Question

For each of the following indicate the expected effect (e.g. increase, decrease, remain unchanged, etc.) in the presence of significant multicollinearity:

Coefficient estimates:

Standard errors of the estimated coefficients:

t-statistics:

R-squared:

Name two possible solutions if you detect multicollinearity in a regression.

Answer 1

Multicollinearity will weaken the precision of the coefficient estimates.When multicollinearity is present coefficients will become very sensitive to the small changes in the model.Due to multicollinearity the standard error of the estimated coefficients will get inflated or increased.When the multicollinearity occurs the larger will be the standard error and it will make the independent variables more insignificant.In the presence of multicolinearity t static will be generally small and becomes more insignificant and makes the rejection of null hypothesis more difficult and R squared will remain unchanged in the presence of multicollinearity because multicolinearity does not affect how well the model will fit or multicolinearity does not affect goodness of fit statistics.

Multicolinearity happens when the independent variables are correlated.When there is multicollinearity the it will difficult to estimate the relationship between the independent variables and dependent variables.The two possible solutions to reduce multicolinearity is to remove the highly correlated independent variables,linearly combine the independent variables by adding them together and perform principal component analysis or partial least square regression for the highly correlated variables.