Consider the file showing data for magazine titles, the cost of a full-color page advertisement (page), audience (subscribers), male percentage of subscribers, and median household income. The main objective of this project is 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 the data set. The following is a minimum guideline about what you should analyze. You need to do more in-depth analysis for a better grade than a C. You may have to use such tools as confidence interval estimates, one or two-sample tests on the data to improve the quality of your report.
a) State your statistical objective for this data set.
b) Construct scatter diagrams for pairs of variables. Describe the relationship that you may see. Do these appear to have some association (linear or non-linear)?
c) Does the linear model appear to hold for any pair of variables? You may want to run some testing including LINE analysis to substantiate why or why not.
d) Apply the best-subsets approach to model building to see if there is any variable that shouldn't be used for this model.
e) 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 approach give you a meaningful (better) output for this model since some households use male names to subscribe any magazine?
f) Can you introduce any other dummy variables to improve your analysis? A new dummy variable can be created within the data or external data. For example, classify magazines as "entertainment" and "professional/hobby," and then apply the same approach of e) to the data set with a new dummy variable.
g) Once you determine which variables are to be used, perform a multiple regression analysis, including collinearity, on this subset of variables.
h) Summarize and comment on your results.