Question

Which answer is the best estimate of the residual value when x = 2?

−1

−0.5

0.5

1

Answer 1

The best estimate of the residual value when x = 2 is:

-0.5

Explanation:

We are asked to find the best estimate of the residual value when, x=2.

We know that:

" A residual is the vertical distance between a data point and the regression line. It is positive if the data point is above the regression line and negative if they are below the regression line ".

Hence, at x=2.

we have value=4.

but the value on the regression line at x=2 is 4.5

Hence, the vertical distance is:

4.5-4=0.5

As the data point lie below the regression line. hence the residual value will be negative.

Hence, the best estimate of the residual value when x = 2 is -0.5.

Answer 2

-0.5

the residual is observed-predicted, and given that x is below the line of best fit, the residual will be negative. to get -0.5 rather than -1, you just have to look at how far the point is from the line.