Project #18531 - stats

BUAD 310 Fall 2013 Case 

Due by 4PM on Friday, December 6 (in HOH 523) 

 

In this case you will apply statistical techniques learned in the Regression part of BUAD 310. 

 

Instructions: 

 

• This assignment uses data from the file MagAds.xlsx, 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) and submit one 

assignment for the whole group. A hard copy of the assignment needs to be 

submitted (rather than an electronic copy) to avoid a penalty on the grade. 

 

• Very important: present the problems in exactly the same order as they are listed. 

 

 

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. 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 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. Perform a Regression analysis to predict pagecost using all three explanatory variables 

 

[Stat → Regression → Multiple Linear, then fill in the proper Y variable and X variables 

(hold the “Ctrl” key when selecting the X variables), then scroll to the bottom of the screen 

and under Save options select (holding Ctrl) Residuals, Predicted values and 95% confidence 

interval for individual prediction. For the prediction interval to be produced you need to first 

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, go to [Graphics→ Scatter Plot], then select Residuals as 

the Y variable and Predicted values as the X variable]. 

 

 

Include the regression output (only the coefficient and ANOVA tables), but not the plot. 

 

 

a. Explain, in simple terms, the R-squared value that you got. 

 

 

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. 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 

1,400,000 readers, 50 percent of which are male, with a median income of $22,000. 

 

Explain in one sentence and in simple terms what this interval means. 

(i have done this. so start from 2 to end. i will upload the answers so u can make the summary for the last question.)

 

 

2. Rerun the regression in part 1 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 follow the guidelines given in part 1]. 

 

 

a. How does this model compare to the previous model using R-squared? Calculate the 

difference in the R-squared values and explain what it 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.) 

 

 

  

3. Rerun the regression in part 2 with LN_pagecost (the natural logarithm of pagecost) as the 

response (i.e. the explanatory variables are LN_circ, percmale and medianincome). 

Include the relevant regression output. 

 

[Stat → Regression → Multiple Linear, then follow the guidelines given in part 1. For the 

prediction interval 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]. 

 

 

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%. 

 

c. 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 1.d (projected audience of 1,400,000 readers, 50 percent of which are male, with 

a median income of $22,000) using the newest model. 

 

 

Explain in one sentence and in simple terms what this interval means. 

Compare with the interval in part 1; which one would you use for prediction and why? 

 

 

 

EXECUTIVE SUMMARY: (roughly about ¾ 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 1-3. Interpret each of these models with 

respect to the relationship between the cost of one-page ad and each explanatory variable 

(interpret each slope coefficient in each model, except the one for LN_circ in part 2; for each 

of the models you will need about one sentence per coefficient). 

 

2. 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.

Subject Business
Due By (Pacific Time) 12/04/2013 12:00 am
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