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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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