Perfect collinearity exists when which of the following is true?

Perfect collinearity exists when which of the following is true?

• A. Exists when a predictor is completely independent of others.
• B. Exists when at least one predictor in a regression model is a perfect linear combination of the others.
• C. Occurs when there is no multicollinearity.
• D. Is the same as homoscedasticity.

Answer: (B)

Perfect collinearity occurs when one predictor is an exact linear combination of the others, so you can predict that predictor perfectly from the remaining variables. This makes the design matrix singular and prevents unique estimation of the regression coefficients because there isn’t enough independent information to separate the effects of the predictors. This is precisely the situation described. The idea that a predictor is independent of the others describes no multicollinearity, which is opposite. Saying there is no multicollinearity contradicts the presence of perfect collinearity. Homoscedasticity, the constant-variance assumption for residuals, is unrelated to whether predictors are linearly dependent.

Perfect collinearity occurs when one predictor is an exact linear combination of the others, so you can predict that predictor perfectly from the remaining variables. This makes the design matrix singular and prevents unique estimation of the regression coefficients because there isn’t enough independent information to separate the effects of the predictors. This is precisely the situation described. The idea that a predictor is independent of the others describes no multicollinearity, which is opposite. Saying there is no multicollinearity contradicts the presence of perfect collinearity. Homoscedasticity, the constant-variance assumption for residuals, is unrelated to whether predictors are linearly dependent.