Question

Apply least squares fitting to derive the normal equations and solve for the coefficients by hand (using Cramer's rule) for the model y a1x + a2x2. Use the data below to evaluate the values of the coefficients. Also solve the normal equations in MATLAB (using backslash) and verify your hand calculations. Lastly, plot the data N) 25 70 380 SS0 points and the model in MATLAB and submit plot with handwork. (m/s)102 F. (N) 25 70 380550 610 1220 830 1450 h) and verify your

Answer 1

dsv daレ dsn dai jaレ co. an 2 .4

ENY: 312850 20yo01260od 1291000 87320000 aL 20SI 6 sOD 20400 1600o 129 G0o0 8 20oo n9 6006 3128S6 ,0d(Dy)ワ130g 300000 Dn

%Matlab code for polynomial least square fit clear all close al1 all x and y points x-10 20 30 40 50 60 70 80); y-25 70 380 550 610 1220 830 1450); All elenents of matrix for polynomial regression xi2-sum(x.*2); xi3-sum(x.*3); xi4-sum(x.4); yxǐngun( x. *y ) ; %finding al and a2 values for given data point %solving using backslash operator soll Alyy fprintf( 'solution using backslash operator \n\tal=%f\n\ta2 n',soll (1),soll (2)) f y nun-soll (1)*x+sol1 (2)x.2; figure(1) hold on plot (x,y) plot (x,y num) xlabel(' in m/s') ylabel ('F ǐn N.) title('F vs. v plot') legend( exact data points, 'least square fit data')

solution using backslash operator a1-7.771024 a2-0.119075

Fvs. v plot 1500 exact data points least nare ft data 1000 500 10 20 30 40 50 60 70 80 vin m/s