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Chapter 12: Q113E (page 781)

Question: Risk management performance. An article in the International Journal of Production Economics (Vol. 171, 2016) investigated the factors associated with a firm鈥檚 supply chain risk management performance (y). Five potential independent variables (all measured quantitatively) were considered: (1) firm size, (2) supplier orientation, (3) supplier dependency, (4) customer orientation, and (5) systemic purchasing. Consider running a stepwise regression to find the best subset of predictors for risk management performance.

a. How many 1-variable models are fit in step 1 of the stepwise regression?

b. Assume supplier orientation is selected in step 1. How many 2-variable models are fit in step 2 of the stepwise regression?

c. Assume systemic purchasing is selected in step 2. How many 3-variable models are fit in step 3 of the stepwise regression?

d. Assume customer orientation is selected in step 3. How many 4-variable models are fit in step 4 of the stepwise regression?

e. Through the first 4 steps of the stepwise regression, determine the total number of t-tests performed. Assuming each test uses an a = .05 level of significance, give an estimate of the probability of at least one Type I error in the stepwise regression.

Short Answer

Expert verified

Answer

a. 5 1-variable models are fitted.

b. 4 2-variable models are fitted.

c. 3 3-variable models are fitted.

d. 2 4-variable models are fitted.

e. A total of 14 t-tests are performed throughout step 1 to 4. The stepwise procedure tends to perform a large number of t-tests, increasing the overall probability of a Type I error.

Step by step solution

01

1-variable model

Since there are 5 independent variables, k no of models are 1-variable models are fitted in step 1 of stepwise regression.

So, 5 1-variable models are fitted.

02

2-variable model

Since there are 5 independent variables, (k-1) no of models are 2-variable models are fitted in step 2 of stepwise regression.

Thus, 4 2-variable models are fitted.

03

3-variable model

Since there are 5 independent variables, (k-2) no of models are 3-variable models are fitted in step 3 of stepwise regression.

Hence, 3 3-variable models are fitted.

04

4-variable model

Since there are 5 independent variables, (k-3) no of models are 4-variable models are fitted in step 3 of stepwise regression.

Therefore, 2 4-variable models are fitted.

05

Type I error

A total of 14 t-tests are performed throughout step 1 to 4. The stepwise procedure tends to perform a large number of t-tests, increasing the overall probability of a Type I error.

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Most popular questions from this chapter

Can money spent on gifts buy love? Refer to the Journal of Experimental Social Psychology (Vol. 45, 2009) study of whether buying gifts truly buys love, Exercise 9.9 (p. 529). Recall those study participants were randomly assigned to play the role of gift-giver or gift-receiver. Gift-receivers were asked to provide the level of appreciation (measured on a 7-point scale where 1 = 鈥渘ot at all鈥� and 7 = 鈥渢o a great extent鈥�) they had for the last birthday gift they received from a loved one. Gift-givers were asked to recall the last birthday gift they gave to a loved one and to provide the level of appreciation the loved one had for the gift.

  1. Write a dummy variable regression model that will allow the researchers to compare the average level of appreciation for birthday gift-giverswith the average for birthday gift-receivers.
  2. Express each of the model鈥檚 尾 parameters in terms ofand.
  3. The researchers hypothesize that the average level of appreciation is higher for birthday gift-givers than for birthday gift-receivers. Explain how to test this hypothesis using the regression model.

Question: Suppose you fit the interaction model y=尾0+尾1x1+尾2x2+尾3x1x2+蔚 to n = 32 data points and obtain the following results:SSyy=479,鈥�SSE=21,鈥�尾^3=10, and s尾^3=4

a. Find R2and interpret its value.

b. Is the model adequate for predicting y? Test at 伪=.05

c. Use a graph to explain the contribution of the x1 , x2 term to the model.

d. Is there evidence that x1and x2 interact? Test at 伪=.05 .

Question: Tilting in online poker. In poker, making bad decisions due to negative emotions is known as tilting. A study in the Journal of Gambling Studies (March, 2014) investigated the factors that affect the severity of tilting for online poker players. A survey of 214 online poker players produced data on the dependent variable, severity of tilting (y), measured on a 30-point scale (where higher values indicate a higher severity of tilting). Two independent variables measured were poker experience (x1, measured on a 30-point scale) and perceived effect of experience on tilting (x2, measured on a 28-point scale). The researchers fit the interaction model, . The results are shown below (p-values in parentheses).

  1. Evaluate the overall adequacy of the model using 伪 = .01.

b. The researchers hypothesize that the rate of change of severity of tilting (y) with perceived effect of experience on tilting (x2) depends on poker experience (x1). Do you agree? Test using 伪 = .01.

Question: The complete modelE(y)=尾0+尾1x1+尾2x2+尾3x3+尾4x4+蔚was fit to n = 20 data points, with SSE = 152.66. The reduced model,E(y)=尾0+尾1x1+尾2x2+蔚, was also fit, with

SSE = 160.44.

a. How many 尾 parameters are in the complete model? The reduced model?

b. Specify the null and alternative hypotheses you would use to investigate whether the complete model contributes more information for the prediction of y than the reduced model.

c. Conduct the hypothesis test of part b. Use 伪 = .05.
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