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Tags Quantitative Research Analysis Of Variance Regression Analysis Student's T Test
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Page 1

Applied Statistical Inference

with MINITAB®

C6583_C000.indd 1

Page 230

214 Applied Statistical Inference with MINITAB

0.50.0–0.5–1.0

2

1

0

–1

–2

Residual

z-
sc

or
e

Scatterplot of z-score vs Residual

Figure 6.25
Scatter plot of z-score versus ordered residuals for the data in Table 6.1.

Figure 6.26
MINITAB graphs dialog box to select the normal plot of residuals.

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© 2010 by Taylor & Francis Group, LLC



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Page 231

More on Simple Linear Regression 215

diagonal straight line. This line can be obtained by finding the z-score for
any given percentage and multiplying the z-score by the standard deviation
of the residuals. For instance, if we consider 95% of the normal distribution,
and if the standard deviation of the residuals is 0.512, as it is for this example,
then the theoretical value of the residual that corresponds to 95% of the nor-
mal distribution is

1 645 0 512 0 842. . .× ≈

Therefore, one point on the diagonal reference line would be (0.842, 95).
The points in a normal probability plot should generally fall along a diago-

nal straight line if the residuals are normally distributed. If the points on the
normal probability plot depart from the diagonal line, then the assumption
that the errors are normally distributed may have been violated.

MINITAB also provides a scatter plot of the residual values versus the fit-
ted or estimated values that can be used to assess the linearity and constant
variance assumptions. This plot can be created by checking the Residuals
versus fits box in the Graphs dialog box, as in Figure 6.28.

The graph of the residuals versus the fitted values is given in Figure 6.29.
This plot should show a random pattern of residuals on both sides of the
0 line. There should not be any obvious patterns or clusters in the residual
versus fitted plot. If the residual versus fitted plot shows any kind of pat-
tern, this may suggest that the assumption of linearity has been violated.
Furthermore, if there are differences in the amount of variation for certain

1.00.50.0–0.5–1.0–1.5

99

95
90
80
70
60
50
40
30
20
10

5

1

Residual

Pe
rc

en
t

Normal Probability Plot
(response is GPA)

Figure 6.27
MINITAB-generated normal plot of the residuals versus the percentile of Ai.

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© 2010 by Taylor & Francis Group, LLC

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