Section 7.3: Summary of Tests Concerning Regression Coefficients

1. Explain why one might want to test if many regression coefficients at a time are equal to zero in the context of a larger model.
2. State the null and alternative hypotheses for a given claim about more than one regression coefficient in the context of a larger model.
3. State the test statistic used in a hypothesis test about more than one regression coefficient in the context of a larger model.
4. Explain, qualitatively, why an \(F\)-statistic, as used in Multiple Linear Regression, will be large when the null hypothesis is false.
5. State the null and alternative hypotheses for an “overall \(F\)-test” for a multiple linear regression.

Performing an \(F\)-test in R (Lecture Notes for Lecture 17)

1. Interpret the output of anova for an \(F\)-test.
2. Perform an \(F\)-test for a given claim about more than one regression coefficient in the context of a larger model using anova.

Common Misinterpretations of \(F\)-tests (Lecture Notes for Lecture 17)

1. Give examples where non-significant overall \(F\)-tests do not indicate that the predictors are not relevant to predicting the response.
2. Give examples where significant overall \(F\)-tests do not indicate that the MLRGN model is correct.

Section 8.3: Qualitative Predictors

1. Give examples of predictors that are appropriately modeled as categorical rather than quantitative variables.
2. Explain how to introduce a categorical predictor taking two categories into a multiple linear regression using an indicator (“dummy”) variable.
3. Interpret the coefficient on an indicator variable for a binary categorical predictor.
4. Interpret the intercept in a multiple linear regression with a single binary categorical predictor.
5. Describe, geometrically, what the coefficient on an indicator variable does to the multiple linear regression surface.
6. Explain how to introduce a categorical predictor taking more than two categories into a multiple linear regression using indicator variables.
7. Interpret the coefficients on indicator variables for a >binary categorical predictor.
8. Interpret the intercept in a multiple linear regression with a single >binary categorical predictor.

Fitting Regressions with Categorical Variables in R (Lecture Notes for Lecture 18)

1. Describe the data type used by R for categorical variables.
2. Use relevel to set the baseline level of a factor.
3. Fit a multiple linear regression with a categorical predictor in R, and interpet the resulting coefficients in the context of the problem.
4. Given the design matrix for a multiple linear regression with a categorical predictor and knowledge of which category is treated as the baseline, identify the category of a given unit using the design matrix.
5. Explain how analysis of variance (ANOVA) and analysis of covariance (ANCOVA) are related to multiple linear regression.