Problem 2: (Revised 6.3) Magazine Advertising: In a study of revenue from advertising, data were collected for 41 magazines list as follows. The variables observed are number of pages of advertising and advertising revenue. The names of the magazines are listed as: (use sas) Magazine   P    R    Cosmopolitan    25 50 Redbook    15 49.7 Glamour    20 34 Southern Living    17 30.7 Vogue    23 27 Sunset    17 26.3 House and Garden    14 24.6 New York Magazine    22 16.9 House Beautiful    12 16.7 Mademoiselle    15 14.6 Psychology Today    8 13.8 Life Magazine    7 13.2 Smithsonian    9 13.1 Rolling Stone    12 10.6 Modern Bride    1 8.8 Parents    6 8.7 Architectural Digest 12 8.5 Harper's Bazaar    9 8.3 Apartment Life    7 8.2 Bon Appetit    9 8.2 Gourmet    7 7.3 Town and Country    1 7 True Story    77 6.6 Brides    13 6.2 Book Digest Magazine    5 5.8 W    7 5.1 Yankee    13 4.1 Playgirl    4 3.9 Saturday Review    6 3.9 New Woman    3 3.5 Ms.    6 3.3 Cuisine    4 3 Mother Earth News    3 2.5 1001 Decorating Ideas    3 2.3 Self    5 2.3 Decorating Craft Ideas   4 1.8 Saturday Evening Post    4 1.5 McCall's Needlework and Craft 3 1.3 Weight Watchers    3 1.3 High Times    4 1 Soap Opera Digest    2 0.3 Fit a linear regression equation relating advertising revenue to advertising pages. Verify that the fit is poor. Choose an appropriate transformation of the data and fit the model to the transformed data. Evaluate the fit. You should not be surprised by the presence of a large number of outliers because the magazines are highly heterogeneous and it is unrealistic to expect a single relationship to connect all of them. Find outliers and high leverage points. Delete the outliers and obtain an acceptable regression equation that relates advertising revenue to advertising pages. For the deleted data, check the homogeneity of the variance. Choose an appropriate transformation of the data and fit the model to the transformed data. Evaluate the fit.

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Problem 2: (Revised 6.3) Magazine Advertising: In a study of revenue from advertising, data were collected for 41 magazines list as follows. The variables observed are number of pages of advertising and advertising revenue. The names of the magazines are listed as:

(use sas)

Magazine   P    R   
Cosmopolitan    25 50
Redbook    15 49.7
Glamour    20 34
Southern Living    17 30.7
Vogue    23 27
Sunset    17 26.3
House and Garden    14 24.6
New York Magazine    22 16.9
House Beautiful    12 16.7
Mademoiselle    15 14.6
Psychology Today    8 13.8
Life Magazine    7 13.2
Smithsonian    9 13.1
Rolling Stone    12 10.6
Modern Bride    1 8.8
Parents    6 8.7
Architectural Digest 12 8.5
Harper's Bazaar    9 8.3
Apartment Life    7 8.2
Bon Appetit    9 8.2
Gourmet    7 7.3
Town and Country    1 7
True Story    77 6.6
Brides    13 6.2
Book Digest Magazine    5 5.8
W    7 5.1
Yankee    13 4.1
Playgirl    4 3.9
Saturday Review    6 3.9
New Woman    3 3.5
Ms.    6 3.3
Cuisine    4 3
Mother Earth News    3 2.5
1001 Decorating Ideas    3 2.3
Self    5 2.3
Decorating Craft Ideas   4 1.8
Saturday Evening Post    4 1.5
McCall's Needlework and Craft 3 1.3
Weight Watchers    3 1.3
High Times    4 1
Soap Opera Digest    2 0.3
  1. Fit a linear regression equation relating advertising revenue to advertising pages. Verify that the fit is poor.
  2. Choose an appropriate transformation of the data and fit the model to the transformed data. Evaluate the fit.
  3. You should not be surprised by the presence of a large number of outliers because the magazines are highly heterogeneous and it is unrealistic to expect a single relationship to connect all of them. Find outliers and high leverage points. Delete the outliers and obtain an acceptable regression equation that relates advertising revenue to advertising pages.
  4. For the deleted data, check the homogeneity of the variance. Choose an appropriate transformation of the data and fit the model to the transformed data. Evaluate the fit.
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