MATH141

Name:____________________

Linear Regression Activity – Car Depreciation

Modeling Depreciation Using Linear regression

1. State the make, model and MSRP of the chosen car:

2. Data collected from Kelly Blue Book:

Year of

manufacture

Trade in

value

3. Data adjusted for creating a linear regression model of the car’s depreciation:

Let x represent the age of the car in years and y represent the trade in value in dollars

x

y

4. The Linear Regression Model obtained from the data is:

Draw a scatterplot and complete graph of the linear regression model for your car. Make sure to

include the following in the graph above:

• Label axes with appropriate variables

• Label axes with subtitles

• Label the graph with its equation

• Label the horizontal intercept as a coordinate pair

• Label the vertical intercept as a coordinate pair

Interpretation of the Linear Regression Model:

1. Give the slope:

Interpret the slope in the context of the problem:

2. Give the vertical intercept:

Interpret the vertical intercept in the context of the problem:

3. Give the horizontal intercept:

Interpret the horizontal intercept in the context of the problem:

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. 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.

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 make sense to offer a car loan ranging up to

30 years.

LinearRegression Activity – Modelling Car Depreciation

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.

The following steps should be recorded on the Linear Regression Activity worksheet:

• State the make and model of your chosen car

• State the MSRP (Manufacturer’s Suggested Retail Price) of your chosen car

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

past 10 years. (It is recommended that you collect your data from Kelley Blue Book,

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

calls the market price of its cars the “Fair Purchase Price,” but other sites may use a

different term)

• Organize the collected data in a table.

• Prepare a new table that allows you to estimate how the value of the car changes over the

time. This table should have the following two variables: the age of the car in years and

the corresponding market value of the car

• Calculate the linear regression equation modeling your car’s depreciation over time using

your graphing calculator, Desmos or any other software with regression capability

• Graph the linear regression and the scatterplot of your data on your worksheet. You may

also graph it using technology, print the graph and attach it to the worksheet.

• Answer the questions on the worksheet

http://www.kbb.com/

Data Collection:

The following are instructions on how to collect data using Kelly Blue Book. Note that you may

not use the data collected in this example in your report:

o Go to http://www.kbb.com

o Click on the tab “Price New/Used” on top of the page

o Under “Select a Vehicle,” select the make and model of your chosen car and click on

“Next”

o Under “Select a Year,” choose the latest model of your car (2018 in our Chevrolet

example)

o Under “Select a Style,” choose the style that you are considering to purchase (LT in our

Chevrolet example)

o Under “Select Options,” click on the tab “Price Without Added Options”

o Record the “Fair Purchase Price” (Note: in our example, this is the Fair Purchase price of

a new 2018 Chevrolet Traverse LT)

http://www.kbb.com/

o The go to the top of the page and click on the scroll down menu in a window showing

the year (the latest model) of your new car

o In the scroll down menu, go to “Used” and click on the previous year (in our Chevrolet

example, click on “2017” under “Used”)

o Record the “Fair Purchase Price” (Note: this is the Fair Purchase price of a used 2017

Chevrolet Traverse LT. So this is the Fair Purchase price or the resale value of a car that

is 1 year old.)

o Go to the top of the page and click on the scroll down menu in a window showing the

last selected year (in our example, 2017) and choose the previous year under “Used” (in

our example, click on 2016 under “Used”)

o Record the “Fair Purchase Price” (Note: this is the Fair Purchase price of a used 2016

Chevrolet Traverse LT. So this is the Fair Purchase price or the resale value of a car that

is 2 years old.)

o Repeat this process until you collect the Fair Purchase price for 10 consecutive years (in

our example, we would collect the data for years 2009-2018

Note:

In earlier years, the model (EX, DX, LT, etc.) of your car may not exist. In this case choose the

same relative model. For example, if you choose a 2016 Honda Civic EX-T, this is the high

level sporty model. In 2008, the Honda Civic Si appears to be the equivalent model, so find

the used price for this model.