538 CHAPTER 10 Correlation and Regression See the three residual plots below. The leftmost residual plot suggests that the regression equation is a good model. The middle residual plot shows a distinct pattern, suggesting that the sample data do not follow a straight-line pattern as required. The rightmost residual plot becomes thicker, which suggests that the requirement of equal standard deviations is violated. The jackpot>ticket data from Table 10-1 are used to obtain the accompanying Statdisk-generated residual plot, which is a plot of the 1x, y - yn2 values. See that this residual plot satisfies the preceding two general criteria for residual plots. CP EXAMPLE 6 Residual Plot Statdisk Residual Plot Suggesting That the Regression Equation Is a Good Model Residual Plot with an Obvious Pattern, Suggesting That the Regression Equation Is Not a Good Model Residual Plot That Becomes Wider, Suggesting That the Regression Equation Is Not a Good Model Criteria for Residual Plot ■ The residual plot should not have any obvious pattern (not even a straight-line pattern). (This lack of a pattern confirms that a scatterplot of the sample data is a straight-line pattern instead of some other pattern.) ■ The residual plot should not become much wider (or thinner) when viewed from left to right. (This confirms the requirement that for the different fixed values of x, the distributions of the corresponding y values all have the same standard deviation.)
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