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# Regression analysis

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3. 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.

A study of 20 worldwide financial institutions showed the correlation between their assets and
pretax profit to be .86. At the .05 significance level, can we conclude that there is positive correlation
in the population?

A recent article in Business Week listed the "Best Small Companies." We are interested in the current
results of the companies' sales and earnings. A random sample of 12 companies was selected
and the sales and earnings, in millions of dollars, are reported below.

Let sales be the independent variable and earnings be the dependent variable.
a. Draw a scatter diagram.
b. Compute the coefficient of correlation.
c. Compute the coefficient of determination.
d. Interpret your findings in parts b and c.