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Assignment Objective:

The purpose of this project is to apply the linear regression analysis concepts that

you have learned in chapter 4 to a real life application.

Introduction:

Here’s a sample data taken from a population of individuals who are being offered a

certain interest rate based on their FICO scores:

FICO Score

Interest Rate

674

15.27

764

6.03

689

11.71

759

6.03

709

12.42

694

11.71

714

11.71

694

11.71

734

9.91

699

14.27

In this project you will describe and analyze the relationship between FICO Score

and Interest Rate the way it is explained in Chapter 4 (4.1-4.2) using the sample data

that’s provided above.

Instructions:

● To complete this assignment you may choose to work on your own or with

your peers as a group. The group should be limited to a maximum of 4

students.

● For this project you are expected to produce a typed report (using a word

document).

● Use Statcrunch for computations or to generate tables and graphs, copy the

Statcrunch results/tables/graphs into your word document. You can take a

screenshot of Statcrunch results and paste them into your report. For

example your paper must contain the scatter diagram that you generate in

Statcrunch, it should contain the screen shot of Statcrunch chart that shows

the least squares regression line (the linear equation) and etc.

● To create your report answer the questions given below (see the ‘Questions’

section below).

● Once you are done with your report, upload your project report as a word

document or a pdf. If you work as a group, only one project report submission

is required on behalf of the group (assign one of the members to upload the

report on behalf of the group).

● At the end of the report clearly state the name of contributing members,

along with a brief description of who has done what.

● Review the grading rubric to make sure you have included all it’s necessary in

your report. View the rubric by clicking on the three dots on the right top

corner of this assignment for details on grading.

Questions:

1. Identify the two variables in this analysis.

2. Indicate whether each variable is qualitative or quantitative.

3. Indicate whether each quantitative variable is discrete or continuous.

4. Input the given sample data into Statcrunch and create a scatter plot treating

FICO score as the explanatory variable, x, and the Interest Rate as the

response variable, y. Take a screen shot of your scatter plot and include it in

your report.

5. Based on your scatter plot do you suspect a linear relationship between the

two variables? Comment on the direction and the strength of the relationship

based on what you see on the scatter diagram. (This is only based on your

observation of the scatter plot, you will make conclusions after the linear

analysis steps are completed.)

6. Compute the linear correlation coefficient, r, between the two variables

and interpret the meaning specifically for the given data. Use the list of

the critical values given below to determine whether you have enough data to

make any claims based on the linear correlation coefficient obtained. Clearly

explain in your report how you have used the critical value to make the final

determination about the linear relationship between the two variables.

7. Find the least-squares regression line equation using Statcrunch. Be sure to

copy Statcrunch results into your report (Take a screen shot and paste it into

your word document). Additionally rewrite the equation in your report using

the form

8. y=mx+b

9. .

10. Looking at your least-squares regression line equation what is the slope of the

best fitting line?

11. Interpret the slope.

12. Looking at your least-squares regression line equation what is the y-intercept?

13. Interpret the y-intercept if appropriate. (Note that credit scores have a range of

300 to 850).

14. Suppose Bob has a FICO score of 680 and he is offered an interest rate of

8.3%. Is this a good offer? Why? Show detailed work on your report on how

you have concluded your provided answer.

Grading Rubric:

Criteria

Ratings

Understand the

variables

Parts (1) to (3) of

the project.

5 pts

Full Marks

The two variables

have been

identified

accurately and

categorized as

qualitative vs

quantitative, and

as discrete vs

continuous for

quantitative

variables.

Pts

5 pts

Relevance and

completeness of

the analysis of the

data including

appropriate

responses in Parts

(4) through (12).

15 pts

15

Full Marks

4. Scatter diagram

of the data is

included.

Comment has

been made on the

direction and

strength appeared

on the scatter

diagram. 5. The

linear correlation

coefficient

between the two

variables is

computed and

included in the

paper, along with

the interpretation

of the correlation

coefficient

specifically for the

data.

6. The correct

critical value has

been used to

determine whether

there is enough

data to make any

claims 7. The

least-squares

regression line is

found. 8. The

slope is identified.

9. Interpretation

for the slope is

provided. 10. The

y-intercept has

been identified. 11.

If appropriate an

interpretation of

y-int is included.

12. The equation

of the

least-squares

regression line has

been used to

predict the

outcome (y ̂-value)

for the given

x-value.

Overall quality of

the report and

adherence of the

project guidelines

5 pts

Full Marks

Overall quality of

the report and

adherence of the

project guidelines

5

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