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Example 1: Least Squares Fit to a Data Set by a Linear Function. Compute the coefficients of the ...
Example 1: Least Squares Fit to a Data Set by a Linear Function. Compute the coefficients of the best linear least-squares fit to the following data. x2.4 3.6 3.64 4.7 5.3 y| 33.8 34.7 35.5 36.0 37.5 38.1 Plot both the linear function and the data points on the same axis system Solution We can solve the problem with the following MATLAB commands x[2.4;3.6; 3.6;4.1;4.7;5.3]; y-L33.8;34.7;35.5;36.0;37.5;38.1 X [ones ( size (x)),x); % build the matrix X for linear model %...
0 3 X Y 2 4 4 Given to the right are two linear equations and...
0 3 X Y 2 4 4 Given to the right are two linear equations and a set of data points a. Graph the linear equations and data points. b. Complete tables for X. y. y. e, and e? c. Determine which line fits the set of data points better, according to the least squares criterion Line Ay=-1+3x Line : y=1+2x a. Graph the linear equations and data points. Note that Line Ais dashed red and Line B is solid...
4 Suppose that we measure the following four points: 1 1.0 2 1.5 3 3.0 46.0 These could come from...
4 Suppose that we measure the following four points: 1 1.0 2 1.5 3 3.0 46.0 These could come from a process f(x)- -clx + c2x2. Write down a matrix A (which will be 4 x3) by setting 1...4 and vector y and hence write down a least-squares minimisation problem that optimises overc ,c,c2 Now solve that system using the Householder matrices
4 Suppose that we measure the following four points: 1 1.0 2 1.5 3 3.0 46.0 These could...
Given the data points (xi , yi), with xi 0 1.2 2.3 3.5 4 yi 3.5 1.3 -0.7 0.5 2.7 find and plot (using MATLAB) the least-squares basis functions and the resulting least-squares fitting functions toget...
Given the data points (xi , yi), with
xi 0 1.2 2.3 3.5 4
yi 3.5 1.3 -0.7 0.5 2.7
find and plot (using MATLAB) the least-squares basis functions
and the resulting least-squares fitting functions together with the
given data points for the case of
a) a linear monomial basis p(x)= {1 x}T .
b) a quadratic monomial basis p(x)= {1 x
x2}T .
c) a trigonometric basis p(x)= {1 cosx sinx}T
Moreover, determine the coefficients a by the Moore-Penrose...
Problem 5 Six data points are given by (-4, 2),(-1,5), (0, 10), (2, 7), (6, 13),...
Problem 5 Six data points are given by (-4, 2),(-1,5), (0, 10), (2, 7), (6, 13), and (8,9). a) [3 pts) Find the least-squares fit by a linear function. b) [3 pts) Find the least-squares fit by a quadratic function. b) [4 pts) Find the smallest degree polynomial which fits the points exactly.
least squares to fit a straight line Pre-lab A-3 Least Squares Fit to a Straight Line...
least squares to fit a straight line
Pre-lab A-3 Least Squares Fit to a Straight Line Read lab A-3: Least squares fit to a straight line. A set of data is given in the following table and plotted on the right: x(s) y (m) Lab 3 exercise 27 Use the graph on the right to calculate the slope and the intercept of the line. 1 2 3 4 5 Slope Intercept Use equations (6) in the lab manual to calculate...
Consider the curve y = 4 + (2x - 1)3/2 on the Interval 0.5 5 *...
Consider the curve y = 4 + (2x - 1)3/2 on the Interval 0.5 5 * 5 1. The graph is shown below. 4.5 0.4 0.6 0.8 1 1.2 [4] (a) Find the arc length of this curve on the interval 0.5 SX S1. [3] (b) Set up but do not evaluate an integral for the surface area obtained by rotating this curve on the interval 0.5 SXS l about the x-axis.
(a) Suppose you are given the following (x, y) data pairs. x 1 2 6 y...
(a) Suppose you are given the following (x, y) data pairs. x 1 2 6 y 4 3 7 Find the least-squares equation for these data (rounded to three digits after the decimal). ŷ = + x (b) Now suppose you are given these (x, y) data pairs. x 4 3 7 y 1 2 6 Find the least-squares equation for these data (rounded to three digits after the decimal). ŷ = + x (c) In the data for parts...
4. Solve the nonhomogeneous linear system of differential equations 2. Solve the nonhomogeneous linear system of...
4.
Solve the nonhomogeneous linear system of differential equations
2. Solve the nonhomogeneous linear system of anerential equations () u-9" (). 3. Solve the homogeneous linear system of differential equations 1 ( 2 ) uten ( 46 ) + ( ). 4. Solve the nonhomogeneous linear system of differential equations 43,742 cos(46) - 4 sin(40) (10 5 cos(40) ) +847, 7 4cos(46) + 2 sin(40) 5 sin(46) 5. Solve the initial value problem for the nonhomogeneous linear system of differential...
9) Suppose you are given n points: (x,y)(, y). And we wish to fit a cirele to the data. A general...
9) Suppose you are given n points: (x,y)(, y). And we wish to fit a cirele to the data. A general circle, as we all know, is Cr-y+-k. So the question becomes: What are h, k, and r so that the circle becomes the best least squares fit? Show that this problem becomes Th .e. What is a, B and what is M? B, When fitting the cirele to the data points (0,2), (1,2),3,-),(0,-D,6,0) what are the normal equations? GIVE...
Example 1: Least Squares Fit to a Data Set by a Linear Function. Compute the coefficients of the best linear least-squares fit to the following data. x2.4 3.6 3.64 4.7 5.3 y| 33.8 34.7 35.5 36.0 37.5 38.1 Plot both the linear function and the data points on the same axis system Solution We can solve the problem with the following MATLAB commands x[2.4;3.6; 3.6;4.1;4.7;5.3]; y-L33.8;34.7;35.5;36.0;37.5;38.1 X [ones ( size (x)),x); % build the matrix X for linear model %...
0 3 X Y 2 4 4 Given to the right are two linear equations and a set of data points a. Graph the linear equations and data points. b. Complete tables for X. y. y. e, and e? c. Determine which line fits the set of data points better, according to the least squares criterion Line Ay=-1+3x Line : y=1+2x a. Graph the linear equations and data points. Note that Line Ais dashed red and Line B is solid...
4 Suppose that we measure the following four points: 1 1.0 2 1.5 3 3.0 46.0 These could come from a process f(x)- -clx + c2x2. Write down a matrix A (which will be 4 x3) by setting 1...4 and vector y and hence write down a least-squares minimisation problem that optimises overc ,c,c2 Now solve that system using the Householder matrices
4 Suppose that we measure the following four points: 1 1.0 2 1.5 3 3.0 46.0 These could...
Given the data points (xi , yi), with
xi 0 1.2 2.3 3.5 4
yi 3.5 1.3 -0.7 0.5 2.7
find and plot (using MATLAB) the least-squares basis functions
and the resulting least-squares fitting functions together with the
given data points for the case of
a) a linear monomial basis p(x)= {1 x}T .
b) a quadratic monomial basis p(x)= {1 x
x2}T .
c) a trigonometric basis p(x)= {1 cosx sinx}T
Moreover, determine the coefficients a by the Moore-Penrose...
Problem 5 Six data points are given by (-4, 2),(-1,5), (0, 10), (2, 7), (6, 13), and (8,9). a) [3 pts) Find the least-squares fit by a linear function. b) [3 pts) Find the least-squares fit by a quadratic function. b) [4 pts) Find the smallest degree polynomial which fits the points exactly.
least squares to fit a straight line
Pre-lab A-3 Least Squares Fit to a Straight Line Read lab A-3: Least squares fit to a straight line. A set of data is given in the following table and plotted on the right: x(s) y (m) Lab 3 exercise 27 Use the graph on the right to calculate the slope and the intercept of the line. 1 2 3 4 5 Slope Intercept Use equations (6) in the lab manual to calculate...
Consider the curve y = 4 + (2x - 1)3/2 on the Interval 0.5 5 * 5 1. The graph is shown below. 4.5 0.4 0.6 0.8 1 1.2 [4] (a) Find the arc length of this curve on the interval 0.5 SX S1. [3] (b) Set up but do not evaluate an integral for the surface area obtained by rotating this curve on the interval 0.5 SXS l about the x-axis.
4.
Solve the nonhomogeneous linear system of differential equations
2. Solve the nonhomogeneous linear system of anerential equations () u-9" (). 3. Solve the homogeneous linear system of differential equations 1 ( 2 ) uten ( 46 ) + ( ). 4. Solve the nonhomogeneous linear system of differential equations 43,742 cos(46) - 4 sin(40) (10 5 cos(40) ) +847, 7 4cos(46) + 2 sin(40) 5 sin(46) 5. Solve the initial value problem for the nonhomogeneous linear system of differential...
9) Suppose you are given n points: (x,y)(, y). And we wish to fit a cirele to the data. A general circle, as we all know, is Cr-y+-k. So the question becomes: What are h, k, and r so that the circle becomes the best least squares fit? Show that this problem becomes Th .e. What is a, B and what is M? B, When fitting the cirele to the data points (0,2), (1,2),3,-),(0,-D,6,0) what are the normal equations? GIVE...
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