A random sample of 600 high school seniors reports their GPA and the amount of financial aid offered by colleges. Which test assesses whether there is an association between GPA and college aid?

A random sample of 600 high school seniors reports their GPA and the amount of financial aid offered by colleges. Which test assesses whether there is an association between GPA and college aid?

• A. ANOVA
• B. Chi-square test
• C. Correlation coefficient test
• D. Linear Regression t-test with 598 degrees of freedom

Answer: (D)

Testing whether there is a linear relationship between two continuous variables is explored by looking at the slope in a simple linear regression. If GPA is used to predict financial aid, a significant nonzero slope shows that changes in GPA are associated with changes in aid. The t-test for the slope is the formal way to assess this, and the degrees of freedom for that test are n − 2 because you estimate one slope parameter and one intercept. With 600 students, that gives 598 degrees of freedom. This approach directly answers whether a linear association exists and quantifies the relationship as slope, while also providing a p-value to indicate statistical significance. ANOVA and chi-square aren’t appropriate for two continuous variables, and while a correlation test can assess association, the regression slope t-test is the standard formal test for a linear relationship with a clear df calculation.

Testing whether there is a linear relationship between two continuous variables is explored by looking at the slope in a simple linear regression. If GPA is used to predict financial aid, a significant nonzero slope shows that changes in GPA are associated with changes in aid. The t-test for the slope is the formal way to assess this, and the degrees of freedom for that test are n − 2 because you estimate one slope parameter and one intercept. With 600 students, that gives 598 degrees of freedom. This approach directly answers whether a linear association exists and quantifies the relationship as slope, while also providing a p-value to indicate statistical significance. ANOVA and chi-square aren’t appropriate for two continuous variables, and while a correlation test can assess association, the regression slope t-test is the standard formal test for a linear relationship with a clear df calculation.