Question 1: Consider a multiple regression model for a response y, with one quantitative independent variable x1, and one qualitative variable at three levels.
a) Write a first-order model that relates the mean response E(y) to the quantitative independent variable.
b) Add the main effect terms for the qualitative independent variable to the model of part a. Specify the coding scheme you use.
c) Add terms to the model of part b to allow for interaction between the quantitative and qualitative independent variables.
d) Under what circumstances will the response lines of the model in part c be parallel?
e) Under what circumstances will the model in part c have only one response line?
Question 2: For decades people have traveled from all around to see the famous frog-jumping contest each May in Calaveras County, California. Bullfrogs at least four inches long are entered in the contest to see which can move the farthest in three jumps. A small Missouri town decides to hold its own version of this contest. One first-time spectator bets her spouse that the average distance in three jumps for all bullfrogs of this size is 180 inches. Her spouse doubts this claim and takes the bet. There are 13 frogs entered in this competition. The contest begins and the distances recorded are as follows (in inches):
150.50 155.50 158.75 160.50 165.25 181.00 181.75
185.00 185.25 215.75 216.50 220.00 250.25
Assuming these frogs can be considered a representative sample, is there evidence that the “average” distance that bullfrogs at least four inches long travel in three jumps is not 180 inches?