The multivariable regression model
Download
1 / 13

The multivariable regression model - PowerPoint PPT Presentation


  • 138 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'The multivariable regression model' - binah


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
The multivariable regression model
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
Model specification

Recall from Chapter 3 we said that airline ticket sales were a function of three variables, that is:

Q = f(P, PO, Y)

[3.1]

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:



Estimating multivariable regression models using ols
Estimating multivariable regression models using OLS

Let:

Yi = 0 + 1X1i + 2X2i + i

Computer algorithms find the ’s that minimize the sum of the squared residuals:


Spss output
SPSS output

We estimated the multivariable model using SPSS once again.


Results of the regression
Results of the regression

Our equation is estimated as follows:




Comparison of models
Comparison of models

  • Notice that Adjusted R2 for the multivariable model is .720, compared to .557 for the single variable model. Hence we have a considerable increase in explanatory power.

  • The standard error of the regression has decreased from 18.6 to 14.8



The f test
The F test

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


We set up the following null hypothesis an alternative hypothesis:

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

  • COAL is monthly demand for bituminous coal (in tons)

  • FIS is the Federal Reserve Board Index of Iron and Steel production.

  • FEU the FED Index of Utility Production.

  • PCOAL is a wholesale price index for coal.

  • PGAS is a wholesale price index for naturalgas.

Source: Pyndyck and Rubinfeld (1998), p. 218.


ad