In a regression line, the ________ the standard error of the estimate is, the more accurate the predictions are.

false
larger
true
smaller
false
The standard error of the estimate is not related to the accuracy of the predictions.
The standard error of the estimate is a measure of the accuracy of predictions. The regression line is the line that minimizes the sum of squared deviations of prediction (also called the sum of squares error), and the standard error of the estimate is the square root of the average squared deviation.
Linear regression was used to predict Y from X in a certain population. In this population, SSY is 50, the correlation between X and Y is .5, and N is 100. What is the standard error of the estimate?

The standard error of the estimate for a population = sqrt[(1-rho^2)*SSY/N] = sqrt[(1-.5^2)*50/100] = .61
.61
0.011
You sample 10 people in a high school to try to predict GPA in 10th grade from GPA in 9th grade. You determine that SSE = 5.8. What is the standard error of the estimate?

The standard error of the estimate for a sample = sqrt[SSE/(N-2)] = sqrt[5.8/8] = .85
.851
0.003
The graph below represents a regression line predicting Y from X. This graph shows the error of prediction for each of the actual Y values.
Use this information to compute the standard error of the estimate in this sample.

reg_error2.gif
The standard error of the estimate for a sample = sqrt[SSE/(N-2)]. SSE is the sum of the squared errors of prediction, so SSE = (-.2)^2 + (.4)^2 + (-.8)^2 + (1.3)^2 + (-.7)^2 = 3.02; sqrt(3.02/3) = 1.0
1.0
0.004