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Chapter 07
The dummy variables
Some time we have a variable involved in a regression which is not directly interpretable in numbers. For example, suppose we want to see the effect of gender on the educational performance. Along with other variables that determine the educational performance, gender is also a variable. But this variable is not numerical. Gender can take only two values i.e. male or female, which has no direct quantitative representation. In this case, the dummy variables are used to see the effect of such dummy variable on any dependent variable. Consider the following data set
CGPA Study Time Gender 3.3 5 Male 3.7 6 Female 2.5 5 Female 1.9 4 Male 3.9 6 Female
It has been observed in many educational institutions that the female students secure higher grades in the exams. We want to see whether there is some effect of gender on educational performance or the observed difference is just due to the fact that female spend more time for education. To see this we want to use gender as a variable in the regression. We cannot directly use gender in the regression, let me introduce a dummy variable as follows:
Let ๐๐ denote the dummy for male which is defined as follows:
๐๐ = ๏ฟฝ^1 ๐๐^ ๐ ๐ก๐ข๐๐๐๐ก^ ๐ค๐๐ ^ ๐๐๐๐ 0 ๐๐กโ๐๐๐ค๐๐ ๐
We can use this variable instead of the original variable. The data will become
CGPA Study Time Dm 3.3 5 1 3.7 6 0 2.5 5 0 1.9 4 1 3.9 6 0
Note that we were having a variable with two categories, and we have introduced only one dummy. This is because if we have only two possible options, knowledge of one option verifies whether other option exists or not. Technically it is not possible to compute regression with both dummies. Similarly if we have a variable with k-categories, we will introduce k-1 dummies.
Now we can calculate the regression in usual way. The calculated regression output is as follows:
SUMMARY OUTPUT
Regression Statistics Multiple R 0. R Square 0. Adjusted R Square 0. Standard Error 0. Observations 5
ANOVA df SS MS F Regression 2 2.809143 1.404571 122. Residual 2 0.022857 0. Total 4 2.
Coefficients
Standard Error t Stat P-value Intercept -4.24286 0.564241 -7.51959 0. Study Time 1.342857 0.098974 13.56773 0. Dm 0.8 0.151186 5.291503 0.
On basis of this regression output, we can write the regression output as follows;
CGPA=-4.24+1.34Studytime+0.8dm+e
This regression equation can give rise to two regression equations in following way.
๏ง Regression equation for male
If the student was male, dm=1, and we have
CGPA=-4.24+1.34Studytime+0.8+e=-3.44+1.34studytime+e
๏ง Regression equation for female
๏ง If the company is ISO certified, Diso=1 and we get
P= P=0.62+0.26V+0.35Adv+e
๏ง If company is not certified than Diso=0 and regression equation is
P=0.45+0.26V+0.35Adv+e
The intercept for ISO certified is higher; however the difference in the intercepts of two types is not significant on statistical grounds.
