Question

2. Trying to avoid over- or under-allocating labour hours in a particular moving job, the owner of a moving company would like to develop a better method of predicting labour hours (Duration; measured in hours) by using the size of the apartment (Size; measured in cubic feet) moved. A random sample of 36 moves in the past year was randomly selected in the borough of Manhattan in New York City. The data set “S1181 HW2 Q5 Data.xlsx” is available on D2L.

1. Use StatGraphics to produce a scatter diagram, without the least square regression line. Provide a description of the scatter diagram.
2. Use StatGraphics to produce the Regression output (the one that shows correlation coefficient etc.)
3. Can we conclude that there is a significant correlation between the moving hour and size of all apartments? Make sure you use the three-step process and an appropriate decision point to answer this question.
4. Write out the least square regression line.
5. Provide an interpretation of the intercept estimate and the slope estimate.

Note: the interpretation may not make sense, but do it regardless, for the sake of practice.

6. Check all three assumptions. In other words, make sure you provide the correct graph and comment about the validity of the assumptions.
7. How much labour time is needed when the moving unit is 1033 cubic feet? Provide your answer with 95% confidence level.

Hours	Feet
24.00	545
13.50	400
26.25	562
25.00	540
9.00	220
20.00	344
22.00	569
11.25	340
50.00	900
12.00	285
38.75	865
40.00	831
19.50	344
18.00	360
28.00	750
27.00	650
21.00	415
15.00	275
25.00	557
45.00	1028
29.00	793
21.00	523
22.00	564
16.50	312
37.00	757
32.00	600
34.00	796
25.00	577
31.00	500
24.00	695
40.00	1054
27.00	486
18.00	442
62.50	1249
53.75	995
79.50	1397

Answer 1

Project Work Conditions

Job-site labor productivity can be estimated either for each craft (carpenter, bricklayer, etc.) or each type of construction (residential housing, processing plant, etc.) under a specific set of work conditions. A base labor productivity may be defined for a set of work conditions specified by the owner or contractor who wishes to observe and measure the labor performance over a period of time under such conditions. A labor productivity index may then be defined as the ratio of the job-site labor productivity under a different set of work conditions to the base labor productivity, and is a measure of the relative labor efficiency of a project under this new set of work conditions.

The effects of various factors related to work conditions on a new project can be estimated in advance, some more accurately than others. For example, for very large construction projects, the labor productivity index tends to decrease as the project size and/or complexity increase because of logistic problems and the "learning" that the work force must undergo before adjusting to the new environment. Job-site accessibility often may reduce the labor productivity index if the workers must perform their jobs in round about ways, such as avoiding traffic in repaving the highway surface or maintaining the operation of a plant during renovation. Labor availability in the local market is another factor. Shortage of local labor will force the contractor to bring in non-local labor or schedule overtime work or both. In either case, the labor efficiency will be reduced in addition to incurring additional expenses. The degree of equipment utilization and mechanization of a construction project clearly will have direct bearing on job-site labor productivity. The contractual agreements play an important role in the utilization of union or non-union labor, the use of subcontractors and the degree of field supervision, all of which will impact job-site labor productivity. Since on-site construction essentially involves outdoor activities, the local climate will influence the efficiency of workers directly. In foreign operations, the cultural characteristics of the host country should be observed in assessing the labor efficiency.

Non-Productive Activities

The non-productive activities associated with a project should also be examined in order to examine the productive labor yield, which is defined as the ratio of direct labor hours devoted to the completion of a project to the potential labor hours. The direct labor hours are estimated on the basis of the best possible conditions at a job site by excluding all factors which may reduce the productive labor yield. For example, in the repaving of highway surface, the flagmen required to divert traffic represent indirect labor which does not contribute to the labor efficiency of the paving crew if the highway is closed to the traffic. Similarly, for large projects in remote areas, indirect labor may be used to provide housing and infrastructure for the workers hired to supply the direct labor for a project. The labor hours spent on rework to correct unsatisfactory original work represent extra time taken away from potential labor hours. The labor hours related to such activities must be deducted from the potential labor hours in order to obtain the actual productive labor yield.

Example 4-1: Effects of job size on productivity

A contractor has established that under a set of "standard" work conditions for building construction, a job requiring 500,000 labor hours is considered standard in determining the base labor productivity. All other factors being the same, the labor productivity index will increase to 1.1 or 110% for a job requiring only 400,000 labor-hours. Assuming that a linear relation exists for the range between jobs requiring 300,000 to 700,000 labor hours as shown in Figure 4-1, determine the labor productivity index for a new job requiring 650,000 labor hours under otherwise the same set of work conditions.

The labor productivity index I for the new job can be obtained by linear interpolation of the available data as follows:

This implies that labor is 15% less productive on the large job than on the standard project.

In the construction of an off-shore oil drilling platform, the potential labor hours were found to be L = 7.5 million hours. Of this total, the non-productive activities expressed in thousand labor hours were as follows:

• A = 417 for holidays and strikes
• B = 1,415 for absentees (i.e. vacation, sick time, etc.)
• C = 1,141 for temporary stoppage (i.e. weather, waiting, union activities, etc.)
• D = 1,431 for indirect labor (i.e. building temporary facilities, cleaning up the site, rework to correct errors, etc.)

Determine the productive labor yield after the above factors are taken into consideration.

The percentages of time allocated to various non-productive activities, A, B, C and D are:

The total percentage of time X for all non-productive activities is:

The productive labor yield, Y, when the given factors for A, B, C and D are considered, is as follows:

As a result, only 41% of the budgeted labor time was devoted directly to work on the facility.

Example 4-3: Utilization of on-site worker's time

An example illustrating the effects of indirect labor requirements which limit productive labor by a typical craftsman on the job site was given by R. Tucker with the following percentages of time allocation: [4]

Productive time Unproductive time     Administrative delays     Inefficient work methods     Labor jurisdictions and other work restrictions Personal time

40% 20% 20% 15% 5%

In this estimate, as much time is spent on productive work as on delays due to management and inefficiencies due to antiquated work methods.