Question

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

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

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.

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.

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.

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.

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.