Solved: In a paper dealing with the efficiency of energy utilization of the larvae of

Chapter 8, Problem 13

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In a paper dealing with the efficiency of energy utilization of the larvae of the modest sphinx moth (Pachysphinx modesta), L. Schroeder [Schr1] used the following data to determine a relation between W, the live weight of the larvae in grams, and R, the oxygen consumption of the larvae in milliliters/hour. For biological reasons, it is assumed that a relationship in the form of R = bWa exists between W and R. a. Find the logarithmic linear least squares polynomial by using ln R = ln b + a ln W. b. Compute the error associated with the approximation in part (a): E = 37 i=1 (Ri bWa i ) 2 . c. Modify the logarithmic least squares equation in part (a) by adding the quadratic term c(ln Wi)2, and determine the logarithmic quadratic least squares polynomial. d. Determine the formula for and compute the error associated with the approximation in part (c). WRWRWRWRWR 0.017 0.154 0.025 0.23 0.020 0.181 0.020 0.180 0.025 0.234 0.087 0.296 0.111 0.357 0.085 0.260 0.119 0.299 0.233 0.537 0.174 0.363 0.211 0.366 0.171 0.334 0.210 0.428 0.783 1.47 1.11 0.531 0.999 0.771 1.29 0.87 1.32 1.15 1.35 2.48 1.74 2.23 3.02 2.01 3.04 3.59 3.34 2.83 1.69 1.44 4.09 3.58 4.28 3.28 4.29 3.40 5.48 4.15 2.75 1.84 5.45 3.52 4.58 2.96 5.30 3.88 4.83 4.66 5.96 2.40 4.68 5.10 5.53 6.94