Question

1. You are asked to use MATLAB tools to curve fit the data provided as X and Y vectors.

X = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

Y = [-1.5, 16, 44, 90, 141, 207, 292, 398.4, 522, 670]

1. (5 points) Use MATLAB command polyfit to fit the provided data X and Y with a 1st order polynomial function (linear function). Write down the equation y1 = f(x).

2. (5 points) Use MATLAB command polyfit to fit the provided data X and Y with a 2^nd order polynomial function. Write down the equation y2 = f(x).

3. (5 points) Use MATLAB command polyval to evaluate the polynomial function obtained from a) and b) for the given values X. Make them Y1 and Y2, respectively.

4. (10 points) Use MATLAB commands to plot the original data Y, and the curve fitted data Y1, and Y2, on the same figure. There should be three lines on the plot (one for original data points, and two for curve fitted data points). Please include title, axis labels, and legends in the plot.

Answer 1

%Matalb Code for given question
X=[1,2,3,4,5,6,7,8,9,10]
Y=[-1.5,16,44,90,141,207,292,398.4,522,670]
syms x
p=polyfit(X,Y,1) % This fit data X,Y eith 1st order polynomial
y1=p(1)+p(2)*x   %This is linear function y1=f(x) 
p2=polyfit(X,Y,2)  % This fit data X,Y eith 2nd order polynomial
y2=p2(1)+p2(2)*x+p2(3)*x^2  %This is function y2=f(x) 
Y1=polyval(p,X) %This evaluate the polynomial function obtained from(a)at X
Y2=polyval(p2,X)%This evaluate the polynomial function obtained from(a)at X
plot(X,Y,'k')  %This plot the graph of original data points X,Y
hold on
plot(X,Y1,'r')  %This plot the fitted curve obtained by linear polynomial
plot(X,Y2,'c')   %This plot the fitted curve obtained by quadratic polynomial
title('Graph of data points')
xlabel('X-Axis')
ylabel('Y-Axis')
legend(' Original data curve',' linear Y1','Quadratic Y2')

Output