Find the equation of the regression line for the given data

Question

Section 1.1: 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

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

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

x	y	xy	x2	y2
-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 = {n∑xy - (∑x)( ∑y)} / {√{n∑x² - (∑x)² } {√{n∑y² - (∑x)²}}

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 numbers 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

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

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

x	y	xy	x2	y2
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

r = {n∑xy - (∑x)( ∑y)} / [√{n∑x² - (∑x)² } {√{n∑y² - (∑x)²}]

3. Using the r calculated in problem 2c test the significance of the correlation coefficient using a = 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).

1. H₀ :  

H_a:

2. a =

3. t = r / √{(1-r2) / (n - 2)} =

4. The critical value(s) t₀. 

5. Rejection region:

6. Decision:

7. Interpretation:

Section 1.2:  Linear Regression

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.  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.

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 H_a.
2. Specify the level of significance alpha a.

Find the test statistic t = r / √{(1-r2) / (n - 2)}

1. using the given data.
2. Find the critical value(s) t₀.  Use the method specified in the problem statement.
3. Define the rejection region using critical value(s)
4. Make a decision to reject or fail to reject the null hypothesis.
5. Interpret the decision in the context of the original claim.