Collinearity refers to what problem in regression analysis?

Collinearity refers to what problem in regression analysis?

• A. Correlation among the independent variables with each other, which can bias coefficient estimates
• B. Correlation between the dependent variable and the residuals
• C. Lack of linearity
• D. Homoscedasticity

Answer: (A)

Collinearity happens when two or more predictor variables are correlated with each other. This creates redundancy in the information the model uses to explain the outcome, making it hard to tease apart each predictor’s individual effect. Because the predictors share variance, the estimated coefficients can become highly unstable and their standard errors inflate, so the conclusions about which predictor matters most become less reliable. In extreme cases of perfect collinearity, you can’t estimate unique coefficients at all. The other issues listed are different problems. A correlation between the dependent variable and the residuals points to model misspecification or endogeneity rather than predictor redundancy. A lack of linearity means the relationship isn’t well captured by a straight-line (or linear) form. Homoscedasticity refers to the residuals having constant variance across levels of the predictor.

Collinearity happens when two or more predictor variables are correlated with each other. This creates redundancy in the information the model uses to explain the outcome, making it hard to tease apart each predictor’s individual effect. Because the predictors share variance, the estimated coefficients can become highly unstable and their standard errors inflate, so the conclusions about which predictor matters most become less reliable. In extreme cases of perfect collinearity, you can’t estimate unique coefficients at all.

The other issues listed are different problems. A correlation between the dependent variable and the residuals points to model misspecification or endogeneity rather than predictor redundancy. A lack of linearity means the relationship isn’t well captured by a straight-line (or linear) form. Homoscedasticity refers to the residuals having constant variance across levels of the predictor.