Regression Models with Categorical Variables 131
Other regression results are:
SSR: 1.4744e + 006
F-statistic: 76.83
p-value: 0
R^2 = 0.73The Chow test has the value 16.60. The F-statistic and the Chow test sug-
gest that the use of dummy variables has greatly improved the goodness-of-fit
of the regression, even after compensating for the increase in the number of
parameters. The residuals of the model without and with dummy variable D 1
are shown, respectively, in the second and third columns of Table 6.2.
Now let’s use dummy variables to test if there is a regime shift between
the two dates. This is a common use for dummy variables in practice. To this
end, we create a new dummy variable that has the value 0 for the first date
November 28, 2005, and 1 for the second date June 6, 2005. The new equation
is written as in the previous case but with a different dummy variable:
Spreadi = β 0 + β 1 D (^2) i + β 2 Couponi + β 3 D (^2) iCouponi + β 4 CoverageRatioi
- β 5 D (^2) iCoverageRatioi + β 6 LoggedEBITi
- β 7 D (^2) iLoggedEBITi + εi
There are seven explanatory variables and eight parameters to estimate. The
estimated model coefficients and t-statistics are shown as follows:
Coefficient
Estimated
Coefficient
Standard
Error t-Statistic p-Value
β 0 257.26 79.71 3.28 0.00
β 1 82.17 61.63 1.33 0.18
β 2 33.25 7.11 4.67 5.53E-06
β 3 28.14 2.78 10.12 1.45E-19
β 4 –10.79 2.50 –4.32 2.49E-05
β 5 0.00 3.58 0.00 1.00
β 6 –63.20 18.04 –3.50 0.00
β 7 –27.48 24.34 –1.13 0.26
Other regression statistics are:
SSR: 1.5399e + 006
F-statistic: 72.39
p-value: 0
R^2 : 0.71