Applied Statistics Using SPSS, STATISTICA, MATLAB and R

a
4
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Expected Normal Value
-4
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7.3 Building and Evaluating the Regression Model 309
Residuals
130
120 No of obs
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0
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b -1000
Figure 7.14. Distribution of the residuals for the foetal weight example: a) Normal
probability plot; b) Histogram.
7.3.3.2 Evaluating the Linear Model
Distribution of the Residuals
In order to assess whether the errors can be assumed normally distributed, one can
use graphical inspection, as in Figure 7.14, and also perform the distribution fitting
tests described in chapter 5. In the present case, the assumption of normal
distribution for the errors seems a reasonable one.
The constancy of the residual variance can be assessed using the following
modified Levene test:
1. Divide the data set into two groups: one with the predictor values
comparatively low and the other with the predictor values comparatively
high. The objective is to compare the residual variance in the two groups. In
the present case, we divide the cases into the two groups corresponding to
observed weights below and above 3000 g. The sample sizes are n1 = 118
and n2 = 296, respectively.
2. Compute the medians of the residuals ei in the two groups: med1 and med2.
In the present case med1 = −182.32 and med2 = 59.87.
3. Let d i1
= ei1
− med1
and d i2
= ei2
− med 2 represent the absolute
deviations of the residuals around the medians in each group. We now
compute the respective sample means, d1 and d 2 , of these absolute
deviations, which in our study case are: d 1 = 187.
37 , d 2 = 221.
42 .
4. Compute:
* d1
− d 2
t = ~ t n−2
, 7.52
1 1
s +
n n
1
2
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