You must SHOW ALL WORK for full credit (except for plots and things computed entirely in R, in which case just state "from R" and give the key commands for computations). Please staple your assignment if it is more than one page.

Question 1 is worth 50 points, 2 and 3 are 20 each, and 4 is 10 points. There is no lab this week, just follow the examples from class.

Required problems:

1) The bench press abilities of 45 males were measured, collecting data on their age (in years), height (in inches), and the amount of weight (in pounds) they could lift 5 times. The data are in the file bench.
  a) Fit the linear regression model in R using age and height as explanatory variables, and give the regression equation. Which variables are significant?
  b) What is the meaning of the coefficient for height in the context of the problem?
  c) Plot the residuals against the explanatory variables and comment on the plots.
  d) Now add a quadratic term for age, give the regression equation, and state which variables are significant.
  e) Plot the residuals against the explanatory variables and comment on the plots.
  f) Now remove height from the model and give the regression equation. Are all variables significant?
  g) Plot the residuals against the explanatory variables, make a normal probability plot of the residuals, and comment on the plots.
  h) How well does the model fit?

2) Data from Problem 11.3 with modified parts: A 4x2x2 experiment was done to investigate the effects of three factors on the insulation resulting from core-plate coatings on electrical steels. The factors were: A (four different coatings), B (two different curing temperatures), and C (two different stress-relief annealing atmospheres). Four replicate experiments were performed at each combination of factor levels with different rolls of steel. The data are in the file insulation
  (a) Use R to calculate the main effects, two-way interaction effects, and three-way interaction effects (use the lm command, as in the class example; note that the fitted effects from the R model are different from those in the book because of the different parameterization of the factors, and you can just use the values from R, don't worry about matching the book's parameterization).
  (b) What is the predicted value for coating 3 at low curing temperature and high annealing atmosphere?

3) Problem 11.5: Continuing with the data from Problem 11.3
  a) Use R to create the ANOVA table.
  b) Determine which effects are significant at the 0.05 level and interpret the results.

4) Project planning. [You may turn this part in separately on Tuesday, May 10, if you prefer.] You should have some thoughts on the project by now. You still have time to change your mind, but you should be able to give approximate answers to the following.
  a) What question are you trying to answer?
  b) What simulator will you be using?
  c) What is your response variable?
  d) What factors are you considering?
  e) Are you working by yourself? If not, who else are you working with?