In regression, what does orthogonal refer to?

In regression, what does orthogonal refer to?

• A. Variables are perfectly correlated
• B. One variable causes the other
• C. Two predictor variables are perpendicular and uncorrelated
• D. The residuals are heteroscedastic

Answer: (C)

Orthogonal means perpendicular, and in regression this refers to the relationship between two predictor variables. When predictors are orthogonal, they are uncorrelated with each other (their correlation is zero). This makes their effects on the outcome independent in the sense that one predictor’s contribution is not confounded by the other, and the least-squares estimates decouple, which simplifies interpretation and calculation. This does not say anything about causation, so it isn’t saying that one variable causes the other. And it isn’t about residuals being heteroscedastic; heteroscedasticity concerns the spread of residuals, not the relationship between predictors. It also isn’t about variables being perfectly correlated; in fact, perfect correlation would mean a strong dependence, not orthogonality.

Orthogonal means perpendicular, and in regression this refers to the relationship between two predictor variables. When predictors are orthogonal, they are uncorrelated with each other (their correlation is zero). This makes their effects on the outcome independent in the sense that one predictor’s contribution is not confounded by the other, and the least-squares estimates decouple, which simplifies interpretation and calculation.

This does not say anything about causation, so it isn’t saying that one variable causes the other. And it isn’t about residuals being heteroscedastic; heteroscedasticity concerns the spread of residuals, not the relationship between predictors. It also isn’t about variables being perfectly correlated; in fact, perfect correlation would mean a strong dependence, not orthogonality.