Suppose that in a multiple regression the F test statistic is significant, but none of the t test statistics are significant. This means that ________. a. multicollinearity may be present b. autocorrelation may be present c. collinearity may be present d. (a) and (c).
Question
Suppose that in a multiple regression the F test statistic is significant, but none of the t test statistics are significant. This means that ________.
a. multicollinearity may be present
b. autocorrelation may be present
c. collinearity may be present
d. (a) and (c).
Solution
The correct answer is d. (a) and (c).
This situation suggests that multicollinearity or collinearity may be present. Multicollinearity and collinearity refer to a situation in which two or more predictor variables in a multiple regression model are highly correlated, meaning that one can be linearly predicted from the others with a substantial degree of accuracy.
When the F test is significant, it means that at least one of the predictor variables is significantly related to the response variable. However, if none of the t-tests are significant, it suggests that no single predictor variable is significantly contributing to the prediction of the response variable when the effects of all other variables are accounted for. This is a common symptom of multicollinearity or collinearity.
Therefore, the correct answer is d. (a) and (c).
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