In regression, the coefficients are chosen to:

• A. Best account for the variance in the criterion variable
• B. Maximize residual variance
• C. Minimize the number of predictors
• D. Increase multicollinearity

Answer: (A)

In regression, the aim is to explain as much of the outcome’s variability as possible using the predictors. The coefficients are chosen by ordinary least squares to minimize the sum of squared differences between observed values and those predicted by the model. By reducing these residuals, the model captures more of the variance in the criterion variable, effectively maximizing the explained variance (often summarized by R-squared). So the coefficients are selected to best account for the variance in the outcome.

Residual variance isn’t increased—it's minimized. Choosing fewer predictors isn’t about how the coefficients are estimated, but about model complexity, not the estimation objective. Increasing multicollinearity would make coefficient estimates unstable and is not a goal of the estimation process.