Supposeanalysts at a company that produces small appliances are looking at sales of 24 food preparation products in a medium-sized city in the Midwest U.S. They have noticed that sales have not met forecasted values for several months and want to look at the issue in more detail. You'll begin by specifying a model given the data in the file called Food Prep. After answering a series of questions, you'll highlight the key findings of the regression analysis.

Step 1: Specify the Model

Specify (write it out) a regression equation for sales with all of the independent variables included. Use proper subscripts and Greek letters where appropriate.

Step 2: Hypothesize the Signs of the Coefficients

For all four independent variables, hypothesize the sign of each regression coefficient. Explain your reasoning.

Step 3: Summary Statistics

Check the means, maximums, and minimums for each of the variables. Do you see any issues with the data?

Step 4: Estimation

Run the regression using all four independent variables and provide a copy of your regression results.

Step 5: Hypothesis Testing (t-statistics)

Test the slope coefficients of the independent variablesat the 5-percent level of significance. Show your null and alternative hypotheses and list the critical t-statistic used for each hypothesis test. For which coefficients can you reject the null hypothesis?

Step 6: Hypothesis Testing (p-values)

Test the slope coefficients of the independent variablesat the 5-percent level of significance using the probability values. For which coefficients can you reject the null hypothesis?

Step 7: Interpret coefficients

Interpret the coefficient for each independent variable.

Step 8: Model Evaluation

Evaluate the performance of the total model using the R-squared and Adjusted R-Squared values.

Step 9: Overall F-test

Use the overall Fstatistic to test whether the regression is significant at the 5-percent level. Show your null and alternative hypotheses and your decision rule using the F-table.

Step 10: Drawing Conclusions

Highlight key conclusions of the regression. What have you learned from your regression model? What conclusions would you share with the company analysts?

DATA IN THE TABLE BELOW:

Sales ($)	Advertising ($)	# Competitors	Discounts	Warranty (years)
4565	459	1	1	2		Sales = monthly sales ($)
4896	545	0	0	0.25		Advertising = advertising expenditures ($)
4480	472	2	2	1		Number of competitors = number of competing products available
4300	482	3	3	2		Discounts = number of available discount opportunities (sales, coupons, etc) offered during the month
3502	435	3	3	0.25		Warranty = warranty period of the appliance in years
4413	499	3	3	1
5868	604	0	0	1
4527	501	1	1	1
3849	370	3	3	1
5645	605	0	0	2
4665	557	1	0	2
5122	491	0	0	1
5248	443	0	0	1
5619	513	0	0	1
5419	424	1	1	2
5043	577	0	0	0.25
5207	538	1	0	2
4564	460	1	1	1
3799	464	2	2	1
4802	456	1	1	2
4959	525	1	0	1
4830	510	1	1	1
3694	479	3	2	0.25
5036	521	1	0	2