Use of the best-subsets approach to model building

Consider the file advertising.xls showing data for magazine titles, the cost of a full-color page advertisement (page), audience (subscribers), male percentage of subscribers, and household income. The objective of this project is: you are a consultant to a company that has asked you to find out if there is any relationship among variables using regression analysis techniques. You are to write a report about your findings after analyzing this data set. The following is a minimum guideline about what you should analyze. You need to do more analyses for a better grade than a C, for example, adding more variables from your own research and construct a better model.

1. State your statistical objective for this data set.
2. Perform exploratory data analysis, such as numerical measures or the box-and-whisker plot for this data set.
3. Construct scatter diagrams for pairs of variables. Describe the relationship that you may see. Do these appear to be some association?
4. Does the linear model appear to hold for any pair? You may want to run some testing to substantiate why or why not.
5. Apply the best-subsets approach to model building to see if there is any variable that shouldn’t be used for this model.
6. Consider the male percentage of subscribers as categorical data, for example, if it is more than 66%, input as "male magazine," between 66% and 33% as "gender free," and less than 33% as "female magazine." Then introduce dummy variables for these data. Will this give you a meaningful (better) output for this model since some households use male names to subscribe any magazine? Can you introduce dummy variables to this data set so that you can model the data better for multiple regression analysis?
7. Include an interaction term in the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model.
8. Once you determine which variables are to be used, perform a multiple regression analysis, including collinearity, on this subset of variables.
9. Summarize your results.

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Solution: The downloadable solution consists of 21 pages, 1134 words and 34 charts.
Deliverable: Word Document