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Every regression analysis should include a residual analysis as a further check on
To analyze a residual vs. fit plot, such as any of the examples shown in figure 9.4, you
should mentally divide it up into about 5 to 10 vertical stripes. Then each stripe represents
all of the residuals for a number of subjects who have a similar predicted values. For simple
regression, when there is only a single explanatory variable, similar predicted values is
equivalent to similar values of the explanatory variable. But be careful, if the slope is
negative, low x values are on the right. (Note that sometimes the x-axis is set to be the values
of the explanatory variable, in which case each stripe directly represents subjects with
similar x values.)
To check the linearity assumption, consider that for each x value, if the mean of Y falls on
a straight line, then the residuals have a mean of zero. If we incorrectly fit a straight line to a
curve, then some or most of the predicted means are incorrect, and this causes the residuals
for at least specific ranges of x (or the predicated Y ) to be non-zero on average. Specifically
if the data follow a simple curve, we will tend to have either a pattern of high then low then
high residuals or the reverse. So the technique used to detect non-linearity in a residual vs.
fit plot is to find the
Fitted value Fitted value
Figure 9.4: Sample residual vs. fit plots for testing linearity.
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Every regression analysis should include a residual analysis as a further check on To analyze a residual vs. fit plot, such as any of the examples shown in figure 9.4, you should mentally divide it up into about 5 to 10 vertical stripes. Then each stripe represents all of the residuals for a number of subjects who have a similar predicted values. For simple regression, when there is only a single explanatory variable, similar predicted values is equivalent to similar values of the explanatory variable. But be careful, if the slope is negative, low x values are on the right. (Note that sometimes the x-axis is set to be the values of the explanatory variable, in which case each stripe directly represents subjects with similar x values.) To check the linearity assumption, consider that for each x value, if the mean of Y falls on a straight line, then the residuals have a mean of zero. If we incorrectly fit a straight line to a curve, then some or most of the predicted means are incorrect, and this causes the residuals for at least specific ranges of x (or the predicated Y ) to be non-zero on average. Specifically if the data follow a simple curve, we will tend to have either a pattern of high then low then high residuals or the reverse. So the technique used to detect non-linearity in a residual vs. fit plot is to find the Fitted value Fitted value Figure 9.4: Sample residual vs. fit plots for testing linearity. Name: Description: ...
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