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Conducting Simple Regression and Interpretating the Results

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1.The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. A random sample of 12 equalized stores is selected, with the following results.

Store Shelf Space(X) Weekly sales(Y)
1 5 160
2 5 220
3 5 140
4 10 190
5 10 240
6 10 260
7 15 230
8 15 270
9 15 280
10 20 260
11 20 290
12 20 310

a) Construct a scatter plot. For these data, b0 = 145 and b1 = 1 7.4
b) Interpret the meaning of the slope, b1, in this problem
c) Predict the weekly sales of pet food for stores with 8 feet of shelf space for pet food.

2.
In Problem 13.4 on page 481, the marketing manager used shelf for pet food to predict weekly sales (stored in Petfood). For those data SSR = 20,535 and SST = 30,025
a. Determine the coefficient of determination, r2, and interpret its meaning.
b. Determine the standard error of the estimate.
c. How useful do you think this regression model is for predicting sales

3. Circulation is the lifeblood of a publishing business. The larger the sales of a the publisher's reports of magazine newsstand sales and subsequent audits by magazine, the more it can large advertisers. However, a circulation gap has appeared between the Audit Bureau of Circulations give the following results:
Magazine Reported (X) Audited(Y)
YM 621.0 299.6
CosmoGirl 359.7 207.7
Rosie 530.0 325.0
Playboy 492.1 336.3
Esquire 70.5 48.6
TeenPeople 567.0 400.3
More 125.5 91.2
Spin 50.6 39.1
Vogue 353.3 268.6
Elle 263.6 214.3

a. Construct a scatter plot
b. For these data, bo = 26.724 and b1 = 0.5719
c. Interpret the slope, b1, in this problem
d. Predict the audited newsstand sales for a magazine the reports the newsstand sales of 400,000
e. Determine the coefficient of determination, r2,and interpret its meaning
f. Determine the standard of error of the estimate.
g. How useful do you think this regression model is for predicting sales?

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The solution gives detailed steps on conducting the simple regression and interpretating the results.

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Performing Simple Regression and Interpretating Results

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The following problems are to be solved by Excel and/or MegaStat. You need to find the values on the excel regression solutions and interpret them. Part 1 is a simple linear regression as done in the chapter 13 assignment. You should only include Y (fuel consumption) and X1 (temperature) for this analysis. Part 2 is a multiple regression and its solution is just an extension of the linear regression solution. Now you should enter the Y values and both of the X values at the same time. Be sure to include your regression solutions/printouts in your submission using copy/paste.
It was felt by the local utility company that fuel consumption (natural gas) in their small town would be affected by temperature. The following data (ordered by Fuel consumption) was collected for 10 weeks during the winter. FIRST, conduct a linear regression analysis between fuel consumption, Y, and temperature, X1, using Excel or MegaStat. Use alpha = 0.05 and 1.01 for t-tests.
a. What is the Bivariate regression equation using only the first two variables? Interpret it and predict fuel consumption at temperature equal to 50 degrees.
b. Is the slope coefficient in the linear regression model between temperature and fuel consumption statistically significant at alpha=.05 and 0.01? How do you know? Show your test.
d. What is the value of the correlation coefficient, (r)? Interpret. What is the value of the coefficient of determination, R2? Interpret. What is the value of the standard error of the estimate, se?

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