INTERNATIONAL EDITION---Numerical Methods for Engineers, 7th edition
7th Edition
ISBN: 9781259170546
Author: Steven Chapra and Raymond Canale
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 19, Problem 3P
The pH in a reactor varies sinusoidally over the course of a day. Use least-squares regression to fit Eq. (19.11) to the following data. Use your fit to determine the mean, amplitude, and time of maximum pH. Note that the period is 24 hr.
| Time, hr | 0 | 2 | 4 | 5 | 7 | 9 | 12 | 15 | 20 | 22 | 24 |
| pH | 7.6 | 7 | 7.1 | 6.5 | 7.4 | 7.2 | 8.9 | 8.8 | 8.9 | 7.9 | 7 |
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Shown below is a portion of a computer output for a linear regression analysis relating an individual's income (y in thousands of dollars) to age (x1 in years), level of education (x2 ranging from 1 to 5), and the individual's gender (x3 where 0 = female and 1 = male).
Coefficient
Standard Error
t-statistic
p-value
Intercept
15.934
1.389
11.47
0.000
x1
0.625
0.094
6.65
0.000
x2
0.921
0.190
4.85
0.000
x3
–0.510
0.920
–0.55
0.590
Source of
Variation
Sum of squares
Degrees of freedom
Mean square
F-statistic
p-value
Regression
84
3
28
4
0.027
Error
112
16
7
Total
196
19
a. Is there a significant relationship between an individual's income and the set of variables, age, level of education, and gender (based on a significance level α =05 )? Explain why using one of the p-values in the output tables.
b.Which of the three predictor variables are…
A forecaster used the regression equation
Qt = a + bt + c1D1 + c2D2 + c3D3
and quarterly sales data for 2004I–2021IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1, D2 and D3 are dummy variables for quarters I, II, and III.
DEPENDENT VARIABLE:
QT
R-SQUARE
F-RATIO
P-VALUE ON F
OBSERVATIONS:
64
0.8768
107.982
0.0001
VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T-RATIO
P-VALUE
INTERCEPT
30.0
12.80
2.34
0.0224
T
1.5
0.70
2.14
0.0362
D1
10.0
3.00
3.33
0.0015
D2
25.0
7.20
3.47
0.0010
D3
40.0
15.80
2.53
0.0140
What is the estimated intercept of the trend line in the second quarter?
A forecaster used the regression equation
Qt = a + bt + c1D1 + c2D2 + c3D3
and quarterly sales data for 2004I–2021IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1, D2 andD3 are dummy variables for quarters I, II, and III.
DEPENDENT VARIABLE:
QT
R-SQUARE
F-RATIO
P-VALUE ON F
OBSERVATIONS:
64
0.8768
107.982
0.0001
VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T-RATIO
P-VALUE
INTERCEPT
30.0
12.80
2.34
0.0224
T
1.5
0.70
2.14
0.0362
D1
10.0
3.00
3.33
0.0015
D2
25.0
7.20
3.47
0.0010
D3
40.0
15.80
2.53
0.0140
Using the estimation results given above, the predicted level of sales in 2022II is _______ units.
Chapter 19 Solutions
INTERNATIONAL EDITION---Numerical Methods for Engineers, 7th edition
Ch. 19 - The average values of a function can be determined...Ch. 19 - The solar radiation for Tucson, Arizona, has been...Ch. 19 - 19.3 The pH in a reactor varies sinusoidally over...Ch. 19 - 19.4 Use a continuous Fourier series to...Ch. 19 - 19.5 Use a continuous Fourier series to...Ch. 19 - Construct amplitude and phase line spectra for...Ch. 19 - 19.7 Construct amplitude and phase line spectra...Ch. 19 - 19.8 A half-wave rectifier can be characterized...Ch. 19 - 19.9 Construct amplitude and phase line spectra...Ch. 19 - Develop a user-friendly program for the DFT based...
Ch. 19 - 19.11 Use the program from Prob. 19.10 to compute...Ch. 19 - 19.12 Develop a user-friendly program for the FFT...Ch. 19 - 19.13 Repeat Prob. 19.11 using the software you...Ch. 19 - An object is suspended in a wind tunnel and the...Ch. 19 - 19.15 Use the Excel Data Analysis ToolPak to...Ch. 19 - Use the Excel Data Analysis Toolpack to fit a...Ch. 19 - (a) Use MATLAB to fit a cubic spline to the...Ch. 19 - 19.18 Use MATLAB to generate 64 points from the...Ch. 19 - In a fashion similar to Sec. 19.8.2, use MATLAB to...Ch. 19 - Runges function is written as f(x)=11+25x2...Ch. 19 - A dye is injected into the circulating blood...Ch. 19 - In electric circuits, it is common to see current...Ch. 19 - Develop a plot of the following data with (a)...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Similar questions
- The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.arrow_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forward
- Consider the following table containing unemployment rates for a 10-year period. Unemployment Rates Year Unemployment Rate (%) 1 5.85.8 2 3.23.2 3 5.55.5 4 8.68.6 5 6.16.1 6 6.86.8 7 7.57.5 8 5.25.2 9 11.111.1 10 7.47.4 Step 1 of 2 : Given the model Estimated Unemployment Rate=β0+β1(Year)+εi,Estimated Unemployment Rate=�0+�1(Year)+��, write the estimated regression equation using the least squares estimates for β0�0 and β1�1. Round your answers to two decimal places.arrow_forwardThe basal metabolic rate (kcal/day) of large anteaters is believed to be subject to a power law relationship with its weight (kg). A study was performed measuring several anteaters and reported the following data: Weight (kg) 6.0 28.5 16.0 19.0 23.5 11.0 9.0 25.5 22.0 BMR (kcal/day) 80.1 247.0 162.3 172.4 215.1 111.9 104.6 224.6 208.3 Transform the data correctly to perform a linear least-squares regression, then report your model as y=cxpy=cxp. Estimate the BMR for a 27 kg anteater.arrow_forwardThe table contains data on vehicle speed (h) and fuel consumption (lt / 100km) of 5 randomly selected vehicles. Estimate the average fuel consumption of a vehicle traveling at 45 km / h using the simple linear regression equation between vehicle speed and fuel consumption. Speed 55 60 65 70 75 Consumption 13 12 11 10 9 a. 15 b. 8 c. 7 d. 20arrow_forward
- The authors of a paper were interested in how the distance a deer mouse will travel for food is related to the distance from the food to the nearest pile of debris. Distances were measured in meters. The data and computer output are given below. Distance from Debris Distance Traveled 6.94 0.00 5.23 6.13 5.21 11.29 7.10 14.35 8.16 12.03 5.50 22.72 9.19 20.11 9.05 26.16 9.36 30.65 Simple Linear Regression Results: Dependent Variable: Traveled Independent Variable: Debris Sample size: 9 R (correlation coefficient) = 0.5657 R-sq = 0.32002088 Estimate of error standard deviation 8.670711 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept -7.6854587 13.332196 ≠ 0 7 -0.5764586 0.5824 Slope 3.2340908 1.7818117 ≠ 0 7 1.8150575 0.1124 a)What is the least squares regression line for the output given above? b) what is the predicted traveled distance given the distance from debris is 6.5 meters?arrow_forwardThe marketing manager of a supermarket chain would like to determine the effect of shelf spaceon the sales of pet food. A random sample of 10 stores was selected, and the results are presentedbelow. Store shelf space in cm weekly sales in thousand pesos 1 45 18 2 45 21 3 75 15 4 80 18 5 95 23 6 100 26 7 135 22 8 140 27 9 185 25 10 190 28 d. Using the estimated simple linear regression equation Y=15.6414+0.0611X, estimate the weekly sales when theshelf space is 230cm? 250cm? e. Compute the coefficient of determination and interpret its value.arrow_forwardThe table below shows (lifetime) peptic ulcer rates (per 100 population), UU, for various family incomes, xx, as reported by the 1989 National Health Interview Survey. Income 4000 6000 8000 12000 16000 20000 30000 45000 60000 Ulcer rate 14.1 13.1 13.8 12.6 11.8 11.7 11.5 9.3 7.6 (a) Find the equation of the regression line. Ulcer rate, U(x)= . (b) Estimate the peptic ulcer rate for an income level of x0= 25000 according to the linear model in part (a). Ulcer rate, U(x0)= .arrow_forward
- Compute the least-squares regression equation for the given data set. Round the slope and y-intercept to at least four decimal places. 2 4 7 6 6 5 3 3 4 2arrow_forwardThe following data is representative of that reported in an article on nitrogen emissions, with x = burner area liberation rate (MBtu/hr-ft2) and y = NOx emission rate (ppm): x 100 125 125 150 150 200 200 250 250 300 300 350 400 400 y 140 150 180 210 190 310 270 410 440 450 380 600 600 670 (a) Assuming that the simple linear regression model is valid, obtain the least squares estimate of the true regression line. (Round all numerical values to four decimal places.)y = (b) What is the estimate of expected NOx emission rate when burner area liberation rate equals 200? (Round your answer to two decimal places.) ppm(c) Estimate the amount by which you expect NOx emission rate to change when burner area liberation rate is decreased by 60. (Round your answer to two decimal places.) ppm(d) Would you use the estimated regression line to predict emission rate for a liberation rate of 500? Why or why not? Yes, the data is perfectly linear, thus lending to accurate…arrow_forwardThe following partial JMP regression output for the Fresh detergent data relates to predicting demand for future sales periods in which the price difference will be .10. SE Fit = .165360573, s = .628152. Predicted Demand Lower 95% MeanDemand Upper 95% MeanDemand 31 8.181072245 7.842346262 8.519798229 StdErr IndivDemand Lower 95% IndivDemand Upper 95% MeanDemand 0.649552965 6.850522511 9.511621980 Click here for the Excel Data File (a) Report a point estimate of and a 95 percent confidence interval for the mean demand for Fresh in all sales periods when the price difference is .10. (Round your CI answers to 3 decimal places and other answer to 4 decimal places.) (b) Report a point prediction of and a 95 percent prediction interval for the actual demand for Fresh in an individual sales period when the price difference is .10. (Round your PI answers to 3 decimal places and other answer to 4 decimal places.) (c) StdErr Indiv Demand on…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY