EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 17, Problem 26P
The data below represents the bacterial growth in a liquid culture over a number of days.
| Day | 0 | 4 | 8 | 12 | 16 | 20 |
| Amount
|
67 | 84 | 98 | 125 | 149 | 185 |
Find a best-fit equation to the data trend. Try several possibilities – linear, parabolic, and exponential. Use the software package of your choice to find the best equation to predict the amount of bacteria after 40 days.
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As an industrial engineer, you intend to use linear trend (or linear regression) method to solve a forecasting problem. You have decided to use the equation of y = m(x) + c to establish the relationship between the sales (y) and the related month (x). It is known that 8 consecutive months data (Jan to Aug) were used and they resulted to the following parameter values of m = 320 and c = 1017. Using the regression technique, estimate the percentage of sales improvement from December this year to June next year.
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Question 2
Use the least square regression to fit the data in the following
table to the equation yfit = ae*.
1.5 2
y 1.6 3.7 7 13.5 24.6
1
2.5
(A) Determine the values of a and 3.
(B) What is the standard error of this estimation?
(C) Using the fit equation, what
the value of y at r = 2.25?
إضافة ملف
Consider a process to prepare a metal for a certain application. There are five parameters that must be considered:
temperature, quenching rate, cooling time, carbon content, CO₂ concentration. It is desired to determine which of
these parameters has the most influence on the process. There are two levels for each parameter as shown below.
Temperature (°C)
Quenching Rate(°C/s)
Cooling time (s)
Carbon Content (wt% C)
CO₂ Concentration (%)
Eight experiments were defined as follows:
Experiment
Carbon
Content
(wt% C)
1
2
3
4
5
6
7
8
1) What size orthogonal array should be used for evaluation (assume noise is negligible)?
2) Generate the array with the level values (i.e. Level 1 and Level 2).
1
1
1
1
6
6
6
6
Quenching
Rate (°C/s)
35
35
140
140
35
35
140
140
Four trials were run for the experiments defined above:
Experiment
1
2
3
4
5
6
7
8
Level 1
760
35
1
1
5
T1
68.00
69.84
74.36
71.71
91.27
54.39
64.65
60.31
Cooling Time
1
1
300
300
300
300
1
1
T2
61.41
64.76
61.30
58.42
90.89
Level 2
900…
Chapter 17 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 17 - Given these data 8.8 9.5 9.8 9.4 10.0 9.4 10.1 9.2...Ch. 17 - Given these data 29.65 28.55 28.65 30.15 29.35...Ch. 17 - 17.3 Use least-squares regression to fit a...Ch. 17 - 17.4 Use least-squares regression to fit a...Ch. 17 - 17.5 Using the same approach as was employed to...Ch. 17 - Use least-squares regression to fit a straight...Ch. 17 - Fit the following data with (a) A...Ch. 17 - Fit the following data with the power model...Ch. 17 - 17.9 Fit an exponential model...Ch. 17 - 17.10 Rather than using the base-e exponential...
Ch. 17 - 17.11 Beyond the examples in Fig. 17.10, there are...Ch. 17 - 17.12 An investigator has reported the data...Ch. 17 - An investigator has reported the data tabulated...Ch. 17 - 17.14 It is known that the data tabulated below...Ch. 17 - 17.15 The following data are...Ch. 17 - Given these data x 5 10 15 20 25 30 35 40 45 50 y...Ch. 17 - 17.17 Fit a cubic equation to the following...Ch. 17 - Use multiple linear regression to fit x1 0 1 1 2 2...Ch. 17 - Use multiple linear regression to fit x1 0 0 1 2 0...Ch. 17 - Use nonlinear regression to fit a parabola to the...Ch. 17 - 17.21 Use nonlinear regression to fit a...Ch. 17 - 17.22 Recompute the regression fits from Probs....Ch. 17 - Develop, debug, and test a program in either a...Ch. 17 - A material is tested for cyclic fatigue failure...Ch. 17 - The following data show the relationship between...Ch. 17 - 17.26 The data below represents the bacterial...Ch. 17 - The concentration of E. coli bacteria in a...Ch. 17 - 17.28 An object is suspended in a wind tunnel and...Ch. 17 - 17.29 Fit a power model to the data from Prob....Ch. 17 - Derive the least-squares fit of the following...Ch. 17 - 17.31 In Prob. 17.11 we used transformations to...
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