A higher value of R in regression indicates what about the fit between observed and predicted values?

A higher value of R in regression indicates what about the fit between observed and predicted values?

• A. A better fit with smaller residuals
• B. A worse fit with larger residuals
• C. More heteroscedasticity
• D. More multicollinearity

Answer: (A)

R captures how closely the predicted values track the actual observations along a linear trend. A higher R means predictions align more tightly with what was observed, so the residuals (the differences between observed and predicted) tend to be smaller, signaling a better fit. The other ideas—heteroscedasticity (changing spread of residuals) and multicollinearity (interdependencies among predictors)—describe different issues in regression and don’t directly indicate how well the observed values match the predictions. So, a higher R points to a better fit with smaller residuals.

R captures how closely the predicted values track the actual observations along a linear trend. A higher R means predictions align more tightly with what was observed, so the residuals (the differences between observed and predicted) tend to be smaller, signaling a better fit. The other ideas—heteroscedasticity (changing spread of residuals) and multicollinearity (interdependencies among predictors)—describe different issues in regression and don’t directly indicate how well the observed values match the predictions. So, a higher R points to a better fit with smaller residuals.