The article “Earthmoving Productivity Estimation Using

Chapter 8, Problem 6E

(choose chapter or problem)

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 \(\mathrm m^3\) moved per hour):

\begin{aligned} \text { Productivity }=&-297.877+84.787 x_{1}+36.806 x_{2}+151.680 x_{3}-0.081 x_{4}-110.517 x_{5} \\ &-0.267 x_{6}-0.016 x_{1} x_{4}+0.107 x_{4} x_{5}+0.0009448 x_{4} x_{6}-0.244 x_{5} x_{6} \end{aligned}

where

\(x_{1}\) = number of trucks

\(x_{2}\) = number of buckets per load

\(x_{3}\) = bucket volume, in m3

\(x_{4}\) = haul length, in m

\(x_{5}\) = match factor (ratio of hauling capacity to loading capacity)

\(x_{6}\) = truck travel time, in s

a. If the bucket volume increases by 1 \(\(\mathrm m^3\)\), 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.

Equation Transcription:

Text Transcription:

m^3

Productivity=-297.877+84.787x_1+36.806x_2+151.680x_3-0.081x_4-110.517x_5

-0.267x_6-0.016x_1x_4+0.107x4x5+0.0009448x_4x_6-0.244x_5x_6

x_1

x_2

x_3

x_4

x_5

x_6

m^3