When assessing whether there is an association between two quantitative variables, which test provides the p-value for the slope?

When assessing whether there is an association between two quantitative variables, which test provides the p-value for the slope?

• A. Correlation significance test
• B. Two-sample t-test
• C. Linear regression t-test
• D. Paired t-test

Answer: (C)

When you want to know if there's a relationship between two quantitative variables, you assess how Y changes with X by fitting a simple linear regression and testing the slope. The null hypothesis is that the slope is zero, meaning no linear association. The p-value for the slope comes from the regression t-test: you take the estimated slope and divide it by its standard error, forming a t-statistic with n − 2 degrees of freedom. A small p-value indicates that it’s unlikely you’d observe such a slope if there were no real relationship, so you infer an association exists (in a linear form). The sign of the slope shows the direction of the relationship, and the magnitude indicates the change in Y per unit change in X. The correlation significance test, while related, reports a p-value for the correlation coefficient rather than the slope itself. The two-sample t-test and the paired t-test are for comparing means across groups, not for examining how two quantitative variables relate to each other.

When you want to know if there's a relationship between two quantitative variables, you assess how Y changes with X by fitting a simple linear regression and testing the slope. The null hypothesis is that the slope is zero, meaning no linear association. The p-value for the slope comes from the regression t-test: you take the estimated slope and divide it by its standard error, forming a t-statistic with n − 2 degrees of freedom. A small p-value indicates that it’s unlikely you’d observe such a slope if there were no real relationship, so you infer an association exists (in a linear form). The sign of the slope shows the direction of the relationship, and the magnitude indicates the change in Y per unit change in X.

The correlation significance test, while related, reports a p-value for the correlation coefficient rather than the slope itself. The two-sample t-test and the paired t-test are for comparing means across groups, not for examining how two quantitative variables relate to each other.