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Say your supervisor performs a regression and later find that one of your independent variables (X1)...

Say your supervisor performs a regression and later find that one of your independent variables (X1) is correlated with another variable that you did not include the regression (X2), and this other variable might better explain the variance in the dependent variable (Y). Explain what is likely to happen if your supervisor conducts another regression with both of these independent variables included in the model.

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Answer #1

when independent variables have correlation between them, then this situation cuases a lot of issues in the regression analysis. This is the case of multicollinearity.

In this case, x1 and x2 are correlated with each other and this correlation between independent variables x1 and x2 will result in reduced precision of the estimated regression coefficients.

This can also lead to incorrect or different conclusion in hypothesis testing as compared to the earlier regression analysis.

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