EXAMPLE 10.20

Computing s². The estimate of σ² is s², the sum of the squares of the residuals divided by n − 2. The estimated standard deviation about the line is the square root of this quantity.

$$s^2=\frac{\sum e_i^2}{n-2}$$

$$=\frac{{\left(-1.023\right)}^2+{\left(-2.697\right)}^2+\cdots +{\left(2.689\right)}^2}{4}$$

= 22.127

So the estimate of the standard deviation about the line is

$$s=\sqrt{22.12702}=4.704$$