Q1) Expert testimony in homicide trials of battered women. Refer to the Duke Journal of Gender Law and Policy (Summer 2003) study of the impact of expert testimony on the outcome of homicide trials involving battered woman syndrome. Recall that multiple regression was employed to model the likelihood of changing a verdict from not guilty to guilty after deliberations, y, as function of juror gender (male or female) and expert testimony given (yes or no).

• Write a main efforts model for E(y) as a function of gender and expert testimony. Interpret the β coefficients in the model.
• Write an interaction model for E(y) as a function of gender and expert testimony. Interpret the β coefficients in the model.

Based on data collected on individual juror votes from past trials, the article reported that "when expert testimony was present, women jurors were more likely than men to change a verdict from not guilty to guilty after deliberations." Assume that when no expert testimony was present, male jurors were more likely than women to change a verdict from not guilty to guilty after deliberations. Which model, part a or part b, hypothesizes the relationships reported in the article? Illustrate the model with a sketch.

Q2) Insomnia and education. Many workers suffer from stress and chronic insomnia. Is insomnia from stress and chronic insomnia? Is insomnia related to education status? Researchers at the Universities of Memphis, Alabama at Birmingham, and Tennessee investigated this question in the Journal of Abnormal Psychology (February 2005). Adults living in Tennessee were selected to participate in the study using a random-digit telephone dialing procedure. In addition to insomnia status (normal sleeper or chronic insomnia), the researchers classified each participant into one of four education categories (college graduate, some college, high school graduate, and high school dropout). The dependent variable (y) of interest to the researchers was a quantitative measure of daytime functioning called the Fatigue Severity Scale (FSS), with values ranging from 0 to 5.

a. Write a main efforts model for E(y) as a function of insomnia status and education level. Construct a graph that represents the effects hypothesized by the model.

b. Write an interaction model for E(y) as a function of insomnia status and education level. Construct a graph similar that represents the effects hypothesized by the model.

c. The researchers discovered that the mean FSS for people with insomnia is greater than the mean FSS for normal sleepers, but that this difference is the same at all education levels. Based on this result, which of the two models best represents the data?

Q3) Cooling method for gas turbines. Refer to the Journal of Egineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet fogging method for a gas turbine engine. Recall that you analyzed a model for heat rate (kilojoules per kilowatt per hour) for a gas turbine as a function of cycle speed (revolutions per minute) and cycle pressure ratio. Now consider a qualitative predictor, engine type, at three levels (traditional, advanced, and aeroderivative).

a) Write a complete second-order model for heat rate (y) as a function of cycle speed, cycle pressure ratio and engine type.
b) Demonstrate that the model graphs out as three second-order response surfaces, one for each level of engine type.
c) Fit the model to the data in the GASTURBINE file and give the least squares prediction equation.
d) Conduct a global F-test for overall model adequacy.
e) Conduct a test to determine whether the second-order response surface is identical for each level of engine type.

Q4. Potency of a drug. Eli Lilly and Company has developed three methods (G, R_(1 ) and R_2) for estimating the shelf life of its drug products based on potency. One way to compare the three methods is to build regression model for the dependent variable, estimated shelf life y (as a percentage of true shelf life), with potency of the drug (x_1) as a quantitative predictor and method as a qualitative predictor.

a) Write a first-order, main effects model for E(y) as a function of potency (x_1) and method.
b) Interpret the β coefficients of the model, part a.
c) Write first-order model for E(y) that will allow the slopes to differ for the three methods.
d) Refer to part c. For each method write the slope of the y-x_1 line in terms of the β's.