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Exhibit 3.24 Plot of ﬁt for product E quarter 1
linear regression for the independent variable. These coefﬁcients specify the model
and can be used for prediction. For example, the analyst may want to predict an
estimate of the 1st quarterly value for the 7th year. Thus the prediction calculation
results in the following:
Estimated Y for Year 7
= α + β
(Year)
=
12.1
+
7.94(7)
=
67.8
Exhibit 3.24 shows the resulting relationship between the actual and predicted
values for quarter 1. The ﬁt is almost perfect. Note that regression can be applied
to any data set, but it is only when we examine the results that we can determine if
regression is a good predictive tool. When the R-square is low and residuals are not
a good ﬁt, it is time to look elsewhere for a predictive model. Of course, R-square
is a relative measure and should be considered along with other factors. In some
applications, analysts might be quite happy with an R-Square of 0.4, in others it is
of no value.
Now let us determine the ﬁt of a regression line for quarter 4. As mentioned
earlier, a visual observation of Exhibit 3.20 indicates that quarter 4 appears to
be the least suitable among quarters for a linear regression model and Exhibit
3.25 indicates a less impressive R-square of approximately 85.37%. Yet, this is
still a relatively high value. Exhibit 3.26 shows the predicted and actual plot for
quarter 4.
There are other important measures of ﬁt that should be considered for regres-
sion. Although we have not discussed this measure yet, the Signiﬁcance F for
quarter 1 regression is quite small (0.0002304), indicating that we should con-
clude that there is signiﬁcant association between the independent and dependant
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