Question

A linear regression is done on data the line of best fit is y= 1.25x-6.25. What is the residual for the point (1,1)?

Answer 1

6

Explanation:

Find the predicted y value when x=1:

`\hat{y}=1.25x-6.25\\\hat{y}=1.25(1)-6.25\\\hat{y}=1.25-6.25\\\hat{y}=-5`

Find the residual:

`\text{Residual}=\text{Actual Value}-\text{Predicted Value}\\\text{Residual}=y-\hat{y}\\\text{Residual}=1-(-5)\\\text{Residual}=1+5\\\text{Residual}=6`

Because our residual is positive, this is an indicator that our predicted y value is too low.