Numerical Methods for Engineers
Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 20, Problem 18P

The data tabulated below were generated from an experiment initially containing pure ammonium cyanate ( NH 4 OCN ) . It is known that such concentration changes can be modeled by the following equation:

c = c 0 1 + k c 0 t

where c 0 and k are parameters. Use a transformation to linearize this equation. Then use linear regression to predict the concentration at t = 160 min.

t ( min ) 0 20 50 65 150
c   ( mole/L ) 0.381 0.264 0.180 0.151 0.086
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To fit a simple linear regression model to the data and to provide its equation (d = a*t + b), along with R2   Day Date Weekday Daily Demand Weekend 1 4/25/2016 Mon 297 0 2 4/26/2016 Tue 293 0 3 4/27/2016 Wed 327 0 4 4/28/2016 Thu 315 0 5 4/29/2016 Fri 348 0 6 4/30/2016 Sat 447 1 7 5/1/2016 Sun 431 1 8 5/2/2016 Mon 283 0 9 5/3/2016 Tue 326 0 10 5/4/2016 Wed 317 0 11 5/5/2016 Thu 345 0 12 5/6/2016 Fri 355 0 13 5/7/2016 Sat 428 1 14 5/8/2016 Sun 454 1 15 5/9/2016 Mon 305 0 16 5/10/2016 Tue 310 0 17 5/11/2016 Wed 350 0 18 5/12/2016 Thu 308 0 19 5/13/2016 Fri 366 0 20 5/14/2016 Sat 460 1 21 5/15/2016 Sun 427 1 22 5/16/2016 Mon 291 0 23 5/17/2016 Tue 325 0 24 5/18/2016 Wed 354 0 25 5/19/2016 Thu 322 0 26 5/20/2016 Fri 405 0 27 5/21/2016 Sat 442 1 28 5/22/2016 Sun 454 1 29 5/23/2016 Mon 318 0 30 5/24/2016 Tue 298 0 31 5/25/2016 Wed 355 0 32 5/26/2016 Thu 355 0 33 5/27/2016 Fri 374 0 34 5/28/2016 Sat 447 1 35 5/29/2016…
Consider the following data for two variables, x and y.x 2 3 4 5 7 7 7 8 9y 4 5 4 6 4 6 9 5 11a. Does there appear to be a linear relationship between x and y? Explain.b. Develop the estimated regression equation relating x and y.c. Plot the standardized residuals versus yˆ for the estimated regression equation developed in part (b). Do the model assumptions appear to be satisfied? Explain.d. Perform a logarithmic transformation on the dependent variable y. Develop an estimated regression equation using the transformed dependent variable. Do the modelassumptions appear to be satisfied by using the transformed dependent variable?Does a reciprocal transformation work better in this case? Explain

Chapter 20 Solutions

Numerical Methods for Engineers

Ch. 20 - Prob. 11PCh. 20 - The molecular weight of a polymer can be...Ch. 20 - 20.13 On average, the surface area A of human...Ch. 20 - 20.14 Determine an equation to predict metabolism...Ch. 20 - 20.15 Human blood behaves as a Newtonian fluid...Ch. 20 - 20.16 Soft tissue follows an exponential...Ch. 20 - 20.17 The thickness of the retina changes during...Ch. 20 - 20.18 The data tabulated below were generated from...Ch. 20 - The shear stresses, in kilopascals (kPa), of nine...Ch. 20 - 20.20 A transportation engineering study was...Ch. 20 - The saturation concentration of dissolved oxygen...Ch. 20 - For the data in Table P20.21, use polynomial...Ch. 20 - 20.23 Use multiple linear regression to derive a...Ch. 20 - 20.24 As compared to the models from Probs. 20.22...Ch. 20 - 20.25 In water-resources engineering, the sizing...Ch. 20 - 20.26 The concentration of total phosphorus and...Ch. 20 - 20.27 The vertical stress under the corner of a...Ch. 20 - Three disease-carrying organisms decay...Ch. 20 - 20.29 The mast of a sailboat has a cross-sectional...Ch. 20 - 20.30 Enzymatic reactions are used extensively to...Ch. 20 - 20.31 Environmental engineers dealing with the...Ch. 20 - An environmental engineer has reported the data...Ch. 20 - The following model is frequently used in...Ch. 20 - 20.34 As a member of Engineers Without Borders,...Ch. 20 - 20.35 Perform the same computations as in Sec....Ch. 20 - 20.36 You measure the voltage drop V across a...Ch. 20 - Duplicate the computation for Prob. 20.36, but use...Ch. 20 - The current in a wire is measured with great...Ch. 20 - 20.39 The following data was taken from an...Ch. 20 - It is known that the voltage drop across an...Ch. 20 - Ohms law states that the voltage drop V across an...Ch. 20 - 20.42 Repeat Prob. 20.41 but determine the...Ch. 20 - 20.43 An experiment is performed to determine the...Ch. 20 - Bessel functions often arise in advanced...Ch. 20 - 20.45 The population of a small community on the...Ch. 20 - Based on Table 20.4, use linear and quadratic...Ch. 20 - 20.47 Reproduce Sec. 20.4, but develop an equation...Ch. 20 - 20.48 Dynamic viscosity of water is related to...Ch. 20 - 20.49 Hooke’s law, which holds when a spring is...Ch. 20 - 20.50 Repeat Prob. 20.49 but fit a power curve to...Ch. 20 - The distance required to stop an automobile...Ch. 20 - An experiment is performed to define the...Ch. 20 - The acceleration due to gravity at an altitude y...Ch. 20 - The creep rate is the time rate at which strain...Ch. 20 - 20.55 It is a common practice when examining a...Ch. 20 - The relationship between stress and the shear...Ch. 20 - The velocity u of air flowing past a flat surface...Ch. 20 - 20.58 Andrade’s equation has been proposed as a...Ch. 20 - Develop equations to fit the ideal specific heats...Ch. 20 - 20.60 Temperatures are measured at various points...Ch. 20 - 20.61 The data below were obtained from a creep...
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