Which of the following statements is true?
A)If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis.
B)The F statistic is always nonnegative as SSRr is never smaller than SSRur.
C)Degrees of freedom of a restricted model is always less than the degrees of freedom of an unrestricted model.
D)The F statistic is more flexible than the t statistic to test a hypothesis with a single restriction.

Question

Quizplus · Accepted Answer

The F statistic is calculated as the ratio of explained variance and unexplained variance. Since explained variance (SSRr) is never smaller than unexplained variance (SSRur), the F statistic is always nonnegative. Option A is incorrect because if the calculated value of F statistic is higher than the critical value, we reject the null hypothesis in favor of the alternative hypothesis. Option C is incorrect as the degrees of freedom of a restricted model are always less than or equal to the degrees of freedom of an unrestricted model. Option D is incorrect as the F statistic and t statistic are both used to test hypotheses with restrictions, and neither is more flexible than the other.

Which of the Following Statements Is True