4. Consider the following data set for an office structure built by Anderson Con
ID: 3055678 • Letter: 4
Question
4. 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 RCOM. Call this new variable FLRCOMSO. Print HOURS, FLRCOM, and FLRCOMsO Test whether there is a nonlinear relationship between HOURS and floors completed in the equation: HOURS = a + b(FLRCOM) + c(FLRCOMSO). Graph the foregoing equation. Where does it reach a maximum? 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 toExplanation / Answer
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Data Display
Row HOURS FLRCOM FLRCOMSQ
1 800 0.0431 0.0019
2 1575 0.0864 0.0075
3 2708 0.1564 0.0245
4 4110 0.2498 0.0624
5 5721 0.3676 0.1351
6 7955 0.5319 0.2829
7 8012 0.5362 0.2875
8 10765 0.7508 0.5637
9 13757 1.0098 1.0197
10 17257 1.3273 1.7617
11 21121 1.6684 2.7836
12 22435 1.8007 3.2425
13 26194 2.1873 4.7843
14 29971 2.5881 6.6983
15 30266 2.6262 6.8969
16 34296 3.0633 9.3838
17 37027 3.3722 11.3717
18 41556 3.8899 15.1313
19 46015 4.4022 19.3794
20 50516 4.9333 24.3374
21 54067 5.3357 28.4697
Polynomial Regression Analysis: HOURS versus FLRCOM
The regression equation is
HOURS = 1075 + 12580 FLRCOM - 521.8 FLRCOM**2
S = 471.412 R-Sq = 99.9% R-Sq(adj) = 99.9%
We got 99.9% R-sq. which is a good fit
Fitted Line: HOURS versus FLRCOM
The fitted line reaches the maximum when FLRCOM=9. That is
HOURS = 1074.7 + 12579.8 FLRCOM - 521.8 FLRCOMSQ=1074.7 + 12579.8 *9 - 522 *8=72026
Regression Analysis: HOURS versus FLRCOM, FLRCOMSQ
The regression equation is
HOURS = 1075 + 12580 FLRCOM - 522 FLRCOMSQ
Predictor Coef SE Coef T P
Constant 1074.7 205.5 5.23 0.000
FLRCOM 12579.8 219.5 57.32 0.000
FLRCOMSQ -521.82 43.11 -12.11 0.000
S = 471.412 R-Sq = 99.9% R-Sq(adj) = 99.9%
Analysis of Variance
Source DF SS MS F P
Regression 2 5756673868 2878336934 12952.10 0.000
Residual Error 18 4000129 222229
Total 20 5760673997
Predicted Values for New Observations
New
Obs Fit SE Fit 50% CI 50% PI
1 72026 1786 (70796, 73255) (70754, 73297)
Estimated extra hours due to fire is
54067+40750-72026=22791
50% Confidence interval is (70796, 73255) . This means the new fit HOUR for FLOORCOM=9 will fall inside the interval 50% times.
50% Prediction interval is (70754, 73297). This means the HOURS required for FLOORCOM=9 will fall inside the interval 50% times. Note that the prediction interval is wider than CI due to the uncertainity in the new future FLOORCOM.
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