10.29 Interpreting a residual plot. FIGURE 10.18 shows four plots of residuals versus x. For each plot, comment on the regression model conditions necessary for inference. Which plots suggest a reasonable fit to the linear regression model?

FIGURE 10.18 Four plots of residual versus x, Exercise 10.29.

Description Graph a plots residual on the vertical axis, ranging from negative 4 to 16 in increments of 2, versus x on the horizontal axis, ranging from 0 to 30 in increments of 10. A residual line extends horizontally from 0 on the vertical axis. Dozens of points are plotted in a loose cluster across the graph that increases in height from left to right in a fan pattern centered on the residual line.

The points are between negative 2 and 2 on the vertical axis from 0 to 10 on the horizontal axis, then grow to between negative 4 and 4 by 30 on the horizontal axis. Three outliers are plotted at (11, 8), (19, 10), and (22, 16). Graph b plots residual on the vertical axis, ranging from negative 60 to 60 in increments of 10, versus x on the horizontal axis, ranging from 10 to 40 in increments of 10. A residual line extends horizontally from 0 on the vertical axis. Dozens of points are plotted in a loose cluster across the graph that increases in height from left to right in a fan pattern centered on the residual line. The points are between negative 10 and 10 on the vertical axis from 10 to 20 on the horizontal, then grow to between negative 60 and 60 by 30 on the horizontal axis. Graph c plots residuals on the vertical axis, ranging from negative 1 to 3 in increments of 1, versus x on the horizontal axis, ranging from 11 to 31 in increments of 2. A regression line extends horizontally from 0 on the vertical axis.

Dozens of points are plotted high and wide across the graph between negative 1.5 and 2 on the vertical axis and 11 and 30 on the horizontal. Graph d plots residual on the vertical axis, ranging from negative 6 to 10 in increments of 2, versus x on the horizontal axis, ranging from 10 to 40 in increments of 10. A residual line extends horizontally from 0 on the vertical axis. Dozens of points are plotted in a loose curvilinear cluster that falls from (11, 3.5) to (25, negative 5), then rises to (35, 10). All values estimated.