Section 4.3 Summary

1. The sum of squared prediction errors is referred to as the sum of squares error, $\text{SSE}=\Sigma {(y-\hat{y})}^2$. The standard error of the estimate, $s=\sqrt{{\displaystyle \frac{\text{SSE}}{n-2}}}$, 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 $y$ variable is measured by the total sum of squares, $\text{SST}=\Sigma {\left(y-\overline{y}\right)}^2$, and may be divided into the sum of squares regression, $\text{SSR}=\Sigma {\left(\hat{y}-\overline{y}\right)}^2$, and the sum of squares error, $\text{SSE}=\Sigma {(y-\hat{y})}^2$. SSR measures the amount of improvement in the accuracy of estimates when using the regression equation compared with ignoring the $x$ information.
3. The coefficient of determination, $r^2=\text{SSR/SST}$, measures the goodness of fit of the regression equation as an approximation of the relationship between $x$ and $y$. Finally, the correlation coefficient $r$ may be expressed as $r=\pm \sqrt{r^2}$, taking the positive or negative sign of the slope $b_1$.