Question

a guidance counselor wants to determine if there is a relationship between a students number of absences, ( x ), and their grade point average (gpa), ( y ). an analysis is performed on the data for 15 randomly selected students and is displayed in the computer output.

predictor | coef | se coef | t - ratio | p
constant | 3.790 | 0.3120 | 0.046 |
absences | - 0.096 | 0.0393 | - 2.460 | 0.029
( s = 0.691 ) ( r - sq = 31.7% ) ( r - sq(adj) = 23.5% )

which of the following represents the value of the average residual for a student’s gpa?

Explanation:

In linear regression, the sum (and thus the average) of all residuals is always 0. However, looking at the given computer output, the value $s = 0.691$ represents the standard error of the estimate, which is the average size of the residuals (a measure of the typical residual magnitude). The other values correspond to: 0.0393 is the standard error of the slope coefficient, 0.3120 is the standard error of the intercept, and -0.096 is the slope coefficient. The question asks for the value representing the average residual, which corresponds to this standard error of the estimate.

Answer:

0.691