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# Statistics for Observations of Randomly Selected Variables

1. The following sample observations were randomly selected.
Determine the coefficient of correlation and the coefficient of determination. Interpret.

2. The following sample observations were randomly selected.
Determine the coefficient of correlation and the coefficient of determination. Interpret the association between X and Y.

3. Bi-lo Appliance Stores has outlets in several large metropolitan areas in New England. 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:
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.

4. The production department of NDB Electronics wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows.

The dependent variable is production; that is, it is assumed that the level of production depends upon the number of employees.
a. Draw a scatter diagram.
b. Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production? Explain.
c. Compute the coefficient of correlation.
d. Evaluate the strength of the relationship by computing the coefficient of determination.

5. What are the differences between linear and non-linear trends? What are the differences among cyclical, seasonal, and irregular variations? How is each one used?

#### Solution Summary

1. The following sample observations were randomly selected.
Determine the coefficient of correlation and the coefficient of determination. Interpret.

2. The following sample observations were randomly selected.
Determine the coefficient of correlation and the coefficient of determination. Interpret the association between X and Y.

3. Bi-lo Appliance Stores has outlets in several large metropolitan areas in New England. 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:
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.

4. The production department of NDB Electronics wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows.

The dependent variable is production; that is, it is assumed that the level of production depends upon the number of employees.
a. Draw a scatter diagram.
b. Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production? Explain.
c. Compute the coefficient of correlation.
d. Evaluate the strength of the relationship by computing the coefficient of determination.

5. What are the differences between linear and non-linear trends? What are the differences among cyclical, seasonal, and irregular variations? How is each one used?

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