a) Analyze the distribution of Grad.Rate and discuss if the distribution is symmetric, or if you need to apply any transformation (This is the data exploration stage, therefore use the appropriate statics to explore your data).
b) Create scatterplots for Grad.Rate vs each of the independent variables. What conclusions can you draw about the relationships between Grad.Rate and the independent variables? (No need to include the scatterplots in your submission).
c) Build boxplots to evaluate if graduation rates vary by university type (private vs public) and by status (elite vs not elite). Include the boxplots and discuss your findings. (See SAS Procedures section on D2L if you need the code to generate a boxplot).
d) Fit a full model (with all independent variables) to predict Grad.Rate. Discuss the parameter estimates, significance, goodness-of-fit and AdjR2 values. Include the relevant output.
e) Does multi-collinearity seem to be a problem here? What is your evidence? Compute and analyze the VIF statistics. Include the relevant output and discuss your answer.
f) Apply TWO variable selection procedures to find an optimal subset of independent variables to predict Grad.Rate. You can choose any two procedures among the ones we learned in class: backward selection, forward selection, adj-R2, Cp, stepwise. Make sure to include the o/p of the 2 selection methods. No need to discuss the models, include the outputs.
g) Fit a final regression model M1 for Grad.Rate based on the results in f) – i.e. optimal model. Explain your choice. Write down the expression of the estimated model M1.
h) Draw a plot of the studentized residuals against the predicted values. Does the plot show any striking pattern indicating problems in the regression analysis? Include the outputs and explain.
i) Analyze normal probability plot of residuals. Is there any evidence that the assumption of normality is not satisfied? Include the outputs and explain.
j) Are there any outliers or Influential Points? Compute appropriate statistics. Include the outputs. Take any action you think is necessary and explain why/why not you took these actions?
k) Analyze the AdjR2 value for the final model and discuss how well the model explains the variation in graduation rates among the universities.
l) Draw conclusions on graduation rates based on your regression analysis. What are the most important predictors in your model? Does your model show a significant difference in graduation rates between private and public universities? Do “elite” universities have higher graduation rates? Explain.
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