To test whether there is a linear association between two quantitative variables, which test is used?

To test whether there is a linear association between two quantitative variables, which test is used?

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

Answer: (B)

To test whether there is a linear association between two quantitative variables, you assess whether one variable linearly predicts the other by using a simple linear regression model and testing the slope. The key idea is that a nonzero slope indicates that changes in the first variable are linearly related to changes in the second. The null hypothesis is that the slope is zero (no linear relationship) and the alternative is that the slope is not zero. The test statistic is a t-statistic for the slope, calculated as the estimated slope divided by its standard error, with degrees of freedom n minus 2. A small p-value leads to the conclusion that there is evidence of a linear association. It’s also important to check regression assumptions (linearity, constant variance of residuals, independence, and normality of errors) for the test to be valid. The other options don’t fit because they are designed for different data types or questions: a chi-square test of independence handles qualitative data, a 2-proportion z-test compares proportions between groups, and a paired t-test compares means of paired measurements.

To test whether there is a linear association between two quantitative variables, you assess whether one variable linearly predicts the other by using a simple linear regression model and testing the slope. The key idea is that a nonzero slope indicates that changes in the first variable are linearly related to changes in the second. The null hypothesis is that the slope is zero (no linear relationship) and the alternative is that the slope is not zero. The test statistic is a t-statistic for the slope, calculated as the estimated slope divided by its standard error, with degrees of freedom n minus 2. A small p-value leads to the conclusion that there is evidence of a linear association. It’s also important to check regression assumptions (linearity, constant variance of residuals, independence, and normality of errors) for the test to be valid. The other options don’t fit because they are designed for different data types or questions: a chi-square test of independence handles qualitative data, a 2-proportion z-test compares proportions between groups, and a paired t-test compares means of paired measurements.