In this case, we are going to study some data collected from Kelly Blue Book for several hundred 2005 used General Motors (GM) cars. This data allows one to develop regression models to determine car values based on a variety of characteristics such as mileage, make, model, engine size, interior style, and cruise control. 

A representative sample of over eight hundred 2005 GM cars were selected, then retail price was calculated from the tables provided in the 2005 Central Edition of the Kelly Blue Book. The data set containing the following variables:

• Price: suggested retail price of the used 2005 GM car in excellent condition. The condition of a car can greatly affect price. All cars in this data set were less than one year old when priced and considered to be in excellent condition. 

• Mileage: number of miles the car has been driven

• Make: manufacturer of the car such as Saturn, Pontiac, and Chevrolet

• Model: specific models for each car manufacturer such as Ion, Vibe, Cavalier

• Trim (of car): specific type of car model such as SE Sedan 4D, Quad Coupe 2D 

• Type: body type such as sedan, coupe, etc. 

• Cylinder: number of cylinders in the engine 

• Liter: a more specific measure of engine size 

• Doors: number of doors 

• Cruise: indicator variable representing whether the car has cruise control (1 = cruise)

• Sound: indicator variable representing whether the car has upgraded speakers (1 = upgraded)

• Leather: indicator variable representing whether the car has leather seats (1 = leather)

Please find the data her e.

Let us start by asking a question: "Are cars with lower mileage worth more?" Clearly it seems reasonable to expect to see a relationship between mileage (number of miles the car has been driven) and retail value. Hence we can try to fit a simple linear regression model relating price with mileage, and obtain the following results:

Equation 1: Price = b1 – b2 Mileage

Run the model, get all coefficients and interpret. Draw a scatter plot between Price and Mileage. 

In your paper, please try to address the following questions,

• In general, what happens to price when there is one more mile on the car?

• Does the fact that b1 is small (-0.17) mean mileage is not very important? 

• Does mileage help you predict price? What does the p-value tell you?

• Does mileage help you predict price? What does the R-Sq value tell you?

Let us explore a more advanced model.

Equation 2: Price = b0- b1 Mileage + b2 Cylinder - b3 Doors + b4 Cruise - b5 Sound + b6Leather

Show the regression outputs and interpret (include the overall model fit, model implication, and each coefficient). 

Summarize your findings, along with your understanding of regression and its applications in business literatures,