To measure a linear relationship between two quantitative variables, which test is most appropriate?

To measure a linear relationship between two quantitative variables, which test is most appropriate?

• A. Chi-square test of independence
• B. 2-proportion z-test
• C. 2-sample t-test
• D. Linear regression t-test

Answer: (D)

When you want to know if two quantitative variables have a linear relationship, you fit a simple linear regression model and test whether the slope is different from zero. The t-test on the slope coefficient checks if there is a statistically significant linear association: if the slope is not zero, changes in the predictor are associated with changes in the response in a linear way. The other tests don’t fit this goal. A chi-square test of independence is for two categorical variables. A 2-proportion z-test compares proportions between groups. A 2-sample t-test compares means between two groups. Each of these addresses different questions than whether a linear relationship exists between two continuous variables.

When you want to know if two quantitative variables have a linear relationship, you fit a simple linear regression model and test whether the slope is different from zero. The t-test on the slope coefficient checks if there is a statistically significant linear association: if the slope is not zero, changes in the predictor are associated with changes in the response in a linear way.

The other tests don’t fit this goal. A chi-square test of independence is for two categorical variables. A 2-proportion z-test compares proportions between groups. A 2-sample t-test compares means between two groups. Each of these addresses different questions than whether a linear relationship exists between two continuous variables.