Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 4.2, Problem 1E
Fit data to the periodic model
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For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical).
Year Month Units1 Nov 42,1611 Dec 44,1862 Jan 42,2272 Feb 45,4222 Mar 54,0752 Apr 50,9262 May 53,5722 Jun 54,9202 Jul 54,4492 Aug 56,0792 Sep 52,1772 Oct 50,0872 Nov 48,5132 Dec 49,2783 Jan 48,1343 Feb 54,8873 Mar 61,0643 Apr 53,3503 May 59,4673 Jun 59,3703 Jul 55,0883 Aug 59,3493 Sep 54,4723 Oct 53,164
Consider the table of values below.
x
y
2
64
3
48
4
36
5
27
Fill in the right side of the equation y= with an expression that makes each ordered pari (x,y) in the table a solution to the equation.
solving for x
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...
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