Project: Correlation and Linear Regression

Project B:
Correlation and Linear Regression

●
Choose a real world business or relevant data set of at
least 15 pairs of numeric data points. (For example: 15 states in the country
or 15 counties in a specific state).
●
Do not use sports. In fact, spend some time considering
what would be a worthwhile and interesting data set. The more interesting,
relevant, and important to real life, the better.
●
If you use the “goldmine” do not use data about “firms”
because it is not clear what the firms mean (you always want to completely
understand the data you are using).
●
Make sure the two variables are not related by a
formula. Variables related by a formula will have almost perfect correlation,
so perfect correlation is a red flag.
●
Do not use “rank” as a variable. (For example, do not
use as the rank of the state, #1 to #15,
based on population as your x variable and the actual population numbers
as your Y variable. .
●
Google Sheets will not work for this assignment. If you
do not have a hard drive version of Excel already on your computer, see the
“Office Suite Download Guide” for instructions to download a free version of
Excel that works for this project.

Enter the data into Excel and use “Regression” from the
“Data Analysis” add-in to analyze your specific data set. Copy all the
information from Excel into Google Docs in a presentable fashion. Answer the
following questions in Google Docs. Be sure to number them. You will submit
both the link to your Google Doc and your excel file to the drop box; HOWEVER,
everything that you want graded must be in the Google Doc. To be clear: the
excel file is supplemental material and I will only look at it for
clarification purposes, NOT for grading purposes.

Read these directions twice and be sure to follow them
exactly! No excuses…follow directions!

The expectation is that you will provide a thoughtful and
appropriate answer to all the questions. If at least one question is not
answered, or the answer is not appropriate or thoughtful, then this project
will not be evaluated by the professor and you will be asked to schedule a
conference to discuss the topic of meeting expectations. It is also expected
that you complete this project by the due date and time, and not a minute
later. Finally, and most importantly, the expectation is that you make this
project your priority this week and start it as soon as you can.

PART I: CALCULATION
AND ANALYSIS
Correlation

1. Name your source and include the link to where the data
was found. Present your data set in an organized fashion.
2. Explain the variables and what the units mean.
3. Explain the reasoning for why one variable is independent
and the other variable is dependent.
4. Choose α and explain why you chose it.
5. Give your p-value.
6. Compare α and p-value
7. Tell if there is positive, negative or no significant
correlation.
8. Give the bottom line conclusion; does the “y” depend on
the “x”?
9. Give the critical value and r.
10. Compare r and critical value and tell if there is
significant correlation.
11. Give r2 and explain what it means, using the specific
variables of your project.
12. Give other causes
of variation that are not part of the model.

Regression

13. Using Excel, create a scatter plot with the regression
line.
14. Give the regression equation.
15. Explain what the slope ( ) means in the model (for your specific x and
y) and give the units.
16. Pick 3 data points that will be used to find their
residuals. Give the names of the data points, why they were chosen, and why
they are important.
17. Find the residuals for the 3 points chosen in #16.
18. Decide if the residuals are small or large and explain
why. Tip: Large is defined as the absolute value of the residual being more
than 50% of the value of the y it is associated with. The formula is For example, if the residual is -6.2, and the
associated y value is 4, then the residual is of the y. This is greater than 50%, so the
residual is considered large.
19. Make one prediction. For a time series, predict the next
year. Otherwise, make a prediction about a fictional data point that is
realistic and relevant to business, or, if available, a real data point that is
not part of the data set.

PART II: CRITICAL
THINKING AND APPLYING TO THE REAL WORLD

Business Applications

20. Why did you pick this topic and how is it important to
you?
21. How can this model be of use to a real world business?
Can it help solve any problems?
22. Does this model
have Type I Error or Type II Error? Can this be dangerous to a business using
this model? How concerned are you about this and why? Before you answer this
question, look up Type I and Type II Error and reflect on what it means,
because they are subtle.

Misuse of Regression

Please take the time to read the “Guide for Identifying
Misuses of Regression (3C)” before you answer these questions. Base your
answers on what you learned during the lesson and the guide.

For each misuses of regression below, explain why this model
is vulnerable or is not vulnerable to:
23. Correlation and causality
24. Time dependent correlation and causality
25. Randumbness
26. Regression to the moon
27. False linear assumption (Study the scatter plot and
determine if the data might actually not be linear, and if so, what other type
of correlation it might be.)

Learning

28. What did you learn about this topic? Write at least 4
sentences.
29. What did you learn about statistics? Write at least 4
sentences.

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