Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

tha TA a ±ollowing simple linear regressiOnwasrunto that
(11) Road miles = 64842 + 37983 millimeters R 2 = .96
(.02)
where the Euclidean distance is expressed in millimeters according to the
scale of tha map used for the projection (13 millimeters per 10 miles),
The sample was made of 75 origins spread throughout the relevant part of
Illinois. Now, if millimeters are substituted as units of measurement
of the co-ordinates of X and Y on the map, the truck transportation cost
from the point X0Y0 to Chicago can be estimated as
L t + 6.842 C t
.7983 C t (X o 2 +
where C t and L t have the same meaning as in Section 2, and can be estimated
through a linear regression the result of which is given in Table XII.
This formula for the truck cost can be easily incorporated in the boundary
equations, as will be shown below.
2
)
o
For rail transportation the assumption of straight line connection
meant again straight line connection to Chicago. It was found that the
linear regression results of the rail rates on the road miles to Chicago
were slightly better than those of the regressions of the rail rates on the
actual rail distances. Therefore, the above regression (11) could again
be used to convert the millimeters of the co-ordinates into road miles. Then
the rail transportation cost to Chicago could be estimated as
1
L t 6.842
2
C
r
+ .7983 C (X 2 +
r r o
c)
)
'
where L and C
r r
have the same meaning as in Section 2, and are estimated
through linear regressions the results of which are given in Table XI. Again
this cost formula can be easily included in the boundary equations
Something similar had to be devised for water transportation.
Here, the ratio of the actual water mileage from Chicago to Pekin over the
distance in millimeters from Chicago to the perpendicular of Pekin along the
chosen axis (Chicago-Lacon) was used to convert millimeters in actual water
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