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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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