The logic behind the t-test for the individual significance of the estimated slope coefficient $\hat { \beta } _ { 1 }$
Is that if the estimated slope coefficient is likely to be different from 0,then
A)the estimated slope coefficient should be large.
B)the estimated standard error should be large.
C)the ratio of the estimated slope coefficient to the standard error of the estimated slope coefficient should be small.
D)the ratio of the estimated slope coefficient to the standard error of the estimated slope coefficient should be large.

Question

Quizplus · Accepted Answer

The t-test for the individual significance of the estimated slope coefficient is based on the idea that if the estimated slope coefficient is likely to be different from 0, then the ratio of the estimated slope coefficient to the standard error of the estimated slope coefficient (i.e., the t-statistic) should be large. This is because a large t-statistic indicates that the estimated slope coefficient is large relative to its estimated standard error, which suggests that the true population slope coefficient is likely to be significantly different from 0. Therefore, choice D is the best option.

The Logic Behind the T-Test for the Individual Significance of the Estimated