In simple linear regression, the test statistic t is:
A) the square root of the corresponding F statistic.
B) twice the value of the corresponding F statistic.
C) the absolute value of the corresponding F statistic.
D) unrelated to any other statistic.

Question

Quizplus · Accepted Answer

In simple linear regression, the test statistic t is calculated as the ratio of the estimated coefficient and its standard error. When we perform an F-test for simple linear regression, the F statistic is calculated as the ratio of the explained variance and the residual variance. It can be shown that the square of the t statistic for the estimated coefficient is equal to the F statistic for the overall regression model. Therefore, the square root of the F statistic is equal to the t statistic for the estimated coefficient, which is the answer choice A.

In Simple Linear Regression, the Test Statistic T Is