Question

When reviewing the regression analysis output the statistics that must be evaluated the equation to describe the statistical relationship between one or more predictor variables and the response variable. The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (<0.05) indicates that you can reject the null hypothesis. An analyst that has a low p-value is likely to be a meaningful addition to your model because changes in the analyst’s value is related to changes in the response variable. A larger p-value suggests that changes in the analysis are not associated with changes in the response

PLEASE REPLY TO QUESTION: Now, is it possible that a predictor is important, but the p-value is greater than .05, when you dump all the variables in the regression model?

Answer 1

The p-value of a predictor can increase if we remove some other explanatory variables from the model. This is especially true when we have confounding variables. The inclusion of a confounding variable might improve the prediction capability of an existing predictor variable, which manifests in the improved p-value of an existing predictor. On the other hand, excluding the confounding variable can increase the p-value, though the original predictor is indeed important.

As an example, while studying indigestion in kids against Vitamin A supplement intake, the 2 variables are found to be positively correlated (kids who intake Vitamin A supplements are in general expected to be those who suffer with indigestion). While Vitamin A intake decreases indigestion, lack of fiber intake increases indigestion. If we now include the fiber intake into the model, the relationship between indigestion and Vitamin A intake will appear stronger. Hence, adding the new predictor actually increases the predictability or p-value of the original predictor, and removing it decrease the same, though the original predictor is indeed important.