# MAT 411 HW2

Goal: Predict the number of applications received (Apps) using the other variables in the College data set (see Data description).

• Fit a multiple regression model to predict Apps using other variables.
• Provide an interpretation of each coefficient in the model. Be careful—some of the variables in the model are qualitative!
• Write out the model in equation form, being careful to handle the qualitative variables properly.
• For which of the predictors can you reject the null hypothesis H0 : βj = 0?
• On the basis of your response to the previous question, fit a smaller model that only uses the predictors for which there is evidence of association with the outcome.
• Is your smaller model equivalent to your full model? Carry out the F test.

Split the data set into a training set and a test set (half and half). Evaluate your model using test data.

• Find a best model based on the subset method.
• Find a best model based on the forward selection.
• Find a best model based on the backward selection.

Comparing your models, do you get the same model?