The multivariable regression model. Airline sales is obviously a function of fares—but other factors come into play as well (e.g., income levels and fares of rivals). Multivariable regression is a technique that allows for more than one explanatory variable. . Model specification.
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Airline sales is obviously a function of fares—but other factors come into play as well (e.g., income levels and fares of rivals). Multivariable regression is a technique that allows for more than one explanatory variable.
Recall from Chapter 3 we said that airline ticket sales were a function of three variables, that is:
Q = f(P, PO, Y)
Again, Q is the airline’s coach seats sold per flight; P is the fare; P0 is the rival’s fare; and Y is a regional income index.
Our regression specification can be written as follows:
Yi = 0 + 1X1i + 2X2i + i
Computer algorithms find the ’s that minimize the sum of the squared residuals:
We estimated the multivariable model using SPSS once again.
Our equation is estimated as follows:
The F test provides another “goodness of fit” criterion for our regression equation. The F test is a test of joint significance of the estimated regression coefficients.
The F statistic is computed as follows:
Where K - 1 is degrees of freedom in the numerator and n – K is degrees of freedom in the denominator
H0 : 1 = 2 = 3 = 0
HA: H0 is not true
We adhere to the following decision rule:
Reject H0 if F > FC, where FC is the critical value of F at the level of significance selected by the forecaster. Suppose we select the 5 percent significance level. The critical value of F (3 degrees of freedom in the numerator and 12 degrees of freedom in the denominator) is 3.49. Thus we can reject the null hypothesis since 13.9 > 3.49.
Example: The Demand for Coal hypothesis:
COAL = 12,262 + 92.43FIS + 118.57FEU -48.90PCOAL + 118.91PGAS
Source: Pyndyck and Rubinfeld (1998), p. 218.