# 2.03 Residuals

## Interactive practice questions

The following table shows the sets of data $\left(x,y\right)$(x,y) and the predicted $\hat{y}$^y values based on a least-squares regression line. Complete the table by finding the residuals.

 $x$x-values $y$y-values $\hat{y}$^y Residuals $1$1 $3$3 $5$5 $7$7 $9$9 $22.7$22.7 $22.3$22.3 $24.2$24.2 $21.8$21.8 $21.5$21.5 $25.2$25.2 $23.4$23.4 $21.6$21.6 $19.8$19.8 $18$18 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

Easy
Approx 2 minutes

The following table shows the sets of data $\left(x,y\right)$(x,y) and the predicted $\hat{y}$^y-values based on a least-squares regression line. Complete the table by finding the residuals.

If a residual is a positive value, is the actual value of the response variable above or below the least squares regression line?

If a measured point in a data set is below the least squares regression line, will the corresponding residual be positive or negative?

### Outcomes

#### ACMGM058

use a residual plot to assess the appropriateness of fitting a linear model to the data