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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 $1$1 $3$3 $5$5 $7$7 $9$9
$y$y-values $22.7$22.7 $22.3$22.3 $24.2$24.2 $21.8$21.8 $21.5$21.5
$\hat{y}$^y $25.2$25.2 $23.4$23.4 $21.6$21.6 $19.8$19.8 $18$18
Residuals $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
 
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Approx 2 minutes
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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

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