1. The file ToyotaCorolla.xls contains data on used cars (Toyota Corollas) on sale during late summer of 2004 in The Netherlands. It has 1,436 records containing details on 38 attributes, including Price, Age, Kilometers, HP, and other specifications. The goal will be to estimate the price of a used Toyota Corolla based on its specifications. Let Y represent the price, X1 the age ("age_08_04), X2 Guarantee period, and X3 the automatic (yes=1, no=0).

(1) If you have to use a simple linear regression model to estimate the selling price of a car, which X variable do you want to use? Why?

(2) Develop a multiple linear regression model by using X1 and X2. Report coefficients of X1 and X2, and interpret them. Does X2 help to explain the selling price of the cars?

(3) Develop a multiple linear regression model by using X1 and X3, and report their coefficients and interpret them. Does X3 help to explain the selling price of the cars? How much does an automatic option add to the value of a car?

(4) Develop a multiple linear regression model with X1, X2, and X3 and construct a second order polynomial term (e.g., X12, X22, X32) if necessary. Does your polynomial term help to explain the selling price of the cars? Also, provide the scatter plot between the dependent variable and the polynomial term you created. Interpret the effect of the polynomial term.

(5) Develop a multiple linear regression model with X1, X2, and X3 and construct an interaction term if necessary. Does your interaction term help to explain the selling price of the cars? Interpret the effect of the interaction term.

(6) What is your final regression model that you want to recommend to estimate the price of the used Corolla? Justify your recommendation.

You can find the raw file at here

https://github.com/SeongCheol-Kim/2016_summer/blob/master/ToyotaCorolla.xls