What issue arises when two predictor variables are very closely linearly related?

What issue arises when two predictor variables are very closely linearly related?

• A. Homoscedasticity
• B. Autocorrelation
• C. Multicollinearity
• D. Reverse causation

Answer: (C)

When two predictor variables are very closely linearly related, multicollinearity is at play. In regression, you’re trying to estimate how much each predictor uniquely contributes to the outcome. If two predictors carry almost the same information, they become difficult to distinguish in the model. Mathematically, the predictor variables are nearly linearly dependent, which makes the design matrix nearly singular. This instability inflates the standard errors of the coefficient estimates, so the estimated effects can swing a lot with small changes in the data. As a result, you may see one predictor appear non-significant even though the overall model fits well, and the coefficients themselves can be imprecise or counterintuitive. You can spot multicollinearity with diagnostics like a high variance inflation factor or low tolerance values in SPSS. Remedies include dropping one of the highly related predictors, combining them into a single predictor, or using methods designed to handle collinearity, such as ridge regression. Other listed issues aren’t about how predictors relate to each other in the design matrix. Homoscedasticity concerns equal error variance, autocorrelation concerns correlated errors across observations, and reverse causation concerns the direction of the causal relationship.

When two predictor variables are very closely linearly related, multicollinearity is at play. In regression, you’re trying to estimate how much each predictor uniquely contributes to the outcome. If two predictors carry almost the same information, they become difficult to distinguish in the model. Mathematically, the predictor variables are nearly linearly dependent, which makes the design matrix nearly singular. This instability inflates the standard errors of the coefficient estimates, so the estimated effects can swing a lot with small changes in the data. As a result, you may see one predictor appear non-significant even though the overall model fits well, and the coefficients themselves can be imprecise or counterintuitive.

You can spot multicollinearity with diagnostics like a high variance inflation factor or low tolerance values in SPSS. Remedies include dropping one of the highly related predictors, combining them into a single predictor, or using methods designed to handle collinearity, such as ridge regression.

Other listed issues aren’t about how predictors relate to each other in the design matrix. Homoscedasticity concerns equal error variance, autocorrelation concerns correlated errors across observations, and reverse causation concerns the direction of the causal relationship.