Introduction to Probability and Statistics for Engineers and Scientists

430 Chapter 9: Regression

(b) Use the model

√

Y=α+βx+e

and redo part (a).

43.The peak discharge of a river is an important parameter for many engineering

design problems. Estimates of this parameter can be obtained by relating it to the

watershed area (x 1 ) and watershed slope (x 2 ). Estimate the relationship based on

the following data.

Peak

x 1 x 2 Discharge

(m^2 ) (ft/ft) (ft^3 /sec)

36 .005 50

37 .040 40

45 .004 45

87 .002 110

450 .004 490

550 .001 400

1,200 .002 650

4,000 .0005 1,550

44.The sediment load in a stream is related to the size of the contributing drainage

area (x 1 ) and the average stream discharge (x 2 ). Estimate this relationship using

the following data.

Area Discharge Sediment Yield

(× 103 mi^2 ) (ft^3 /sec) (Millions of tons/yr)

8 65 1.8

19 625 6.4

31 1,450 3.3

16 2,400 1.4

41 6,700 10.8

24 8,500 15.0

3 1,550 1.7

3 3,500 .8

3 4,300 .4

7 12,100 1.6

45.Fit a multiple linear regression equation to the following data set.