For a single restriction (q = 1), the F-statistic
A)is the square root of the t-statistic.
B)has a critical value of 1.96.
C)will be negative.
D)is the square of the t-statistic.

Question

Quizplus · Accepted Answer

When q = 1, the F-statistic is equal to the square of the t-statistic. This is because the F-statistic is calculated as the ratio of the explained variance to the unexplained variance, and when there is only one restriction, the explained variance is equal to the variance explained by the single regression coefficient (which is what the t-statistic tests), while the unexplained variance is the residual variance (which is equal to the total variance minus the explained variance). Therefore, the F-statistic is equal to the square of the t-statistic.

For a Single Restriction (Q = 1), the F-Statistic