You are provided with data on the price of the used cars (cPrice in dollars), make of the car (producer), age of the car (age), type of the car (type), number of previous owners (owners), condition of the car (condt), miles on the car (miles), type of sale (private).

cPrice is in thousands of dollars

Producer is a non-ordinal categorical variable taking values 1-5: 1-Toyota, 2-Honda, 3- Mercedes, 4-BUICK, 5-Ford

age is in years.

type is an ordinal categorical variable taking values 1-3: 1-Sedan, 2-SUV, 3-Crossover owners is number of owners condt is an ordinal categorical variable taking values 1-3: 1-Poor, 2-Good, 3-Excellent

miles is the last odometer reading in miles.

private is a binary variable =1 if the car was sold in a private transaction

a) make an equation that would allow you to estimate the effects of type of sale on the price of a car, while controlling for other factors. You should be able to make statements such "car sold in a private transaction is x% less expensive than a car sold by dealer".

b) make a model that would allow you to test whether the effect of type of sale has a different effect depending on miles driven. How would you test if this effect is statistically significant?

c)Explain how would you test whether the effect of a make of a car is statistically important in determining the price of a car? Be very specific. (Hint: Do not forget that Producer is a non-ordinal categorical variable.)