Now suppose that we created a dummy variable for Diesel engines, i.e., the new d

Question

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

Explanation / Answer

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

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