Question

1. (5pts) the regression line for the given data is y = 2.097x - 0.552. determine the residual of a data point for which x = -1 and y = -2.

x	-5	-3	4	1	-1	-2	0	2	3	-4
y	-10	-8	9	1	-2	-6	-1	3	6	-8

Explanation:

Step1: Predict y - value

Substitute $x=-1$ into the regression line equation $y = 2.097x-0.552$.
$y_{predicted}=2.097\times(-1)-0.552$
$y_{predicted}=-2.097 - 0.552=-2.649$

Step2: Calculate the residual

The formula for the residual $e=y - y_{predicted}$. Here, $y=-2$ and $y_{predicted}=-2.649$.
$e=-2-(-2.649)$
$e=-2 + 2.649=0.649$

Answer:

$0.649$