Question

Indictator(s) that multicollinearity might be a problem are:

• A. The regression has statistically significant t statistics on the slope coefficients and the F statistic is not significant.

• B. The R-squared value is low in a regression of one Xj on the other regressors.

• C. The coefficients on the independent variables have the wrong signs.

• D. None of these issue indicate a potential problem with multicollinearity.

Answer 1

Multicollinearity can affect any regression model with more than one predictor. It occurs when two or more predictor variables overlap so much in what they measure that their effects are indistinguishable.

Here are some common indicators of multicollinearity-

1. Very high standard errors for regression coefficients
When standard errors are orders of magnitude higher than their coefficients, that’s an indicator.

2. The overall model is significant, but none of the coefficients are
Remember that a p-value for a coefficient tests whether the unique effect of that predictor on Y is zero. If all predictors overlap in what they measure, there is little unique effect, even if the predictors as a group have an effect on Y.

3. Large changes in coefficients when adding predictors
If the predictors are completely independent of each other, their coefficients won’t change at all when you add or remove one. But the more they overlap, the more drastically their coefficients will change.

4. Coefficients have signs opposite what you’d expect from theory
Be careful here as you don’t want to disregard an unexpected finding as problematic. Not all effects opposite theory indicate a problem with the model. That said, it could be multicollinearity and warrants taking a second look at other indicators.

5. Coefficients on different samples are wildly different
If you have a large enough sample, split the sample in half and run the model separately on each half. Wildly different coefficients in the two models could be a sign of multicollinearity.

6. High Variance Inflation Factor (VIF) and Low Tolerance
These two useful statistics are reciprocals of each other. So either a high VIF or a low tolerance is indicative of multicollinearity. VIF is a direct measure of how much the variance of the coefficient (ie. its standard error) is being inflated due to multicollinearity.

according to above theories option c is correct since The coefficients on the independent variables have the wrong signs according to the indicator point 4 . i.e Coefficients have signs opposite what you’d expect from theory.