Question

Which is the best estimate of the residual when x = 4?
–2
2
2.5
–2.5

Answer 1

the residual is the difference of the line position to the dot at x=4

line: ~4.4ish (we are estimating and don't know the exact value)
dot: 2
2-4.4ish=-2.4ish

so the answer is the last option: -2.5

Answer 2

-2.5

Explanation:

First, we need to know what is the residual is

The residual is the vertical distance between the regression line and a data point. If the distance is positive, the point is above the line and vice versa if the distance is negative, the point is below the point.

In this question, at x= 4 the we have the value is 2 but the value on the line is 4.5 so the vertical distance is:

2-4.5 =-2.5

As the data point lie below the regression line. hence the residual value will be negative. So we choose -2.5

Hope it will find you well.