Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 4.5, Problem 9CP
a.
To determine
To find out the data to fit model using lavenberg-marquardt method.
b.
To determine
To find out the data to fit model using lavenberg-marquardt method.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/ 24 hr).
Predictor Coef SE Coef T PConstant 0.8570 0.4148 2.06 0.84Weight 0.38243 0.02978 13.52 0.000
S = 0.517508 R-Sq = 97.4%
(a) Write out the least-squares equation.
y^= ______ + _____x
(b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.)
The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/ 24 hr).
Predictor
Coef
SE Coef
T
P
Constant
0.8651
0.4148
2.06
0.84
Weight
0.40619
0.02978
13.52
0.000
S = 0.517508
R-Sq = 97.0%
(a) Write out the least-squares equation.
y =
+ x
(b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.)(c) What is the value of the correlation coefficient r? (Use 3 decimal places.)
Find the least-squares equation for the following pairs of data:
x = earthquake magnitude
2.9
4.2
3.3
4.5
2.6
3.2
3.4
y = depth of earthquake (in km)
5
10
11.2
10
7.9
3.9
5.5
A. y = 2.16 + 0.221x
B. y = 0.221 + 2.16x
C. y = 2.16 + 0.312x
D. y = 0.221 + 2.82x
Chapter 4 Solutions
Numerical Analysis
Ch. 4.1 - Solve the normal equations to find the least...Ch. 4.1 - Find the least squares solutions and RMSE of the...Ch. 4.1 - Find the least squares solution of the...Ch. 4.1 - Let mn, let A be the mn identity matrix (the...Ch. 4.1 - Prove that the 2-norm is a vector norm. You...Ch. 4.1 - Let A be an nn nonsingular matrix. (a) Prove that...Ch. 4.1 - Find the best line through the set of data points,...Ch. 4.1 - Find the best line through the set of data points,...Ch. 4.1 - Find the best parabola through each data point set...Ch. 4.1 - Find the best degree 3 polynomial through each set...
Ch. 4.1 - Assume that the height of a model rocket is...Ch. 4.1 - Given data points...Ch. 4.1 - Form the normal equations, and compute the least...Ch. 4.1 - Prob. 2CPCh. 4.1 - Prob. 3CPCh. 4.1 - Prob. 4CPCh. 4.1 - 5. A company test-markets a new soft drink in 22...Ch. 4.1 - What is the slope of the parabola y=x2on[ 0,1 ] ?...Ch. 4.1 - Find the least squares (a) line (b) parabola...Ch. 4.1 - Let A be the 10n matrix formed by the first n...Ch. 4.1 - Prob. 9CPCh. 4.1 - The following data, collected by U.S. Bureau of...Ch. 4.2 - Fit data to the periodic model...Ch. 4.2 - Fit the data to the periodic models...Ch. 4.2 - Fit data to the exponential model by using...Ch. 4.2 - Prob. 4ECh. 4.2 - Fit data to the power law model by using...Ch. 4.2 - Prob. 6ECh. 4.2 - Fit the monthly data for Japan 2003 oil...Ch. 4.2 - Prob. 2CPCh. 4.2 - Prob. 3CPCh. 4.2 - Prob. 4CPCh. 4.2 - Prob. 5CPCh. 4.2 - Prob. 6CPCh. 4.2 - Prob. 7CPCh. 4.2 - The file scrippsy. txt, available from the...Ch. 4.2 - The file scrippsm.txt, available from the textbook...Ch. 4.3 - Apply classical Gram-Schmidt orthogonalization to...Ch. 4.3 - Apply classical Gram-Schmidt orthogonalization to...Ch. 4.3 - Apply modified Gram--Schmidt orthogonalization to...Ch. 4.3 - Apply modified Gram-Schmidt orthogonalization to...Ch. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Find the QR factorization and use it to solve the...Ch. 4.3 - Prove that a square matrix is orthogonal if and...Ch. 4.3 - Prove that the product of two orthogonal mm...Ch. 4.3 - Show that the Gram-Schmidt orthogonalization of an...Ch. 4.3 - Show that the Householder reflector method for the...Ch. 4.3 - Let P be the matrix defined in (4.29). Show (a)...Ch. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Write a MATLAB program that implements the...Ch. 4.3 - Apply the classical Gram-Schmidt, modified...Ch. 4.3 - Prob. 3CPCh. 4.3 - Write a MATLAB program that implements (a)...Ch. 4.3 - Prob. 5CPCh. 4.3 - Use the MATLAB QR factorization to find the least...Ch. 4.3 - Prob. 7CPCh. 4.3 - Let x1,...,x11be11 be evenly spaced points in...Ch. 4.4 - Solve Ax=b for the following A and b=[ 1,0,0 ]T,...Ch. 4.4 - Prob. 2ECh. 4.4 - Let A=[ 10a1301a23001 ]. Prove that for any x0 and...Ch. 4.4 - Prob. 4ECh. 4.4 - Prob. 1CPCh. 4.4 - Prob. 2CPCh. 4.4 - Prob. 3CPCh. 4.4 - Let A be the matrix from Computer Problem 3, but...Ch. 4.4 - Prob. 5CPCh. 4.5 - The Gauss-Newton Method can be applied to find the...Ch. 4.5 - Prob. 2ECh. 4.5 - Prove that the distance from a point (x,y) to a...Ch. 4.5 - Prob. 4ECh. 4.5 - Find the matrix Dr needed for the application of...Ch. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 1CPCh. 4.5 - Prob. 2CPCh. 4.5 - Prob. 3CPCh. 4.5 - Prob. 4CPCh. 4.5 - Prob. 5CPCh. 4.5 - Prob. 6CPCh. 4.5 - Prob. 7CPCh. 4.5 - Prob. 8CPCh. 4.5 - Prob. 9CPCh. 4.5 - Prob. 10CPCh. 4.5 - Prob. 11CPCh. 4.5 - Prob. 1SACh. 4.5 - Prob. 2SACh. 4.5 - Prob. 3SACh. 4.5 - Prob. 4SACh. 4.5 - Now repeat Step 4 with a more tightly grouped set...Ch. 4.5 - Decide whether the GPS en-or and condition number...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject 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_forwardThe position of a particle x(t) on an axis has been monitored. The results are shown in the following table. t x(t)0 41 114 129 12 By the least squares method, fit the data to a quadratic model: Report x(10)arrow_forwardTable 14.17 The Least Squares Point Estimates for Exercise 14.51 Bo = 10.3676 (.3710) B1 = .0500 (<.001) B2 = 6.3218 (.0152) B3 = -11.1032 (.0635) B4 = -.4319 (.0002) Questions Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05? Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .01. Which independent variables are significantly related to y in the model with α = .01? Find the p-value for testing Ho: βj = 0 versus Ha: βj ≠ 0 on the output. Using the p-value, determine whether we can reject Ho by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the independent variables in the model? Calculate the 95 percent confidence interval for βj. Discuss one practical application of this interval. Calculate the 99 percent confidence interval for…arrow_forward
- The following table lists the birth weights (in pounds), x, and the lengths (in inches), y, for a set of newborn babies at a local hospital. Birth Weights and Lengths Birth Weight (in Pounds), x 1212 1010 88 1111 1111 33 55 44 77 66 Length (in Inches), y 2121 2020 1717 2222 2222 1616 1717 1616 1919 1919 Copy Data Step 1 of 2 : Find an equation of the least-squares regression line. Round your answer to three decimal places, if necessary.arrow_forwardGiven the table of data points x −1 1 2 y 1 3 3 find the best least squares fit by a linear function f (x) = c1 + c2x.arrow_forwardThe following information regarding a dependent variable (y) and an independent variable (x) is provided. y x 5 3 3 2 4 3 7 4 9 5 The least squares estimate of the y-intercept is....arrow_forward
- To study the tensile strength of a certain type of wire, the following pairs of observations were recorded, wherex is the diameter in cm and y is the mass supported in kg/cm.x: 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4y: 14 26 50 56 42 98 82 88 134 124 Calculate the least-squares regression line and extrapolate the regression line to a diameter of 0.2 cm. Alsoexplain your result.arrow_forwardConsider 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_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
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