Question

which statements describe a residual plot for a line of best fit that is a good model for a scatterplot? check all that apply. there are about the same number of points above the x - axis as below it. the points are randomly scattered with no clear pattern. the points lie on a line. the points lie on a curve. the number of points is equal to those in the scatterplot. the y - coordinates of the points are the same as the points in the scatterplot.

Explanation:

• For a residual plot of a good - fit line:
• The number of positive residuals (points above the \(x\) - axis) and negative residuals (points below the \(x\) - axis) should be approximately equal. This is because the line is balancing the over - predictions and under - predictions.
• The points should be randomly scattered. If there is a clear pattern (like a line or a curve), it indicates that the linear model is not appropriate and there is some underlying non - linear relationship or other systematic error in the model.
• The number of points in the residual plot is equal to the number of data points in the scatterplot because each data point has a corresponding residual.

• If the points lie on a line, the residual plot would imply a perfect linear relationship in residuals, which is not the case for a good (but not perfect) linear model. If the points lie on a curve, it means the linear model is not capturing the relationship well. The \(y\) - coordinates of the points in the residual plot are the residuals (\(y - \hat{y}\)), not the same as the \(y\) - coordinates in the scatterplot.

Answer:

• There are about the same number of points above the \(x\) - axis as below it.
• The points are randomly scattered with no clear pattern.
• The number of points is equal to those in the scatterplot.