Page 125 - Intermediate Statistics for Dummies

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Part II: Making Predictions by Using Regression
Standardized Residual Plots for Sales
Residuals versus the Fitted Values
99
90
50
10
−2
18
9
12
15
0
−1
−2
2
1
Fitted Value
Standardized Residual
Histogram of the Residuals
Figure 5-5:
Standard-
3.6
ized residual
2.4
plots for the
−1
ads and
1.2
−2
plasma TV Frequency Percent 4.8 1 Normal Probability Plot of the Residuals Standardized Residual Standardized Residual −1 2 1 0 2 1 0 6 Residuals versus the Order of the Data
0.0
example. −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2 4 6 8 10 12 14 16 18 20 22
Standardized Residual Observation Order
In the following sections, you see how to check the residuals to see whether
these three conditions are met in your data set.
Meeting the first condition
The first condition to meet (outlined in the previous section “Noting the con-
ditions”) is that the residuals must have a normal distribution with mean
zero. The upper-left plot of Figure 5-4 shows how well the residuals match a
normal distribution. If the residuals fall in a straight line, that means the nor-
mality condition is met. By the looks of this plot, I’d say that condition is met
for the ad and sales example.
The upper-right plot of Figure 5-4 shows what the residuals look like for the
various estimated y values. Look at the horizontal line going across that plot;
it’s at zero as a marker. The residuals should average out to be at that line
(zero). This Residuals versus Fitted Values plot checks the mean-of-zero con-
dition and holds for the ads and sales example looking at Figure 5-4.
You need the regular residual plots to see whether the mean of the residuals
equals zero (via the plot on the upper right of Figure 5-4). If you look at the
standardized residuals, they will always have mean zero due to the fact that
they have been standardized to have a mean of zero. If the mean of zero con-
dition isn’t met for the regular residuals, that means that many of the esti-
mated values are off in the same direction by a certain amount, which would
not be good.