Buad 310 Case Analysis Instruction

BUAD 310 Spring 2013 Case Due by 4PM on Friday, May 3rd (in BRI 400C) In this case you will apply statistical techniques learned in the Regression part of BUAD 310. Please read the following instructions carefully before you start: • This assignment uses data from the file MagAds13S. XLS, which you can download from Blackboard. After you download the file go to Data > Load data > from file in StatCrunch to open it (you don’t need to change any of the options when loading this data. ) • The entire report should be typed and clearly presented without typos and grammatical errors.

Copy and paste the relevant (explained further in more detail) regression output into your document. Do not attach any graphs. • You are encouraged to work in groups (maximum size is 5). Any group submits only one report, in which the first page should have all the names and USC ID of the group members. A hard copy of the report needs to be submitted (an electronic copy is NOT acceptable). Before May 3rd, you can also hand in the report during class. When I am not in my office (BRI 400C), please drop the report in the office through the gap between the door and floor. Very important: present the problems in exactly the same order as they are listed. • A note to Mac user: you might need to hold “shift” when selecting variables for the X-variables with multiple linear regression in StatCrunch. Magazine Advertising What factors influence the price of advertisements in magazines? Suppose you are part of a team of consultants hired by a retail clothing company wishing to place advertisements in at least one magazine. They are curious about what types of costs they can expect for magazines with different readership bases so they most effectively utilize their advertising budget.

Your team has collected cost data on 44 consumer magazines. In addition, your team has measured some other characteristics of the magazines and their audiences that may be useful in understanding the advertisement costs better. The variables are as follows, pagecost: Cost of a four-color, one-page ad (in dollars) circ: Circulation (projected, in thousands) percmale: Percent male among the predicted readership medianincome: Median household income of readership (in dollars) Some natural logarithms of the variables are also provided for your convenience.

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Your goal is to analyze the data with StatCrunch using Multiple Linear Regression methods and choose the best model to explain the differences in advertising costs between the different titles, and then to predict what the retail clothing company should expect to pay for advertising in the different magazines. Answer the following questions (with reasonable detail, not just “yes” or “no”, use one or two sentences per question). 1. Visually examine the scatter plots of the response variable, pagecost, versus each of the explanatory variables (circ, percmale, medianincome).

In StatCrunch you can go to [Graphics( Scatter Plot] to do each plot. Describe the form and the direction of each relationship. Do not attach any graphs. 2. Perform a Regression analysis to predict pagecost using all three explanatory variables [Stat ( Regression ( Multiple Linear, then fill in the proper Response and Predictor variables, then click Next twice and under Save options select Residuals, Predicted values and 95% interval for either the mean or an individual (you will have to decide which one you need for part d! ). For he CI (or PI) to be produced you need to enter the values from part d in the row underneath the data table, in appropriate columns. Note that the value for circ has to be entered in the same units as all the values in the circ column. To produce a residual plot do a Scatter plot as in question 1, selecting Residuals as the Y variable and Predicted values as the X variable]. Include the regression output, but not the plot. a. Use the R-squared and the F-test to comment on the usefulness of the regression model you fitted (use the significance level of 5% for the test). b.

Evaluate the regression assumptions by assessing the residual plot. c. Examine each of the explanatory variables individually to determine which are contributing significantly to the model. (Use the significance level of 5 %. Do NOT actually eliminate any variables from the regression at this stage. ) d. Using the same model with all the variables, provide an appropriate 95%-level interval to the retail clothing company for the amount that they would pay for a full-page ad in a magazine with a projected audience of 2,000,000 readers, 55 percent of which are male, with a median income of $30,000.

Explain in one sentence and in simple terms what this interval means. 3. Rerun the regression in part 2 with circ replaced by LN_circ (the natural logarithm of the variable circ), keeping all the other variables the same. Include the relevant regression output (only the coefficient and ANOVA tables). [Stat ( Regression ( Multiple Linear, then fill in the proper Response and Predictor variables, then click Next twice and under Save options select Residuals and Predicted values. Produce a residual plot the same way as in question 2]. a.

How does this model compare to the previous model using R-squared? Explain what this difference in the R-squared values means in simple terms. b. Evaluate the regression assumptions by assessing the residual plot. c. Examine each of the independent variables individually to determine which are contributing significantly to the newest model. (Use the significance level of 5 %. Do NOT actually eliminate any variables from the regression at this stage. ) 4. Rerun the regression in part 3 with LN_pagecost (the natural logarithm of pagecost) as the response (i. . the explanatory variables are LN_circ, percmale and medianincome). Include the regression output. [Stat ( Regression ( Multiple Linear, then fill in the proper Response and Predictor variables, then click Next twice and under Save options select Residuals, Predicted values and 95% interval for either the mean or an individual (you will have to decide which one you need for part d! ). For the CI (or PI) to be produced you need to enter the values from part d in the row underneath the data table, in appropriate columns.

Note that the value for LN_circ has to be entered in the same units as all the values in the LN_circ column. Also note that the interval will be produced for the LN_pagecost variable. To produce a residual plot do a Scatter plot as in question 1, selecting Residuals as the Y variable and Predicted values as the X variable]. a. Evaluate the regression assumptions by assessing the residual plot. b. Examine each of the explanatory variables individually to determine which are contributing significantly to the new model. Use a significance level of 5%. . Remove the variables you find insignificant and re-run the model. Include the regression output for the new model. d. Using the new model, provide an appropriate 95% -level interval to the retail clothing company for the amount they would pay for a full-page ad in a magazine with the values given in 2. d (projected audience of 2,000,000 readers, 55 percent of which are male, with a median income of $30,000) using the newest model. Explain in one sentence and in simple terms what this interval means. EXECUTIVE SUMMARY: (roughly about ? to 1 page)

You are given the task of summarizing your findings for the board of directors of the retail clothing company. Since they are not very well-versed in regression techniques, you will need to explain things in easy-to-understand, simple and practical terms. Make sure to answer the following questions within the summary: 1. Describe each of the models you considered in parts 2-4 and how these models estimate the relationship between the cost of one-page ad and each of the explanatory variables (for each of the models you will need about one sentence per explanatory variable). . Specify which model you would recommend to best forecast the cost of one-page advertisements. Explain why this model should work well and why you picked this particular model from the ones you tried (go over the positives you see for this model and the negatives for the other models). • Reminder: include only the relevant regression output in your final document. Do not attach or include any graphs.

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