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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’s 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

Question: Adverse effects of hot-water runoff. The Environmental Protection Agency (EPA) wants to determine whether the hot-water runoff from a particular power plant located near a large gulf is having an adverse effect on the marine life in the area. The goal is to acquire a prediction equation for the number of marine animals located at certain designated areas, or stations, in the gulf. Based on past experience, the EPA considered the following environmental factors as predictors for the number of animals at a particular station:

X1 = Temperature of water (TEMP)

X2 = Salinity of water (SAL)

X3 = Dissolved oxygen content of water (DO)

X4 = Turbidity index, a measure of the turbidity of the water (TI)

x5 = Depth of the water at the station (ST_DEPTH)

x6 = Total weight of sea grasses in sampled area (TGRSWT)

As a preliminary step in the construction of this model, the EPA used a stepwise regression procedure to identify the most important of these six variables. A total of 716 samples were taken at different stations in the gulf, producing the SPSS printout shown below. (The response measured was y, the logarithm of the number of marine animals found in the sampled area.)

a. According to the SPSS printout, which of the six independent variables should be used in the model? (Use α = .10.)

b. Are we able to assume that the EPA has identified all the important independent variables for the prediction of y? Why?

c. Using the variables identified in part a, write the first-order model with interaction that may be used to predict y.

d. How would the EPA determine whether the model specified in part c is better than the first-order model?

e.Note the small value of R2. What action might the EPA take to improve the model?

Question: Suppose you fit the regression modelE(y)=β0+β1x1+β2x2+β3x1+β4x12+β5x22to n = 30 data points and wish to test H0: β3 = β4 = β5 = 0

a. State the alternative hypothesis Ha.

b. Give the reduced model appropriate for conducting the test.

c. What are the numerator and denominator degrees of freedom associated with the F-statistic?

d. Suppose the SSE’s for the reduced and complete models are SSER = 1,250.2 and SSEC = 1,125.2. Conduct the hypothesis test and interpret the results of your test. Test using α = .05.

Role of retailer interest on shopping behavior. Retail interest is defined by marketers as the level of interest a consumer has in a given retail store. Marketing professors investigated the role of retailer interest in consumers’ shopping behavior (Journal of Retailing, Summer 2006). Using survey data collected for n = 375 consumers, the professors developed an interaction model for y = willingness of the consumer to shop at a retailer’s store in the future (called repatronage intentions) as a function of = consumer satisfaction and = retailer interest. The regression results are shown below.

(a) Is the overall model statistically useful for predicting y? Test using a=0.05

(b )Conduct a test for interaction at a= 0.05.

(c) Use the estimates to sketch the estimated relationship between repatronage intentions (y) and satisfaction when retailer interest is x2=1 (a low value).

(d)Repeat part c when retailer interest is x2= 7(a high value).

(e) Sketch the two lines, parts c and d, on the same graph to illustrate the nature of the interaction.

Explain why stepwise regression is used. What is its value in the model-building process?
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