The regression residuals are computed as

Question

Quizplus · Accepted Answer

The regression residuals are given by the differences between the actual dependent variable values and the predicted values from the regression equation. Hence, the residuals are computed as Y - Y_predicted, where Y is the actual dependent variable value and Y_predicted is the value predicted by the regression equation. In the case of simple linear regression with one predictor variable, the regression equation is Y_predicted = b0 + b1*X. Therefore, the residuals can be computed as Y - (b0 + b1*X), which gives the expression Y*b1 - X*b1^2 - b0. This expression can be written as b1*(Y - X*b1 - b0), which is equivalent to b1*(Y_predicted - Y). Thus, the best choice for computing the regression residuals is the one that involves Y_predicted, Y, b0, and b1. Option C is the only one that satisfies this requirement, as it has Y*b1 - X*b1^2 - b0 in the numerator and b1*(Y_predicted - Y) in the denominator.

The Regression Residuals Are Computed as