regression - function regression global x ynoisy % First do...

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Sheet1 Page 1 function regression global x ynoisy % First do a linear regression example % Assume y = a1+a2*x+a3*x2+a4*cos(x)+a5*sin(x)+a6*cos(2*x)+a7*sin(2*x) fprintf('Linear regression example solved using linear least squares . . .\n\n') coefs = [3 a1 = coefs(1,1) a2 = coefs(2,1) a3 = coefs(3,1) a4 = coefs(4,1) a5 = coefs(5,1) a6 = coefs(6,1) a7 = coefs(7,1) x = linspace(0,100,101)' x2 = x.*x x3 = x2.*x cosx = cos(x) sinx = sin(x) cos2x = cos(2*x) sin2x = sin(2*x) y = a1+a2*x+a3*x2+a4*cosx+a5*sinx+a6*cos2x+a7*sin2x %Add noise to original data noisemag = 20 ynoisy = y+noisemag*(2*rand(101,1)-1) plot(x,y,'k-',x,ynoisy,'kx') legend('Original','Noisy') title('Linear regression sample points') pause A = [ones(101,1) x x2 cosx sinx cos2x sin2x] b = ynoisy coefs = A\b a1 = coefs(1,1) a2 = coefs(2,1) a3 = coefs(3,1) a4 = coefs(4,1) a5 = coefs(5,1) a6 = coefs(6,1) a7 = coefs(7,1) % Compute fitted value of y yfit = a1+a2*x+a3*x2+a4*cosx+a5*sinx+a6*cos2x+a7*sin2x plot(x,yfit,'k-',x,ynoisy,'kx') legend('Fitted','Noisy')
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regression - function regression global x ynoisy % First do...

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