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Regression Analysis 137

and actual sales (column 3). This difference (positive or negative) is referred

to as the estimation error. To measure the overall accuracy of the equation, the

OLS regression method first squares the error for each separate estimate and

then adds up the errors. The final column of Table 4.2 lists the squared errors.

The total sum of squared errors comes to 6,027.7. The average squared error

is 6,027.7/16 376.7.

The sum of squared errors (denoted simply as SSE) measures the equa-

tion’s accuracy. The smaller the SSE, the more accurate the regression equa-

tion. The reason for squaring the errors is twofold. First, by squaring, one treats

negative errors in the same way as positive errors. Either error is equally bad.

(If one simply added the errors over the observations, positive and negative

errors would cancel out, giving a very misleading indication of overall accu-

racy.) Second, large errors usually are considered much worse than small ones.

Squaring the errors makes large errors count much more than small errors in

SSE. (We might mention, without elaborating, that there are also important

statistical reasons for using the sum of squares.)

TABLE 4.2

Predicted versus Actual

Ticket Sales Using

Q  330 P

Year and Predicted Actual

Quarter Sales (Q*) Sales (Q) Q*Q (Q* Q)^2

Y1 Q1 80 64.8 15.2 231.0

Q2 65 33.6 31.4 986.0

Q3 65 37.8 27.2 739.8

Q4 90 83.3 6.7 44.9

Y2 Q1 100 111.7 11.7 136.9

Q2 105 137.5 32.5 1,056.3

Q3 105 109.5 4.5 20.3

Q4 110 96.8 13.2 174.2

Y3 Q1 100 59.5 40.5 1,640.3

Q2 95 83.2 11.8 139.2

Q3 85 90.5 5.5 20.3

Q4 90 105.5 15.5 240.3

Y4 Q1 80 75.7 4.3 18.5

Q2 90 91.6 1.6 2.6

Q3 90 112.7 22.7 513.3

Q4 95 102.2 7.2 51.8

Mean 90.3 87.2 3.1 376.7

Sum of squared errors 6,027.7

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