5 5 linear automobile depreciation answers

MATH 141 – Capstone Project

Overview

In this project, you will consider the purchase of a new vehicle (latest model). You will write a

professional report using appropriate technology and will apply mathematical skills and

techniques learned in class to help you evaluate your purchasing decisions as well as different

financing options.

In part I of this project, you will collect real life-data and use it to model the resale value of your

chosen car over time. Part II of the project will focus on considering different options of

financing the car such as choosing the length of the loan or reducing interest payments.

Guidelines for Being Successful:

 Read and follow instructions carefully

 Review the grading rubric carefully to ensure that you are familiar with the expectations

for each section

 If you need clarification about any part of this project, please be sure to ask your

instructor in a timely manner

o Ten percent will be deducted for each calendar day the project is submitted after

the due date.

o A project is considered as “submitted” when it is available to the professor to

view in Canvas. After you submit the project, please open it up in Canvas to

ensure it is readable

o No credit is given for projects submitted after five days after the due date (2

calendar days for winter/summer terms)

 Submit a neat professional report typed (double-spaced) using your choice of word

processing software. The use of appropriate technology is expected throughout the

project

o All mathematics must be typed using mathematical notation package and all

graphs, charts and diagrams must be created using a mathematical or statistical

software package

o All graphs must be “complete” and embedded into the report. Hand-drawn

graphs or graphs submitted in a separate document will not be accepted

 Group work is not allowed for this project. While you may discuss your ideas with

others, each student must submit his or her own original work.

Getting Help:

 You may discuss the project with others and may consult any available resource

(including your instructor, classmates, LAC and HR230 tutors, or the Internet) provided

that the computations, explanations and graphs in your project are your own original

work

 You must cite all of your resources using APA format

 If you need help with writing, use the HCC Writing Center: For further information, see

the HCC Web page under the heading “Writing Center” or call the Writing Center at

(443) 518-4101. PGCC students at the Laurel College Center should see the PGCC

Writing Center for assistance.

Guidelines for Submission:

 Submit your project via the Canvas link as a PDF file

 VeriCite will be used as a deterrent for plagiarism. This program is integrated into the

Canvas submission process. All submissions will be compared against the VeriCite

database and receive an “originality” rating. To avoid a false flag in VeriCite, do not

copy and paste the instructions/questions into your final submission

Part I – Modelling Car Depreciation

In Part I of the Capstone Project, you will consider purchasing a new car (the latest model). You

will research different cars and their features to assess your personal preferences and

requirements for a car. You will also collect and use real-life data to estimate the depreciation

in the value of your chosen car.

This is a research project and should be written as a narrative.

Introduction (15 points):

In this section, you will choose a new car (latest model) that you would consider purchasing. As

you will be required to collect data on this car, you must choose a car whose make and model

has been on the market for at least 10 years. Please research the cars currently offered on the

market and think about what type of car would best suit your lifestyle, situation and needs. As a

part of your research, identify several features that are essential to you in a car (such as AWD,

heated seats or different safety features).

 State the make and model of the car (2 pts)

 Identify the MSRP (Manufacturer’s Suggested Retail Price) of the car (2 pts)

 Provide a detailed description of the four or more features you find essential in your

chosen car and explain why each of these features matters to you (5 pts)

 Identify two local dealerships that sell the make and model of the car with the features

that you chose. Provide the name, address and contact information for each dealership

(4 pts)

 Identify at least two sources from which you learned about your car. Cite the sources

using APA style and include them in your list of references (in the end of your report)

(2pts)

Data Collection (10 points):

In this section, you will collect and organize data that will be used it to estimate how your new

car will depreciate over time. It is recommended that you collect your data from Kelley Blue

Book, http://www.kbb.com. However other reputable sites may be also used.

 Collect data on the used car value for the make and model of your chosen car over the

past 10 years. (Kelley Blue Book calls the market price of its cars the “Fair Purchase

Price,” but other sites may use a different term.) Assume that you are buying the car

from a dealer and that it is in good condition (5 pts)

 Organize the collected data in a table. You want to estimate how the value of the car

changes over the time, so the table should have the following two variables: the age of

the car in years and the corresponding market value of the car (3 pts)

 Cite the source(s) of your data using APA style and include the citation in your list of

references (2 pts)

Linear Regression Model and Graph (22 points):

In this section, you will investigate and use technology to create a linear regression model using

your data.

 Use technology to create a scatterplot of your data (3 pts)

 Use technology to calculate a linear regression equation using your data. Round all

figures to two decimal places (5 pts)

 Use technology to graph the linear regression line on the same graph as your scatterplot

(2 pts)

 Your graph (scatterplot and regression line) must be a complete graph:

o The graph has a title (2 pts)

o Each axis is labeled with its variable (2 pts)

o Each axis is labeled with a subtitle (2 pts)

o Each axis shows appropriate tick marks and scaling (2 pts)

http://www.kbb.com/
o Each line, curve or function is clearly drawn and labelled with its equation. A

legend may be used when appropriate. Equations must be professionally typed

using correct mathematical notation (2 pts)

o Both horizontal and vertical intercept are shown (if relevant) (2 pts)

o Incorporate your graph into your report in a smooth, professional way. Hand-

drawn graphs or hand-written description will not be accepted. Graphs

submitted in a separate document will not be accepted

Discussion of the Regression Model (28 points):

In this model, you will discuss the meaning of your regression model. Please answer the

following:

1. Using your linear regression equation, find the vertical intercept and interpret its

meaning within the context of the model. (5 pts)

2. Using your linear regression equation, find the horizontal intercept and interpret its

meaning within the context of the model. (5 pts)

3. Using your linear regression equation, find the slope and interpret its meaning within

the context of the model. (5 pts)

4. Use your regression model to determine the predicted resale value of your car 5 years

after its purchase (when the car is 5 years old) (5 pts)

5. Do you expect all cars (different make and models) to depreciate in the same way (to

have the same linear regression model)? Explain your answer. (4 pts)

6. Most banks and credit unions provide car loans ranging from 24 to 72 months (2 to 7

years), while the most common mortgages range from 10 to 30 years. Use your

regression model to explain why it would not makes sense to offer a car loan ranging up

to 30 years. (4 pts)