Project B

QMB 3600 Quantitative Methods in Business Professor Decker

Project B: Correlation and Linear Regression

Choose a real world business or relevant data set of at least 15 pairs of numeric data points.

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 in 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 your x variable the rank of the state (#1 to #15) based on population and y as the population.

Immediately check to see if the p-value is less than 0.10. If p-value is greater than 0.10, use a different data set.

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 it. 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. Submit the link to the Google Doc and upload the Excel file into the dropbox.

To be clear: Put everything you want me to grade in the Google Doc.

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. Give your data set in an organized, presentable 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 the 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. Large is defined as the absolute value of the residual being more than 30% of the value of the y it is associated with. For example, if the residual is -6.2, and the associated y value is 4, then the residual is (|-6.2| - 4)/4 *100 = 55%, which is greater than 30%, 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. If all the available data points were used in the data set (for example, if the data is states, and all 50 states were used in the data set), the fictional data point should be interesting, such as being very large, very small, equal to the average, or having any other characteristic the author feels makes it interesting.

PART II: CRITICAL THINKING AND APPLYING TO THE REAL WORLD

The total length of Part II should be at least one double spaced typed page of text.

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. Explain what Type I Error would be for this model and how Type I Error can 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 Error and reflect on what it means, because Type I Error is 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.