Question

An analyst wanted to predict the time required to complete a construction project using four variables - size of the contract ?1x1 (in $1000 units), number of workdays adversely affected by the weather ?2x2, number of subcontractors involved in the project ?4x4, and a variable ?3x3 that measured the presence ( ?3=1x3=1) or absence ( ?3=0x3=0) of a workers' strike during the construction. Fifteen construction projects were randomly chosen, and each of the four variables as well as the time to completion were measured. The full model shown below uses ?1x1, ?2x2, ?3x3, ?4x4, ?1?3x1x3, ?2?3x2x3, and ?4?3x4x3.

	Estimate	Std. Error	t value
(Intercept)	13.692	8.674	1.579
x1	0.028	0.016	1.708
x2	-1.046	0.838	-1.248
x3	66.781	86.623	0.771
x4	2.068	1.624	1.274
x1:x3	-0.035	0.018	-1.942
x2:x3	5.105	1.567	3.257
x4:x3	-7.297	9.122	-0.8

a) Find the estimaing equation for the presence of workers on strike.
?̂ y^ =  -  ?1x1 +  ?2x2 -  ?4x4

b) Find the estimating equation for the absence of workers on strike.
?̂ y^ =  +  ?1x1 -  ?2x2 +  ?4x4

c) Interpret ?2(???)=0.9102R2(adj)=0.9102
% of the variation in   time to completion contract size workdays affected number subcontractors workers strike status  can be explained by   time, contract size, workdays affected, and number subcontractors contract size, workdays affected, number subcontractors, and worker strike status time, workdays affected, number subcontractors, and worker strike status time, contract size, number subcontractors, and worker strike status .

Answer 1

The estimated regression equation is,

y =13.692 + 0.028 x1 - 1.046 x2 + 66.781 x3 +   2.068 x4 - 0.035 x1:x3 + 5.105 x2:x3 - 7.297 x4:x3

a.

Estimated equation for the presence of workers on strike (x3 = 1)

y =13.692 + 0.028 x1 - 1.046 x2 + 66.781 x3 +   2.068 x4 - 0.035 x1:x3 + 5.105 x2:x3 - 7.297 x4:x3

y =13.692 + 0.028 x1 - 1.046 x2 + 66.781 (1) +   2.068 x4 - 0.035 x1:1 + 5.105 x2:1 - 7.297 x4:1  

y = (13.692 + 66.781) + (0.028 - 0.035 ) x1 + (-1.046 + 5.105 ) x2 + (2.068 - 7.297 ) x4

y = 80.473 - 0.007 x1 + 4.059 x2 - 5.229 x4

b.  

Estimated equation for the absence of workers on strike (x3 = 0)

y =13.692 + 0.028 x1 - 1.046 x2 + 66.781 x3 +   2.068 x4 - 0.035 x1:x3 + 5.105 x2:x3 - 7.297 x4:x3

y =13.692 + 0.028 x1 - 1.046 x2 + 66.781 (0) +   2.068 x4 - 0.035 x1:0 + 5.105 x2:0 - 7.297 x4:0  

y = 13.692 + 0.028 x1  - 1.046 x2 +   2.068 x4

c.

91.02%  of the variation in time to completion of project is explained by variables size of the contract ?1, number of workdays adversely affected by the weather ?2, number of subcontractors involved in the project ?4, and a variable ?3 that measured the presence or absence of a workers' strike during the construction.