In simple linear regression,if the error variable is normally distributed,the test statistic for testing is t-distributed with n - 2 degrees of freedom.

Question

In simple linear regression,if the error variable  is normally distributed,the test statistic for testing  is t-distributed with n - 2 degrees of freedom.

Quizplus · Accepted Answer

This statement is true. The test statistic for testing the significance of the regression coefficient in simple linear regression is calculated as t = (b1 - 0) / SE(b1), where b1 is the estimated regression coefficient, 0 is the null hypothesis value (usually 0), and SE(b1) is the standard error of the regression coefficient. If the error variable is normally distributed, the distribution of the test statistic will be t-distributed with n - 2 degrees of freedom, where n is the number of observations. This follows from the fact that the estimated regression coefficient has a sampling distribution that is normal with mean equal to the true regression coefficient and standard error equal to the standard error of the regression divided by the square root of the sample size. The t distribution is used to account for the fact that the standard error estimate is based on the sample, rather than the population.

In Simple Linear Regression,if the Error Variable Is Normally