In a regression predicting electrical usage from average monthly temperature, which test assesses whether the temperature coefficient is different from zero?

In a regression predicting electrical usage from average monthly temperature, which test assesses whether the temperature coefficient is different from zero?

• A. Linear regression t-test with 10 degrees of freedom
• B. Chi-square test of independence
• C. ANOVA
• D. Paired t-test

Answer: (A)

Testing whether the temperature coefficient is different from zero focuses on the slope of the regression line. In linear regression, you assess H0: beta = 0 for that coefficient with a t-test using the estimated standard error of the slope. If the t-statistic is large in magnitude (or the p-value is small), you conclude that temperature has a significant effect on electrical usage. In simple regression, this t-test for the slope is directly related to the overall F-test for the model, but it specifically answers whether the temperature term matters, not just whether the model fits better in general. The other tests aren’t about the coefficient: a chi-square test of independence handles relationships between categorical variables, ANOVA assesses differences across group means or the overall model variance, and a paired t-test compares two related samples. Therefore, the regression coefficient’s t-test is the appropriate method to determine if the temperature effect differs from zero.

Testing whether the temperature coefficient is different from zero focuses on the slope of the regression line. In linear regression, you assess H0: beta = 0 for that coefficient with a t-test using the estimated standard error of the slope. If the t-statistic is large in magnitude (or the p-value is small), you conclude that temperature has a significant effect on electrical usage. In simple regression, this t-test for the slope is directly related to the overall F-test for the model, but it specifically answers whether the temperature term matters, not just whether the model fits better in general. The other tests aren’t about the coefficient: a chi-square test of independence handles relationships between categorical variables, ANOVA assesses differences across group means or the overall model variance, and a paired t-test compares two related samples. Therefore, the regression coefficient’s t-test is the appropriate method to determine if the temperature effect differs from zero.