R language:

Data:

library(faraway)

hsb = faraway : : hsb

6. The "High School and Beyond" data is found in hab. (a) Model the math score in terms of the five factors: gender, race, ses, schtyp and prog. Include all second-order interactions but no higher order interactions. How many regression parameters does your model use? Explain how this can be calculated in terms of the number of levels for each factor. (b) Determine whether some two-way interactions can be eliminated using the anova function. (c) Determine whether some two-way interactions can be eliminated but now us- ing the dropl function. Why do the results differ from the previous question? Which method of testing should be preferred? (d) Fit a model with only main effects and compare it to the model with all two- way interactions. Which model should be preferred? (e) Determine which main effects are statistically significant and report on the differences you find. (f) Check the regression diagnostics for the main effects only model and report on any anomalies