Question 11.43

11.43 Significance test for a regression coefficient.

For each of the settings in the previous exercise, test the null hypothesis that the coefficient of $x_{1}$ is zero versus the two-sided alternative.

11.43

$t = 10.3 / 5 = 2.06$ for all cases. (a) $d f = 25, P -value = 0.05$ ; technically, this is significant. (b) $d f = 50, 0.04 < P -value < 0.05$ ; this is significant. (c) $d f = 24, 0.05 < P -value < 0.10$ ; this is not significant. (d) $d f = 49$ use $40, 0.04 < P -value < 0.05$ ; this is significant.