Now suppose that we created a dummy variable for Diesel engi

Now suppose that we created a dummy variable for Diesel engines, i.e., the new dummy would have a value of 0 whenever the Gasoline dummy is 1, and it would have a value of 1 whenever the Gasoline dummy is 0. If instead of the regression in part (a) we ran a regression that has the maintenance cost as the dependent variable and the age, miles per month, and the Diesel dummy as independent variables, what would be the coefficient (slope) estimate on the Diesel dummy? Why?

(This is PART A question for any reference needed:

Run a multiple regression that has the maintenance cost as the dependent variable and the age, miles per month, and Gasoline dummy variable as independent variables. )

Maintenance cost per month (in Gasoline Dumimy (J: Diesel, 1 = 3 Dollars Age (in years) Miles per month

Solution

The output of the multiple regression of part (A) would be -

So, here we can see that the coefficient of the slope for the dummy variable \"Gasoline Dummy\" is = -1.9218807.

So, now if we reverse the coding of the dummy variable where \'0\' corresponds to the \"Gasoline\" and \'1\' corresponds to the \"Diesel\" then the coefficent of the variable \"Gasoline Dummy\" will have the same magnitude but the opposite sign.

That means the new coefficient would be = +1.9218807.

This is because the mean of the variable will change to a new value which is difference of the older mean and 1. So, sign changes.

You can verify it from the regression output of the new coded values as shown below -

And the new data is -

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.71175999
R Square	0.50660228
Adjusted R Square	0.47135959
Standard Error	47.3387529
Observations	46
ANOVA
	df	SS	MS	F	Significance F
Regression	3	96639.11015	32213.04	14.37468	1.38E-06
Residual	42	94120.21594	2240.958
Total	45	190759.3261
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	6.00948252	122.0095523	0.049254	0.96095	-240.2158	252.23473	-240.21576	252.234728
Age (in years)	9.8210935	3.304420426	2.972108	0.004879	3.1525031	16.489684	3.1525031	16.4896839
Miles per month	0.44439384	0.164554161	2.700593	0.009936	0.1123101	0.7764776	0.11231009	0.77647758
Gasoline Dummy (0 = Diesel, 1 = gasoline)	-1.9218807	14.76415848	-0.13017	0.897052	-31.71716	27.873397	-31.717159	27.8733973