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HOA-3 Car Manufacturer

Homework Assignment

A team charged with designing a new car in an automobile manufacturing company is concerned about the gasoline mileage that can be achieved. With the growing pressure from the government, the team is worried that the car’s mileage will result in violation of Corporate Average Fuel Economy (CAFE) regulations for vehicle efficiency, generating bad publicity and fines. Because of the anticipated weight of the car, the mileage attained in city driving is of particular concern.

The design team has a good idea of the characteristics of the car, right down to the type of leather to be used for the seats. However, the team does not know how these characteristics will affect the mileage.

You are hired to help the team. Your goal is two folds. First, you need to learn which characteristics of the design are likely to affect city mileage. The engineers want a model that they can rely on to predict the associated mileage for a car when designed.

You have access to the data file: CarsData.jmp. The data variables in the file are summarized in the following table.

Manufacturer The Name of the Automobile Company Model The model of the car Vehicle Category The category of vehicle: small, midsize, compact, large, van, sporty Maximum Price Maximum price of the vehicle in thousand dollars Minimum Price Minimum price of the vehicle in thousand dollars Midrange Price Midrange price of the vehicle in thousand dollars City Mileage (MPG) Mileage in City (in Miles per Gallon) Engine Rev per mile (at highest gear)

Indicates the number of times a tire revolves while it covers the distance of one mile

Engine size Size of the engine in liters Maximum Horsepower Maximum horsepower of the car RPM at Max Horsepower Revolutions per minute at maximum horsepower Fuel tank capacity Maximum gallons of gas the tank can hold Passenger capacity Number of passenger seats the car has Length The length of the car in inches Width The width of the car in inches Wheel base The distance between the front and rear axles of the car U-turn space The space in feet driver would need to do a U-turn Rear seat rooms Rooms in the back seat in inches Luggage capacity Amount of luggage the car can fit in cubic ft. Weight Weight of the car in pound

Case question:

1. In order to develop a model, you want to know the relationships between the data variables. Create a scatter plot matrix by using all 17 numeric variables and explain what you learn from the correlation matrix. Which two variables have highest correlation and which two variables have lowest correlation? [5 points]

HOA-3 Car Manufacturer

2. Use the least square method to develop a linear model to predict the city mileage of a car given all other continuous attributes of a car in the data file. Show screenshot of “Effect Summary” from JMP. [2 points]

a. Remove the insignificant parameters from the model one by one by checking the log(worth) of each parameter and removing the least important parameter first from the model.

b. Keep doing it until you are left with parameters that are significant (p-value less than 5%). Show the screenshot of Effect summary and parameter estimates and Analysis of Variance tables from JMP analysis. [3 points]

c. What is the R2 of your final model? Explain the meaning of the obtained R2. [3 points] d. Based on the model, what is the most and least important variables in predicting the

city mileage of a car? [2 points] e. Did you find any multicollinerity effect in the model? Show parameter estimate tables

obtained from the model with information on VIF to support your answer. [2 points] f. Show “Residual by Predicted” plot and explain what you see in the scattered

distribution. [3 points] g. Write down the equation of the model and explain how a manager would determine the

expected city mileage of a newly designed car. [5 points]