Question

1. 4.4 Given a 95% confidence interval for β4 is (−0.12, 0.05) in a multiple regression analysis, which of the following is true?

   (A) There is enough evidence to conclude x4 is useful in predicting y.
   (B) The value of b4 equals −0.035.
   (C) There is enough evidence to conclude that x4 and y are positively associated. (D) There is enough evidence to conclude that x4 and y are negatively associated. (E) None of the x variables are useful in predicting y.

Answer 1

Answer:

(B) The value of b4 equals −0.035

Explanation:

(A) incorrect.

because the 95% confidence interval includes the 0 which means the variable x4 is not useful in predicting y. (such that the null hypothesis, slope coefficient, = 0 is not rejecting hence there is no contribution of variable x4 in predicting y)

(B) Correct.

Solving for

(C) Incorrect,

Since the 95% confidence interval includes the 0, there is not enough evidence to conclude that x4 and y are associated

(D) Incorrect,

Since the 95% confidence interval includes the 0, there is not enough evidence to conclude that x4 and y are associated

(E) Incorrect,

Since the 95% CI for the other variables are not given, we can not conclude about other variables.