1. Consider some masurement data is given below. x_data = [-2.26 -2.01 -1.41 -0.62 0 0.52...
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1. Consider some masurement data is given below. x_data = [-2.26 -2.01 -1.41 -0.62 0 0.52 1.07 1.21 1.86 2.63 2.88]; y_data = [-2.00 -3.91 -2.62 -3.15 0 1.56 2.42 1.97 1.37 1.86 1.00]; i) Find linear function in form of f(x) = ax + b which minimizes square error If (xdata) - Ydatal2 and calculate this error (Write analytical expression explicitly.). (10p) ii) Find second order polynomial function in form of f(x) = a₁ + a₁x + a₂x² which minimizes square error ||f(xdata) — Ydatall, and calculate this error (Write analytical expression explicitly.). (10p) iii) Consider part i). Pick up 100 value between -5 and 5 for both a and b. Calculate |lf (xdata) - Ydata||₂ for each (a, b) pair by computer code. Check that whether there is a value lower than the error found in i). Comment the result. (5p) iv) Plot the measurement data and the function found in i) in a same figure. (Consider "scatter, plot, hold on" commands for MATLAB). (5p) v) Plot the measurement data and the function found in ii) in a same figure. (Consider "scatter, plot, hold on" commands for MATLAB). (5p) vi) Let [A1]11x2[b, a]2x1 = [b]11x1 the matrix equation constructed by the data and given model in i). Show that (ATA)-¹ATb gives same result found in i). (Use computer code) (5p) vii) Let [A1]11x3[ao, a1, a2l3x1 = [b]11x1 the matrix constructed by the data and given model in ii). Show that (ATA)-1ATb gives same result found in ii). (Use computer code) (5p) 1. Consider some masurement data is given below. x_data = [-2.26 -2.01 -1.41 -0.62 0 0.52 1.07 1.21 1.86 2.63 2.88]; y_data = [-2.00 -3.91 -2.62 -3.15 0 1.56 2.42 1.97 1.37 1.86 1.00]; i) Find linear function in form of f(x) = ax + b which minimizes square error If (xdata) - Ydatal2 and calculate this error (Write analytical expression explicitly.). (10p) ii) Find second order polynomial function in form of f(x) = a₁ + a₁x + a₂x² which minimizes square error ||f(xdata) — Ydatall, and calculate this error (Write analytical expression explicitly.). (10p) iii) Consider part i). Pick up 100 value between -5 and 5 for both a and b. Calculate |lf (xdata) - Ydata||₂ for each (a, b) pair by computer code. Check that whether there is a value lower than the error found in i). Comment the result. (5p) iv) Plot the measurement data and the function found in i) in a same figure. (Consider "scatter, plot, hold on" commands for MATLAB). (5p) v) Plot the measurement data and the function found in ii) in a same figure. (Consider "scatter, plot, hold on" commands for MATLAB). (5p) vi) Let [A1]11x2[b, a]2x1 = [b]11x1 the matrix equation constructed by the data and given model in i). Show that (ATA)-¹ATb gives same result found in i). (Use computer code) (5p) vii) Let [A1]11x3[ao, a1, a2l3x1 = [b]11x1 the matrix constructed by the data and given model in ii). Show that (ATA)-1ATb gives same result found in ii). (Use computer code) (5p)
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i To find the linear function in the form of fx ax b that minimizes the square error we need to minimize the squared difference between the predicted values fxdata and the actual values Ydata Lets den... View the full answer
Related Book For
Understanding Basic Statistics
ISBN: 9781111827021
6th Edition
Authors: Charles Henry Brase, Corrinne Pellillo Brase
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