The article ??Earthmoving Productivity Estimation Using Linear Regression Techniques?? (S. Smith, Journal of Construction Engineering and Management, 1999:133??141) presents the following linear model to predict earthmoving productivity (in m³moved per hour):

Where

x₁ = Number of trucks

x₂ = Number of buckets per load

x₃ = Bucket volume, in m³

x₄ = Haul length, in m

x₅ = Match factor (ratio of hauling capacity to loading capacity)

x₆ = Truck travel time, in s

a. If the bucket volume increases by 1 m³, while other independent variables are unchanged, can you determine the change in the predicted productivity? If so, determine it. If not, state what other information you would need to determine it.

b. If the haul length increases by 1 m, can you determine the change in the predicted productivity? If so, determine it. If not, state what other information you would need to determine it.

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Productivity = - 297.877+ 84.787x, + 36.806x, + 151.680x; – 0.081x4 – 110.517x, - 0.267x6 – 0.016x1x4 + 0.107x4X5 + 0.0009448x4x6 – 0.244x5.x6