Cost Modeling. General Widget Corporation has collected data on the daily output and daily production cost of widgets produced at its factory. (Data for the study are shown in the table below.) The company believes that daily output (DO) and daily production cost (PC) ought to be linearly related. Thus, for some numbers a and b:

PC = a + b x DO

Build a least-squares model to estimate the parameters a and b in the linear relationship. In other words, minimize the sum of squared differences between the model’s predicted values and the observations. What are the best values of the parameters a and b for this criterion?

a. What is the minimum value of the objective function? (Verify your results by using Excel’s Regression tool.)

b. Suppose, instead, that a better criterion is thought to be minimizing the sum of absolute deviations between the model’s predicted values and the observations. What are the best values of the parameters a and b for this criterion? What is the minimum value of the objective function?

c. Suppose, instead, that a better model than the linear model is thought to be the power function PC = a(DO)^b

Using the sum of absolute deviations (as in the previous part), what values of a and b provide the best fit? What is the minimum value of the objective function?

Transcribed Image Text:

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 Output 5,045 6,127 6,360 6,645 7,220 9,537 9,895 10,175 10,334 10,855 Production Cost 2,542 2,812 2,776 3,164 4, 102 4,734 4,238 4,524 4,869 4,421