A European used car dealer built a multiple linear regression model to predict the resale price of a used car based on its conditions and features. The model with estimated coefficients is:

Descriptions of the variables in the model:

a. Price: Offer price in Euros
b. Age: Age in months as of August 2004
c. Weight: Weight in kilograms
d. HP: Horsepower
e. KM: Cumulative kilometers on odometer
f. Quarterly_Tax: Quarterly road tax in Euros
g. Fuel_Type: Fuel type (Petrol, Diesel, CNG)

Interpret the meaning of coefficient ( 16.44) of variable Quarterly_Tax.

It means that one Euro increase in Quarterly road tax will lead to a 16.44 Euros increase in the Offer price. Or, one Euro decrease in Quarterly road tax will lead to a 16.44 Euros increase in the Offer price.

Explanation:

Using a0 represent the intercept, a1 to a6 to represent the coefficient, and u to represent the coefficient, the estimated multiple linear regression model can be presented as follows:

Price = a0 + a1(Age) + a2(Weight) + a3(HP) + a4(KM) + a5(Quarterly_Tax) + a6(Fuel_Type) + u

In the model, the coefficient of all the independent variables are assumed to be positive.

Given that a5 = 16.44, it means that one Euro increase in Quarterly road tax will lead to a 16.44 Euros increase in the Offer price. Or, one Euro decrease in Quarterly road tax will lead to a 16.44 Euros increase in the Offer price.