Question

In a multiple linear regression model, the presence of

Q: Answer-In a multiple linear regression model, the presence of perfect multicollinearity among the explanato...

Solution Multicollinearity refers to a high linear correlation among two or more independent variables. Perfect Multicollinearity means one explanatory variable is an exact linear function of one or more others e.g., X22X15. Mathematical Result OLS requires calculating XX1, the inverse of the matrix of sums of squares and cross-products of the regressors. Perfect multicollinearity makes the XX matrix singular its determinant is zero, meaning its inverse XX1 does not exist. Without this inverse, the OLS estimators XX1Xy cannot be computed or are undefined.

perfect multicollinearity among the explanatory variables will primarily result in which of the following issues?

A The OLS estimates will be biased and inconsistent.

B The OLS estimates will be inefficient (not BLUE).

C The OLS estimates will be undefined, making estimation impossible.

D The residual variance will be non-constant (heteroskedasticity).

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