Reference exercise 55

The article “Bank Full Discharge of Rivers” (Water Resources J., 1978: 1141–1154) reports data on discharge amount (q, in m3/sec), flow area (a, in m2), and slope of the water surface (b, in m/m) obtained at a number of floodplain stations. A subset of the data follows. The article proposed a multiplicative power model .

  

                                                                                                  

    

a. Use an appropriate transformation to make the model linear, and then estimate the regression parameters for the transformed model. Finally, estimate α, β, and  γ (the parameters of the original model). What would be your prediction of discharge amount when flow area is 10 and slope is .01?

  

b. Without actually doing any analysis, how would you fit a multiplicative exponential model

  

c. After the transformation to linearity in part (a), a 95% CI for the value of the transformed regression function when a = 3.3  and b = .0046 was obtained from computer output as (.217, 1.755). Obtain a 95% CI for  when a = 3.3  and b = .0046.

 
 
 
 

let y = In(q), x, = In(a), and x, = In(b). Consider fitting the model Y = Bo + Bx, + B,x2 + e. a. The resulting h's are .138, .302, .266, .604, .464, .360, .215, .153, .214, and .284. Does any observation appear to be influential? b. The estimated coefficients are B, = 1.5652, B, = .9450, and B, = .1815, and the corresponding estimated standard deviations are s. = .7328, sa = .1528, and sa, .1752. S8, = The second standardized residual is e = 2.19. When the second observation is omitted from the data set, the resulting estimated coefficients are B, = 1.8982, B, = 1.025, and B, = .3085. Do any of these changes indicate that the sec- ond observation is influential? c. Deletion of the fourth observation (why?) yields B, = 1.4592, B, = 9850, and B, = .1515. Is this obser- vation influential?