# Correlation & Regression

See attached file.

Section 9.1 : Correlation

Section 9.2: Linear Regression

Total points are 40. Points are included with each problem.

Included with each section or problem are reference examples and end of section exercises that can be used as a guide. Be sure to show your work in case partial credit is awarded. To receive full credit, work must be shown if applicable.

See the instructions at the end of the project for copying a graph from Excel into a Word document. The technology manual that was packaged with your book has an Excel section that can help with the graphing.

Section 9.1 : Correlation

1. Construct a scatter plot using excel for the given data. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. Complete the table and find the correlation coefficient r.

The data for x and y is shown below.

x -5 -3 4 1 -1 -2 0 2 3 -4

y 11 6 -6 -1 3 4 1 -4 -5 8

a: Scatter plot (3.5 points)

b: Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation) (2.5 points)

c: Complete the table and find the correlation coefficient r rounded to 4 decimals.(6 points)

x y xy x^2 y^2

-5 11

-3 6

4 -6

1 -1

-1 3

-2 4

0 1

2 -4

3 -5

-4 8

Use the last row of the table to show the column totals.

n = 10

r =

2. Construct a scatter plot and include the regression line on the graph using excel for the given data. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. Complete the table and find the correlation coefficient r. (References: example 1 - 4 pages 498 - 500; end of section exercises 15 - 22 pages 508 - 509)

A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representative's travel per month and the amount of sales (in thousands of dollars) per month.

Miles traveled, x 2 3 10 7 8 15 3 1 11

Sales, y 31 33 78 62 65 61 48 55 90

a: Scatter plot with regression line (3.5 points)

b: Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation). (2.5 points)

c: Complete the table and find the correlation coefficient r rounded to 4 decimals.

(7 points)

x y xy x^2 y^2

2 31

3 33

10 78

7 62

8 65

15 61

3 48

1 55

11 90

Use the last row of the table to show the column totals.

n = 9

3. Using the r calculated in problem 2c test the significance of the correlation coefficient using  = 0.01 and the claim rho = 0. Use the 7-steps hypothesis test shown at the end of this project. (References: example 7 page 505; end of section exercises 23 - 28 pages 510 - 511). (7 points) (Note: Round the computed t to 3 decimals)

1. H0 :

Ha :

2.  =

3.

4. the critical value(s) t0.

5. Rejection region:

6. Decision:

7. Interpretation:

Section 9.2: Linear Regression

(References: example 1 - 3 pages 514 - 516; end of section exercises 13 -22 pages 518 - 520)

4. A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representative's travel per month and the amount of sales (in thousands of dollars) per month.

Miles traveled, x 2 3 10 7 8 15 3 1 11

Sales, y 31 33 78 62 65 61 48 55 90

Use the table developed in #2.

a. Find the equation of the regression line for the given data. Round the line values to the nearest two decimal places. (4 points) Show your work.

b. Using the equation found in part a, predict the sales when the mileage is 400 (remember the mileage is given in hundreds so convert 400 to hundreds). Round to the nearest thousand. (4 points)

Unit Projects should be uploaded to the Dropbox for the appropriate Unit.

Projects will be submitted as a Microsoft Word document with a doc file. All Projects are due by Tuesday at 11:59 PM ET of the assigned Unit.

NOTE: Project problems should not be posted to the Discussion threads. Questions on the project problems should be addressed to the instructor by sending an email or by attending office hours.

Instruction to copy a graph from Excel to a Word document

1. Create the graph in Excel.

2. Put your mouse in the graph area and left click. You will see little black boxes top, bottom, sides and the corners. (If desired, you can resize your graph by dragging these boxes with your mouse.)

3. With the boxes showing, choose EDIT COPY from the top menu.

4. Go to the Word document, place your mouse pointer when you want the graph and choose EDIT PASTE form the top menu.

5. Save your document.

Guidelines -- Hypothesis Testing Steps:

1. State H0 and Ha.

2. Specify the level of significance alpha .

3. Find the test statistic using the given data.

4. Find the critical value(s) t0. Use the method specified in the problem statement.

5. Define the rejection region using critical value(s)

6. Make a decision to reject or fail to reject the null hypothesis.

7. Interpret the decision in the context of the original claim.

Would you like a Math Center tutor to review your project?

Students in KU122 and MM207 may submit their projects to the Math Center for review. Tutors will not grade or correct the project, but they will provide guidance for improvement. Students should submit assignments early enough to receive feedback and make corrections before the project due date (24 hour turn-around times Monday-Thursday and 48 hour turn-around times on weekends are typical).

Email projects to: kumc@kaplan.edu. Please put "project review" in the subject line of the message.

#### Solution Summary

The solution provides step by step method for the calculation of correlation coefficient, test statistic for significance of correlation coefficient and regression analysis. Formula for the calculation and Interpretations of the results are also included.