Operations Managers Often Use Work Sampling to Estimate How Much $\quad\quad y =$

question 112

Multiple Choice

Operations managers often use work sampling to estimate how much time workers spend on each operation. Work sampling-which involves observing workers at random points in time-was applied to the staff of the catalog sales department of a clothing manufacturer. The department
Applied regression to the following data collected for 40 consecutive working days:
TIME: $\quad\quad y =$ Time spent (in hours) taking telephone orders during the day
ORDERS: $\quad x _ { 1 } =$ Number of telephone orders received during the day
WEEK: $\quad\quad x _ { 2 } = 1$ weekday, 0 if Saturday or Sunday

Consider the following 2 models:

Model 1: $E ( \mathrm { y } ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } \left( \mathrm { x } _ { 1 } \right) ^ { 2 } + \beta _ { 3 } x _ { 2 } + \beta _ { 4 } x _ { 1 } x _ { 2 } + \beta _ { 5 } \left( x _ { 1 } \right) ^ { 2 } x _ { 2 }$
Model 2: $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 3 } x _ { 2 }$
What strategy should you employ to decide which of the two models, the higher-order model or the simple linear model, is better?

• A) Always choose the more parsimonious of the two models, i.e., the model with the fewest number of \(\beta\)-coefficients.
• B) Compare \(R ^ { 2 }\) values; the model with the larger \(R ^ { 2 }\) will always be the better model.
• C) Compare the two models with a t-test, i.e., test the null hypothesis, \(H _ { 0 } : \beta _ { 1 } = 0\).
• D) Compare the two models with a nested model F-test, i.e., test the null hypothesis, \(H _ { 0 } : \beta _ { 2 } = \beta _ { 4 }\) \(= \beta _ { 5 } = 0\).

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