Interpret the estimated value of the coefficient on Age ie e

Interpret the estimated value of the coefficient on “Age,” i.e., explain what the number means in this regression.

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

Solution

If you copy this data sheet onto excel(or any available data analysis tool) and run multiple linear regression on the data with maintanence cost as the dependent variable(y) and the age(x1), miles per month(x2) and gasoline dummy(x3) as the three independent variables i.e. predictors then you will get the value of the coeffecient of age. say you get the coeffecients to the three predictors as a1, a2, a3 with a1 being the coeffecient of age. (if you can provide me the data in excel format then I can run it for you) however coming to the interpretation part: a1 is interpreted as follows: a1 is the increase in the value of y (maintanence cost) for unit increase in value of age(x1) keeping the other two predictors constant(unchanged). This is clear from the following calculation.

Suppose the regreession equation is as follows:

Y = (a1*x1) + (a2*x2) + (a3*x3). At x1 = d, Y= (a1*d) + (a2*x2) + (a3*x3) say this value of Y is Y1. Now increasing the value of x1 from d to d+1 and keeping the other predictors at their initial value, we have y=(a1*(d+1)) + (a2*x2) + (a3*x3). say this value of Y is y2. So the incease in value of y is y2-y1 = ( (a1*d) + (a2*x2) + (a3*x3)) - ((a1*(d+1)) + (a2*x2) + (a3*x3)) = a1.hence proved that a1 is the increase in the value of y (maintanence cost) for unit increase in value of age(x1) keeping the other two predictors constant(unchanged).

Also a1 indicates the importance of the value of age in the regression equation. The value of a1 can be tested in hypotheses testing. If the null hypotheses of a1 =0 is rejected then it will imply that age is an important predictor of maintanence cost.