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    Question

    In a multiple linear regression model, the presence of

    perfect multicollinearity among the explanatory variables will primarily result in which of the following issues?
    A The OLS estimates will be biased and inconsistent. Correct Answer Incorrect Answer
    B The OLS estimates will be inefficient (not BLUE). Correct Answer Incorrect Answer
    C The OLS estimates will be undefined, making estimation impossible. Correct Answer Incorrect Answer
    D The residual variance will be non-constant (heteroskedasticity). Correct Answer Incorrect Answer

    Solution

    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., X2=2X1+5). · Mathematical Result: OLS requires calculating (X′X)−1, the inverse of the matrix of sums of squares and cross-products of the regressors. Perfect multicollinearity makes the X′X matrix singular (its determinant is zero), meaning its inverse (X′X)−1 does not exist. Without this inverse, the OLS estimators (β^=(X′X)−1X′y) cannot be computed or are undefined.

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