The standard error of the estimate for a multiple regression model with two explanatory variables X₁ and X₂: A)measures the variation around the predicted regression equation. B)measures the proportion of variation in Y that is explained by X₁ and X₂_. C)measures the proportion of variation in Y that is explained by X₁ holding X₂ constant. D)has the same sign as b₁.

Question

Quizplus · Accepted Answer

The standard error of the estimate measures the variation around the predicted regression equation, indicating the degree of scatter around the regression line. It gives an estimate of the average amount by which the observed Y values differ from the predicted Y values based on the regression equation. It is not related to the proportion of variation explained by the explanatory variables or the regression coefficients. The sign of the regression coefficients (b) reflects the direction of the relationship between the explanatory variables and the response variable, but the standard error of the estimate is not directly related to it.

The Standard Error of the Estimate for a Multiple Regression