FLOOD01900

• County: Statewide
• Community: Nationwide
• Title: Techniques of Weather-Resources Investigations of the USGS Book 4, Chapter A1
• Date: 1/1/1968
• Floodplain - Doc Type: Educational/Technical/Reference Information

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TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS

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Figure 21.-Multiple linear regression bv the method of residue Is.

4. Lines of equal S are logarithmically spaced
at twice the logarithmic scale of the paper
and are parallel.
To solve, separate the regression into two
parts by introducing an intermediate variable
Q"j (to an arbitrary scale) so that

Q'dj j(A, P)

and

Q,dj~j(S, QIO)'

Consider the first relation. For a fixed P, the
model would be

QIJ(lj=KAn,

in which K is the intercept on the Q'dj scale
(at A=I) and n is the slope of the line. In this
example, n= 1.28, which is the ratio of the
linear vertical to horizontal lengths. When
P= 1.20, the intercept K is 78. To obtain this
intercept graphically requires a long curve
extension. It is simpler to compute the intercept
from some other value of A than one. For

instance, for Qodj=I,OOO, A=7.3. Then

1,000=K(7.3)1.28, from which K=78.

Similarly, for Qodj= 10,000, A=44.5 and K=78.
Introducing P as a variable makes it neces-
sary to define the intercept K in terms of P
(because the intercept is d:ifl'erent for each
value of P). The interval per tenth difference
in P when projected on the Q'dj scale is 1.36,
that is, for each tenth increase in P, the inter-
cept increases 1.36 times (the intercept is on a
logarithmic scale). This increase can be meas-
ured for individual intervals or computed from
the total increase: For instance, for A= 10:

Qodj=I,480 for P=1.2,

and

Qodj=17,000 for P=2.0.

The increase for eight intervals IS 17,000;
1,480=11.5, and (1.356)'=11.5.
Then

.

K=78(1.36)1O(P-l.2) ,