Multiple Regression Analysis

Group Assignment 2

Multiple Regression Analysis

Problem 2

Detroit Steel Ltd has just accepted an order to produce 500 pieces of a new component. Each piece will require 7 operations in the production process. The product manager, Roger Clark, has promised delivery within three weeks, which means that the production time between starting the job and having the batch ready for shipping would have to be no more than 15 days (360 hours), assuming it could be started at 10 am tomorrow.

“Can we start this order tomorrow at 10 am, Pete, and can it be done within 360 hours?” Roger inquired of his production scheduler, Pete Williams.

“Yes, there’s no problem with starting at 10 am tomorrow, but I do not know whether we will be able to finish it in 360 hours. We have not done a job exactly like this before. If you areworried, why don’t you designate it as a ‘rush’ order? We can save a few hours through having a ‘progress-chaser’ assigned to an order.”

Roger was reluctant to commit himself to the ‘rush’ designation. The allocation of a ‘progress chaser’ would cost an extra $1,000 and he was not convinced that it would actually make any difference. He had some data on the previous 20 orders of a similar nature (Table 2) and decided to see if he could somehow estimate the required time.

TIME = time to complete the job


PIECES = number of pieces in the job


OPS = number of operations per piece


RUSH = a dummy variable equal to 1 if the job is a ‘rush’

1. What is the estimated model (equation) that relates production time to the number of pieces in an order, the number of operations per piece and whether they were “rushed”? Should any variables be deleted from the model? How useful is the model as a whole for prediction?

2. What is the average effect of designating an order as a “rush”?

3. Roger thought more about the production process and speculated that total machining time, expressed as the product of pieces and operations, could be a more important variable.

Create an additional variable—OPS*PIECES— by multiplying number of pieces in the job
by number of operations per piece. Run new regression analysis. Explain the results.

4. Try to improve your model by removing irrelevant variables. Run new regression analysis. Explain the results.

5. What is your assessment of the time this order is going to take? Explain your view.
Should Roger designate it a ‘rush’ order? Why or why not? 
Are there other assumptions of regression analysis you would like to check before accepting the above conclusions?

Table  2 Data  on  Orders

ORDER TIME PIECES OPS RUSH 1 153 100 6 0 2 192 35 11 0 3 162 127 7 1 4 240 64 12 0 5 339 600 5 1 6 185 14 16 1 7 235 96 11 1 8 506 257 13 0 9 260 21 9 1

10 161 39 8 0 11 835 426 14 0 12 586 843 6 0 13 444 391 8 0 14 240 84 13 1 15 303 235 9 1 16 775 520 12 0 17 136 76 8 1 18 271 139 11 1 19 385 165 14 1 20 451 304 10 0

Table 2Data on Orders

ORDERTIMEPIECESOPSRUSH

115310060

219235110

316212771

424064120

533960051

618514161

723596111

8506257130

92602191

101613980

11835426140

1258684360

1344439180

1424084131

1530323591

16775520120

171367681

18271139111

19385165141

20451304100