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Here are the requirements for data analysis in your case report.
A. Describe your data using plots (scatter plots, histograms, box plots, etc.) and other statistical tools you find appropriate (a table of descriptive statistics for each variavle is pretty common).
B. Analyze the data set using linear regression models. Carry out model diagnostic analysis. If there are any violations of the model assumptions, propose and carry out possible remedies. Select the “best” model for the data set.
The minimum requirement for the data analysis includes: exploratory data analysis of your data set (summaries, plots, etc.), linear regression models and model diagnostic analysis, and appropriate remedies (e.g., transformations, if necessary). You will use the alumni giving rate as the response variable ( \(Y\) ) of interest. The potential predictors should include the percentage of classes with fewer than 20 students ( \(X_1\) ), student/faculty ratio ( \(X_2\) ), and the indicator variable private ( \(X_3\) ) (i.e., a 1 indicates a private school).
An excellent case study needs to work on selecting the “best” model for the data and/or carrying out appropriate remedies to improve the statistical inferences (e.g., you can try Box-Cox transformation if necessary). (Optional) Applying models and/or methods that are not covered in our course materials is a plus. For example, you may collect additional data/predictor variables to improve the prediction performance as a lot of useful information may be available online. You can check the out-of-sample prediction by validating the performance on the test data. You may apply different tests if needed.