Consider the following data. ti 1.0 1.5 2.0 2.5 3.0 Yi 1.1 1.2 1.3 1.3 1.4...

  

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Consider the following data. ti 1.0 1.5 2.0 2.5 3.0 Yi 1.1 1.2 1.3 1.3 1.4 (a) Set up an overdetermined system of the form (3.1.3) for a straight line passing through the data points. Use the standard basis polynomials 1(t) = 1, 02(t) = t (b) Use MATLAB to calculate the least-squares solution of the system from part (a). This is a simple matter. Given an overdetermined system Ax = b, the MATLAB command x = A\b computes the least squares solution. Recall that this is exactly the same command as would be used to tell MATLAB to solve a square system Ax = b by Gaussian elimination.2 Some useful MATLAB commands: t = 1.5:3; t = t'; s = ones (5,1); A = [st]; We already know that MATLAB uses Gaussian elimination with partial pivot- ing in the square case. In the next two sections you will find out what MATLAB does in the overdetermined case. (c) Use the MATLAB plot command to plot the five data points and your least squares straight line. Type help plot for information about using the plot command. (d) Use MATLAB to compute ||r||2, the norm of the residual. Consider the following data. ti 1.0 1.5 2.0 2.5 3.0 Yi 1.1 1.2 1.3 1.3 1.4 (a) Set up an overdetermined system of the form (3.1.3) for a straight line passing through the data points. Use the standard basis polynomials 1(t) = 1, 02(t) = t (b) Use MATLAB to calculate the least-squares solution of the system from part (a). This is a simple matter. Given an overdetermined system Ax = b, the MATLAB command x = A\b computes the least squares solution. Recall that this is exactly the same command as would be used to tell MATLAB to solve a square system Ax = b by Gaussian elimination.2 Some useful MATLAB commands: t = 1.5:3; t = t'; s = ones (5,1); A = [st]; We already know that MATLAB uses Gaussian elimination with partial pivot- ing in the square case. In the next two sections you will find out what MATLAB does in the overdetermined case. (c) Use the MATLAB plot command to plot the five data points and your least squares straight line. Type help plot for information about using the plot command. (d) Use MATLAB to compute ||r||2, the norm of the residual.