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Hypothesis testing and Regression

1. Bi-lo Appliance Stores has outlets in several large metropolitan areas. The general sales manager plans to air a commercial for a digital camera on selected local TV stations prior to a sale starting on Saturday and ending Sunday. She plans to get the information for Saturday - Sunday digital camera sales at the various outlets and pair them with the number of times the advertisement was shown on the local TV stations. The purpose is to find whether there is any relationship between the number of times the advertisement was aired and digital camera sales.

The pairings are:
Location of TV Station Number of Airings Saturday-Sunday Sales ($ thousands)
Buffalo 4 15
Albany 2 8
Erie 5 21
Syracuse 6 24
Rochester 3 17

a. What is the dependent variable?
b. Draw a scatter diagram.
c. Determine the coefficient of correlation.
d. Determine the coefficient of determination.
e. Interpret these statistical measures.

2. The Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the correlation was .78. At the .01 significance level, is the correlation in the population greater than zero?

3. The following sample observations were randomly selected.

X: 5 3 6 3 4 4 6 8
Y: 13 15 7 12 13 11 9 5

a. Determine the regression equation.
b. Determine the value of Y when X is 7.