is the dependent variable. During the study regression analysis will also be used. The regression line takes the following form:

Y= Bo + BX + e……whereY is the dependent variable (affirmative action), Bo is the constant, X is the independent variable (education) and finally e is the error term.

Hypothesis Statement

Ho: there is no relationship between education and affirmative action.

Ha: there is relationship between grade in elementary and high school and affirmative action.

In hypothesis testing we shall use the SPSS results found in Anova tables. The level of significance is 0.05. The p-value is 0.127 with 29 degrees of freedom.

The p-value (0.127)>0.05. Therefore we reject the null hypothesis but accept the alternative hypothesis. Therefore we conclude that there is a relationship between grade in elementary and high school and affirmative action.

Results

Regression

Y= -20.600 +0.67X + e

Interpretation of the regression at 95% confidence level

(-20.600) is the constant of the regression line. The coefficient of the independent variable (education) is given by 0.67. This means that; holding other factors constant, an increase in the level of education by one unit will raise the level of affirmative action by 0.67.

Correlation coefficients

Using Pearson correlation from the SPSS output, the coefficient between highest grade in elementary or high school and affirmative action is 0.67. This is a strong positive correlation; meaning that they both move in the same direction. Increasing grade in elementary and high school will result to a positive increase in affirmative action.