# Statistics – correlation and regression analysis

## BUS 4025 – Assignment 6

For these problems, please use Excel to show your work, and submit the Excel spreadsheet along with your completed assignment.

1.      Look at the scatter plot below.  Does it demonstrate a positive or negative correlation?  Why?                      Are there any outliers?  What are they?

2.      Look at the scatter plot below.  Does it demonstrate a positive or negative correlation?  Why?  Are there any outliers?  What are they?

3.       A friend of yours is discussing statistics, and says she was working on a study in regard to her profession. In conducting her analysis she tells you the correlation between the two variables she is studying is 1.02.  What is your response to this analysis?

4.      You tell your supervisor that there is a strong negative correlation between the number of overtime hours worked and the level of productivity in an employee. Your supervisor thinks that because it is a “negative” correlation it is bad. What would you tell your supervisor about negative correlations to clarify?

5.      Explain the statement, “correlation does not imply causality.”

6.      The data below represents the GPA of high school seniors as well as their ACT test scores. Display the data in a scatterplot and then calculate the sample correlation coefficient r. Is there a positive, negative, or no correlation between the variables? What are your conclusions?

ACT        GPA

22.0       3.0

32.0       3.78

33.0       3.68

21.0       2.94

27.0       3.38

25.0       3.21

30.0       3.65

7.      Technology: For the following data sets find the equation of the regression line and construct a scatter plot of the data and draw a regression line in the scatterplot. Can you form an estimate about the sign and magnitude of r? Calculate r and check your estimate. Use Microsoft Excel to perform these tests.

a.      The number of hours spent playing video games on the weekend and the age (in years) of 8 children).

 Age 8 12 13 11 9 14 13 15 Hours 4 6 6 7 5 8 8 5

b.      The average time spent watching television and the average time spent playing sports each day for 8 children. This is measured in minutes.

 Television 35 30 15 60 100 45 40 35 Sports 30 30 45 60 15 30 30 50

8.      Application: You need to develop a study of something of interest to you. Create a data set with at least 20 records and state a null and alternate hypothesis. Conduct correlation and regression analysis on the data set and full explain your analysis. Make sure to also include your output to show how you came to your conclusions.