In: Statistics and Probability
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:
(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.