In multiple linear regression, what does multicollinearity imply?

In multiple linear regression, what does multicollinearity imply?

• A. Independent variables are independent of the dependent variable.
• B. Independent variables are not highly correlated.
• C. Dependent variable is not correlated with residuals.
• D. Errors are heteroscedastic.

Answer: (B)

Multicollinearity occurs when two or more predictors in a regression are highly correlated with each other. This redundancy makes it hard to separate each predictor’s unique contribution to the outcome, so the estimated coefficients become unstable and their standard errors inflate. As a result, some predictors may appear non-significant or have coefficients that flip sign with small changes in the data, even though the overall model fit may be reasonable. It does not describe the relationship between predictors and the dependent variable being weak, nor does it involve the residuals being correlated with the outcome or heteroscedasticity. When detected (for example, via high VIF values), solutions include removing one of the correlated predictors, combining them into a single measure, or using regularization techniques that can handle correlated predictors.

Multicollinearity occurs when two or more predictors in a regression are highly correlated with each other. This redundancy makes it hard to separate each predictor’s unique contribution to the outcome, so the estimated coefficients become unstable and their standard errors inflate. As a result, some predictors may appear non-significant or have coefficients that flip sign with small changes in the data, even though the overall model fit may be reasonable. It does not describe the relationship between predictors and the dependent variable being weak, nor does it involve the residuals being correlated with the outcome or heteroscedasticity. When detected (for example, via high VIF values), solutions include removing one of the correlated predictors, combining them into a single measure, or using regularization techniques that can handle correlated predictors.