Introduction to Probability and Statistics for Engineers and Scientists

380 Chapter 9: Regression

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Random data and regression line

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(^05101520)
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Residuals
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Standard residual
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Data and regression line
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.06 .09 .12 .15 .18 .21
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FIGURE 9.9 (continued )
residual plot shows a discernible pattern, in that the residuals appear to be first decreasing
and then increasing as the input level increases. This often means that higher-order (than
just linear) terms are needed to describe the relationship between the input and response.
Indeed, this is also indicated by the scatter diagram in this case. The third standardized
residual plot also shows a pattern, in that the absolute value of the residuals, and thus their
squares, appear to be increasing, as the input level increases. This often indicates that the
variance of the response is not constant but, rather, increases with the input level.