The director of a training program for a large insurance company has the busines
ID: 3175238 • Letter: T
Question
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 groups 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. 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. Complete parts a through f below.
a.State the multiple regression equation. Use proficiency exam score as X1. Define the dummy variable X2 as X2 = 1 if the training method is classroom, X2 = 0 otherwise. Define the dummy variable X3 as X3 = 1 if the training method is online, X3 = 0 otherwise.
b. Interpret the regression coefficients in a.
c. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model.
d. Construct and interpret a 95% confidence interval estimate of the population slope foe the relationship between the endoftraining exam score and the proficiency exam score.
e. 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.
f. On the basis of the results of c and e, which model is more appropriate?
End_of_Training Proficiency Method 14 94 classroom 18 96 classroom 18 97 classroom 39 101 classroom 40 101 classroom 26 105 classroom 41 110 classroom 28 110 classroom 36 111 classroom 65 130 classroom 37 79 online 35 85 online 43 90 online 44 97 online 61 97 online 62 112 online 93 115 online 74 117 online 76 120 online 79 119 online 55 92 courseware_app 53 95 courseware_app 54 100 courseware_app 52 102 courseware_app 34 102 courseware_app 47 104 courseware_app 57 106 courseware_app 55 109 courseware_app 41 111 courseware_app 80 117 courseware_appExplanation / Answer
(a)
(b) using software the regression alalysis showed following information
regression equation y=-63.47+1.12X1-22.2X2+8.38X3
(b and c) X1 has significant positive impact and X2 has significant negative impact, X3 has non-significant positive impact at 5% level of significance
(d) (1-alpha)*100% confidence interval for beta=beta±t(alpha/2,error df)*SE(beta)
95% confidence interval for X1=1.12±t(0.05/2, 26)*0.1611=1.12±2.06*0.1611=1.12±0.33=(0.79,1.55)
95% confidence interval for X2=-22.2±t(0.05/2, 26)*4.34=-22.2±2.06*4.34=
95% confidence interval for X3=8.38±t(0.05/2, 26)*4.33=1.12±2.06*4.33
(e) after adding the interaction term the following information is generated, and none of the interaction term is significant at alpha=0.05 so adding interaction term is not required
X12 is interaction of X1 and X2
X13 iis interaction of X1 and X2
( f) first model is appropriate i.e. without interaction model
y X1 X2 X3 14 94 1 0 18 96 1 0 18 97 1 0 39 101 1 0 40 101 1 0 26 105 1 0 41 110 1 0 28 110 1 0 36 111 1 0 65 130 1 0 37 79 0 1 35 85 0 1 43 90 0 1 44 97 0 1 61 97 0 1 62 112 0 1 93 115 0 1 74 117 0 1 76 120 0 1 79 119 0 1 55 92 0 0 53 95 0 0 54 100 0 0 52 102 0 0 34 102 0 0 47 104 0 0 57 106 0 0 55 109 0 0 41 111 0 0 80 117 0 0