Question

1. Least Squares with polynomial functions

Generate some data for x in the range of 0 to 2 using the following function:

y = x^5 – 3*x^3 -5x + 7 + 0.5*rand(x, ‘normal’);

Create polyfit and polyeval functions to come up with coefficients for the generated data.

Please write your answer very clearly.

Answer 1

MATLAB Code:

close all
clear
clc

% Data points
x = linspace(0, 2, 10); % 10 samples from 0 to 2
y = x.^5 - 3*x.^3 -5*x + 7 + 0.5*rand();

% Curve fitting
p = polyfit(x, y, 5); % Fitting 5-th degree polynomial to the data points
fprintf('Model: y = (%.4f)*x^5 + (%.4f)*x^4 + (%.4f)*x^3 + (%.4f)*x^2 + (%.4f)*x + (%.4f)\n', p)

x5 = linspace(0, 2); % Bunch of new samples for a smoother plot
y5 = polyval(p, x5);
plot(x, y, 'o'), hold on % Plot the data points
plot(x5, y5), hold off % Plot the fitted curve
xlabel('x'), ylabel('y')
legend('Data Points', 'Fitted Curve')

Output:

Model: y = (1.0000)*x^5 + (0.0000)*x^4 + (-3.0000)*x^3 + (0.0000)*x^2 + (-5.0000)*x + (7.2844)

Plot: