3. Consider the following data set for an office structure built by Anderson Construction Co. The completed building is nine stories. However, construction was interrupted by a fire after 5.3357 floors were completed. At the time of the fire, Anderson had used 54,067 hours of labor to construct the first 5.3357 stories of the building. It then took Anderson an additional 40,750 labor hours to complete this nine-story building.
In this problem, FLRCOM is the number of floors completed, and HOURS is cumulative labor hours to complete the number of floors given by FLRCOM.
Enter the data for FLRCOM and HOURS in Minitab and use one command to create a variable which is the square of FLRCOM. Call this new variable FLRCOMSQ.
a. Estimate the function:
HOURS = a + b(FLRCOM) + c(FLRCOMSQ).
b. Graph this equation.
c. Assume that the fire caused construction to slow down and caused a reduction in efficiency in completing the building. Estimate the number of labor hours needed to complete the building if there were no slow down related to the fire. Assume that the relationship that existed between HOURS and FLRCOM and FLRCOMSQ before the fire would have continued to exist to the completion of the building had the fire not occurred.
d. Estimate the extra labor hours traceable to the fire.
Row |
HOURS |
FLRCOM |
1 |
800 |
0.0431 |
2 |
1575 |
0.0864 |
3 |
2708 |
0.1564 |
4 |
4110 |
0.2498 |
5 |
5721 |
0.3676 |
6 |
7955 |
0.5319 |
7 |
8012 |
0.5362 |
8 |
10765 |
0.7508 |
9 |
13757 |
1.0098 |
10 |
17257 |
1.3273 |
11 |
21121 |
1.6684 |
12 |
22435 |
1.8007 |
13 |
26194 |
2.1873 |
14 |
29971 |
2.5881 |
15 |
30266 |
2.6262 |
16 |
34296 |
3.0633 |
17 |
37027 |
3.3722 |
18 |
41556 |
3.8899 |
19 |
46015 |
4.4022 |
20 |
50516 |
4.9333 |
21 |
54067 |
5.3357 |
When doing these multiple regression problems (i.e., regression work when there is more than one independent variable on the right side of the equation), use the following Minitab commands to get your output:
Stat,
Regression,
Regression,
Fit Regression Model.
When doing a problem with a dummy variable, follow the same sequence of commands. However, it is best (but not necessary) to put the name of the dummy variable in the Categorical Predictor box. In addition, Minitab will give you a nice graph when you use:
Graph,
Scatterplot,
With Regression and Groups.
Then specify your Y, X, and Categorical Variable.
When creating a new variable like FLRCOMSQ, you can create the new variable in Excel and simply copy and paste it into Minitab. As an alternative, you can create the new variable in Minitab. To do that, click on the following:
Calc,
Calculator.
Then, put the name of the new variable into Store Result in Variable box (e.g., FLRCOMSQ). Then define the new variable in the Expression box (e.g., FLRCOM*FLRCOM). If you have trouble doing this in Minitab, it may be easier to simply create the new variable in Excel; and, as I mentioned, copy and paste into Minitab. In addition, Minitab will give you a graph of a quadratic function when you use:
Stat,
Regression,
Fitted Line Plot.
Then click on the Quadratic button.
a. Estimate the function:
HOURS = a + b(FLRCOM) + c(FLRCOMSQ).
HOURS = 1,074.7336 + 12,579.8092(FLRCOM) - 521.8212(FLRCOMSQ).
b. Graph this equation.
c. Assume that the fire caused construction to slow down and caused a reduction in efficiency in completing the building. Estimate the number of labor hours needed to complete the building if there were no slow down related to the fire. Assume that the relationship that existed between HOURS and FLRCOM and FLRCOMSQ before the fire would have continued to exist to the completion of the building had the fire not occurred.
72025.50247
d. Estimate the extra labor hours traceable to the fire.
8958
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