The standard error of the estimated sample regression function $\left( s _ { y \mid x } \right)$
Is
A)the square root of the unexplained sum of squares.
B)the square root of the explained sum of squares.
C)the square root of the unexplained sum of squares divided by the degree of freedom of the regression.
D)the square root of the explained sum of squares divided by the degree of freedom.

Question

Quizplus · Accepted Answer

The standard error of the estimated sample regression function (s-y|x) measures the variability of the observed response about the regression line. It is calculated as the square root of the unexplained sum of squares (SSE), divided by the degrees of freedom of the regression (n - p - 1), where n is the sample size and p is the number of predictors. This gives an estimate of the standard deviation of the errors in the regression model, and is used to construct confidence intervals for the regression coefficients and to perform hypothesis tests on the significance of the regression model. Therefore, the best choice is C.

The Standard Error of the Estimated Sample Regression Function (sy∣x)\left( s _ { y \mid x } \right)(sy∣x​)

The Standard Error of the Estimated Sample Regression Function $\left( s _ { y \mid x } \right)$