# Project #18531 - stats

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:

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.

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

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

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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