Chapter 4.5, Problem 1E

To determine

To define residual positive and when it is negative.

Answer to Problem 1E

Residuals are positive if the points lie above the regression line.

Residuals are negative if the points lie below the regression line.

Explanation of Solution

Given:

N/A

Formula Used:

A residual is the vertical distance between a data point and the regression line. Each data point has one residual. They are positive if they are above the regression line and negative if they are below the regression line.

Calculation:

As per the above definition of a residual and the positive and negative residuals, we have:

Residuals are positive if the points lie above the regression line.

Residuals are negative if the points lie below the regression line.

Conclusion:

Residuals are positive if the points lie above the regression line.

Residuals are negative if the points lie below the regression line.