Section 4.3 Summary

1. The sum of squared prediction errors is referred to as the sum of squares error, . The standard error of the estimate, , is an indicator of the precision of the estimates derived from the regression equation because it provides a measure of the typical residual or prediction error.
2. The total variability in the variable is measured by the total sum of squares, , and may be divided into the sum of squares regression, , and the sum of squares error, . SSR measures the amount of improvement in the accuracy of estimates when using the regression equation compared with ignoring the information.
3. The coefficient of determination, , measures the goodness of fit of the regression equation as an approximation of the relationship between and . Finally, the correlation coefficient may be expressed as , taking the positive or negative sign of the slope .