Question

question number 12. suppose you have the following data:

y	x
37	2
29	3
21	4
20	5
13	6

and the lsrl is \\(\hat{y}=-5.971x + 48.07\\). find the residual value for x = 5.
1.785
-1.785
18.215
none of the above

Explanation:

Step1: Calculate predicted y - value

The least - squares regression line (LSRL) is $\hat{y}=-5.971x + 48.07$. Substitute $x = 5$ into the equation.
$\hat{y}=-5.971\times5+48.07=-29.855 + 48.07=18.215$

Step2: Calculate the residual

The residual is given by $e=y-\hat{y}$. From the data table, when $x = 5$, $y = 20$.
$e=20 - 18.215=1.785$

Answer:

1.785