Chapter 14, Problem 49PS

The director of a training program for a large insurance company has the business objective of determining which training method is best for training underwriters. The three methods to be evaluated are classroom, online, and courseware app. The 30 trainees are divided into three randomly assigned group of 10. Before the start of the training, each trainee is given a proficiency exam that measures mathematics and computer skills. At the end of the training, all students take the same end-of-training exam.

The results are organized and stored in Underwriting.

Develop a multiple regression model to predict the score on the end-of-training exam, based on the score on the proficiency exam and the method of training used. For (a) through (k), do not include and interaction term.

a. State the multiple regression equation.

b. Interpret the regression coefficients in (a).

c. Predict the mean end-of-training exam score for a student with a proficiency exam score of 100 who had courseware app-based training.

d. Perform a residual analysis on the model score for a student with a proficiency exam score of 100 who had courseware app-based training.

e. Is there a significant relationship between the end-of-training exam score and the independent variables (proficiency score and training method) at the 0.05 level of significance?

f. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.

g. Construct and interpret a $\text{95\%}$ confidence interval estimate of the population slope for the relationship between the end-of-training exam score and the proficiency exam score.

h. Construct and interpret a $\text{95\%}$ confidence interval estimate of the population slope for the relationship between the end-of-training exam score and type of training method.

i. Compute and interpret the adjusted $r^2.$

j. Compute the coefficients of partial determination and interpret their meaning.

k. What assumption about the slope of proficiency score with end-of-training exam scare do you need to make in this problem?

l. Add interaction terms to the model and, at the 0.05 level of significance, determine whether any interaction terms make a significant, contribution to the model.

m. On the basis of the results of (f) and (l), which model is most appropriate? Explain.