(Least Squares Fit to a Data Set by a Linear Function) The following table of x and y

Chapter 5, Problem 2

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(Least Squares Fit to a Data Set by a Linear Function) The following table of x and y values was given in Section 5.3 of this chapter (see Figure 5.3.3). x 1.0 0.0 2.1 2.3 2.4 5.3 6.0 6.5 8.0 y 1.02 0.52 0.55 0.70 0.70 2.13 2.52 2.82 3.54 The nine data points are nearly linear and hence the data can be approximated by a linear function z = c1x + c2. Enter the x and y coordinates of the data points as column vectors x and y, respectively. Set V = [ x, ones(size(x))] and use the MATLAB \ operation to compute the coefficients c1 and c2 as the least squares solution to the 9 2 linear system Vc = y. To see the results graphically, set w = 1 : 0.1 : 8 and z = c(1) w + c(2) ones(size(w)) and plot the original data points and the least squares linear fit, using the MATLAB command plot(x, y, x, w, z)