Table 4.5 lists the predictions, prediction errors, and squared errors for
this regression equation. The equation’s sum of squared errors is 2,616.4, much
smaller than the SSE of any of the previously estimated equations. The addi-
tional variables have significantly increased the accuracy of the equation. A
quick scrutiny of Table 4.5 shows that, by and large, the equation’s predictions
correspond closely to actual ticket sales.
This example suggests the elegance and power of the regression approach.
The decision maker starts with uncontrolled market data. The airline’s own
price, the competitor’s price, and regional income all varied simultaneously
from quarter to quarter over the period. Nonetheless, the regression approach
has produced an equation (a surprisingly accurate one) that allows us to meas-
ure the separate influences of each factor. For instance, according to Equation
4.3, a $10 cut in the competitor’s price would draw about 10 passengers per
flight from the airline. In turn, a drop of about $5 in the airline’s own price
would be needed to regain those passengers. Regression analysis sees through
the tangle of compounding and conflicting factors that affect demand and thus
isolates separate demand effects.140 Chapter 4 Estimating and Forecasting DemandTABLE 4.5
Predicted versus Actual
Ticket Sales Using
Q 28.84 2.12P
1.03P3.09YYear and Predicted Actual
Quarter Sales (Q*) Sales (Q) Q* Q(Q* Q)^2
Y1 Q1 77.7 64.8 12.9 166.4
Q2 38.2 33.6 4.6 20.9
Q3 32.5 37.8 5.3 28.0
Q4 91.7 83.3 8.4 70.4
Y2 Q1 97.4 111.7 14.3 203.3
Q2 117.8 137.5 19.7 387.1
Q3 97.6 109.5 11.9 140.7
Q4 103.2 96.8 6.4 40.8
Y3 Q1 88.2 59.5 28.7 822.0
Q2 94.0 83.2 10.8 117.7
Q3 83.7 90.5 6.8 46.7
Q4 91.7 105.5 13.8 190.7
Y4 Q1 60.7 75.7 15.0 224.9
Q2 92.2 91.6 .6 .4
Q3 111.3 112.7 1.4 2.1
Q4 114.7 102.2 12.5 155.0
Sum of squared errors 2,616.4c04EstimatingandForecastingDemand.qxd 9/5/11 5:49 PM Page 140