4. You are the assistant manager of a gift shop at the mall. The shop specializes in merchandise with a College theme. The store’s 2006 operating statements provide the following data:

You buy your merchandise from various suppliers and mark it up, so that after paying for all the freight, damage, shrinkage, and obsolescence costs, you achieve an average gross margin of 50%. Thus, for a $20 sale, your cost of goods will be $10. Your lease requires that you pay a monthly minimum of $2,000 plus 10% of any sales over $40,000. For example, in May, 2006, sales were $42,440 so the lease payment was $2,000 + $244. All of your other costs, except the cost of goods, lease payment, wages, and utilities, take 10% from each sales dollar.

You are preparing your budget for 2007 and would like to estimate your various expenses. You believe that both wages and utilities are related to sales volume. You will run simple linear regression models to predict either wages or utilities from sales volume.

THE QUESTIONS:

1. According to the EXCEL print out, what is the estimated regression to predict wages from sales volume? What practical interpretation can we give to the regression’s estimated slope? What sort of relationship exists between wages and sales volume? Is it direct or indirect? What is the correlation coefficient between these two variables?
2. According to the EXCEL print out, what is the estimated regression to predict utilities from sales volume? What practical interpretation can we give to the regression’s estimated slope? What sort of relationship exists between utilities and sales volume? Is it direct or indirect? What is the correlation coefficient between these two variables?
3. What percentage of the variability in wages can be explained by the simple linear regression with sales volume? What percentage of the variability in utilities can be explained by the simple linear regression with sales volume?
4. Is sales volume a useful predictor for wages? For utilities? Explain briefly.
5. Create an Excel spreadsheet to forecast your operating profit for 2007. You project that month-by-month sales volume will be 20% higher than their 2006 levels.
   1. Determine your projected sales volume for each month of 2007.
   2. Using the estimated regression equations, predict (1) wages and (2) utilities for each month of 2007.
   3. Using the forecasted sales volume data, compute the predicted levels of rent and other costs for each month. What will be your predicted monthly operating profit for each month of 2007?

5. Suppose a large consumer products company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, two types of advertising media are to be considered: radio and television advertising and newspaper advertising (including the cost of discount coupons). A sample of 22 cities with approximately equal populations is selected for study during a test period of 1 month. Each city is allocated a specific expenditure level for both radio and television advertising and newspaper advertising. The sales of the product (in thousands of dollars) and also the levels of media expenditure during the test month are recorded with the following results:

1. Find the least squares regression equation.
2. Interpret the meaning of the slope for Newspaper.
3. What is the error (residual) degree of freedom?
4. Use an F test to investigate the usefulness of the model in part 1, with = 0.01. State your conclusion in the context of the problem.
5. Test H ₀ : ₁ = 0 versus ₁ 0 using = 0.05. Do the results of your test suggest that the level of expenditure in Radio and TV is a useful predictor of Sales?
6. Find R ² , and interpret its value in the context of the problem.
7. Using a 95% confidence interval, predict the sales for a city in which radio and television advertising is $20,000 and newspaper advertising is $20,000.
8. Is Newspaper a useful predictor of Sales? Explain.
9. Find a 90% confidence interval for ₂ . Interpret your result in the context of the problem.
10. What is value of adjusted R ² ? Interpret this number.
    6. USE THE FOLLOWING INFORMATION FOR THE NEXT THREE QUESTIONS :
    The owners of the Hooters franchise in Southwest Florida want to obtain a regression model to predict sales of their new hot weather treat: A chocolate-covered frozen Spotted Owl. We expect sales to be higher on weekends and in the warmer months. So we used a dummy variable WKEND which is 1 for Saturday or Sunday and 0 otherwise. And dummy variables for quarter 2, 3, 4. (Quarter 1 was the base level). The regression model we used for daily sales was:
    E(SALES) = 0 +1 WKEND + 2 Q2 +3 Q3 +4 Q4

    Regression Statistics
    Multiple R
    R Square
    Adjusted R Square
    Standard Error	23.2265
    Observations	19
    ANOVA
    	Df	SS	MS	F	p
    Regression	4	21095.44			0.0002
    Residual	14	7552.56
    Total	18	28648.00
    	Coefficients	Standard Error	t Stat	P-value
    Intercept	12.790	1.410	9.071	0.0000
    WKEND	17.690	13.152	1.34	0.1000
    Q2	13.780	4.280	3.220	0.0062
    Q3	37.200	6.110	6.088	0.0000
    Q4	8.200	1.480	5.541	0.0001

    1. Predict the sales of chocolate-covered frozen Spotted Owls on a Saturday in the second quarter of the year, with a high temperature of 80 degrees and an expected crowd of 2100 people on Galveston Beach.
    2. Compute R-Square.
    3. Test (at = 0.05) to see if there is a significant relationship between the SALES and WKEND. What is the p-value for the test?

7 . Ms. Jones is an employee of a well-known accounting firm’s management services division. She is currently on a consulting assignment to the Apex Corporation, a firm that produces corrugated paper for use in making boxes and other packing materials. Apex called in consulting help to improve its cost control program, and Ms. Jones is analyzing manufacturing costs to understand more fully the important influences on these costs. She has assembled monthly data on a group of variables and she is using regression analysis to help her assess how these variables are related to total manufacturing costs. The variables Ms. Jones has selected to study are

y, total manufacturing cost per month in thousands of dollars (COST)

x ₁ , total production of paper per month in tons (PAPER)

x ₂ , total machine hours used per month (MACHINE)

x ₃ , total variable overhead costs per month in thousands of dollars (OVERHEAD)

x ₄ , total direct labor hours used each month (LABOR)

Using the EXCEL printout below to answer the following questions:

1. If Ms. Jones wants use a cost function to estimate the total manufacturing cost per month, developed by means of regression analysis, what would that function look like?
2. Conduct the F test for overall fit of the regression. What conclusion can be drawn from the result of the test and why? Use a 5% level of significance.
3. In the cost-accounting literature, the sample regression coefficient corresponding to x _k is regarded as an estimate of the true marginal cost of output associated with the variable x _k . Find a 95% confidence interval estimate of the true marginal cost associated with total paper production per month.
4. Using a 95% confidence interval, forecast the total manufacturing cost per month when x ₁ = 845, x ₂ = 376, x ₃ = 200, and x ₄ = 590.

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