Section 8.1: Polynomial Regression Models

1. Define a polynomial regression.
2. Construct a design matrix for a given polynomial regression.
3. Explain why it is not, generally, a good idea to fit a very high degree polynomial to predict a response variable from a predictor variable.
4. Fit a polynomial regression in R using poly.
5. Fit a polynomial regression in R using poly with the argument raw = TRUE, and explain how this differs from using poly with the argument raw = FALSE.
6. Explain why it may make sense to use a polynomial regression even when you do not believe the expected relationship between the predictor and the response is polynomial.

Section 8.2: Interaction Regression Models

1. State the definition of non-interaction between two or more variables in terms of an appropriate partial derivative.
2. Construct a design matrix that would incorporate a simple product interaction into a multiple linear regression model.
3. Interpret the coefficient on a product term of two quantitative predictors in a multiple linear regression.
4. Explain why the “expected change in the response for a unit change in the predictor, holding all other predictors constant” interpretation of a coefficient no longer makes sense when an interaction term is included in a multiple linear regression.
5. Fit a multiple linear regression model with interaction terms in R using : and *.
6. Interpret the output of lm when used to fit a multiple linear regression model with an interaction term.
7. Give examples of models with interactions where an estimated multiple linear regression (without the interaction term) and its coefficient estimates would be highly significant, but the model is clearly wrong.

Section 8.5: Modeling Interactions Between Quantitative and Qualitative Predictors

1. Construct a multiple linear regression model with an interaction between two categorical predictors.
2. Interpret the coefficients in a multiple linear regression model with an interaction between two categorical predictors.
3. Construct a multiple linear regression model with an interaction between a categorical predictor and a quantitative predictor.
4. Interpret the coefficients in a multiple linear regression model with an interaction between a categorical predictor and a quantitative predictor.
5. Explain, geometrically, what an interaction between a categorical predictor and a quantitative predictor incorporates into a multiple linear regression model.