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Explain why the following statement is not correct: All explanatory variables that are significantly correlated with...

Explain why the following statement is not correct:

All explanatory variables that are significantly correlated with the response variable will have a statistically significant correlation coefficient in multiple regression

Math   Statistics-And-Probability   
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Answer #1

If all the explanatory variables are significantly correlated with the response variable or the dependent variable, there might be a case incase of multiple regression that if all the explanatory variables are taken in the multiple regression model, the effect of the explanatory variables might be less because of the multicollinearity present between the variables. Suppose if X1 was significantly correlated with the response variable and now X2 is also taken in the regression, one needs to see what new variation in Y is explained by X2. The estimated effect of X1 on Y might decrease because of the correlation between X1 and X2.

Hence, the given statement is not correct.

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