Problem Description: Read Chapter 15, "General Linear Least-Squares and Nonlinear Regression," from Chapra's textbook.

Using the same approach as was employed to derive Eqs. (14.15) and (14.16), derive the least-squares fit of the following model:

y = a1*x + a2*x^2

That is, determine the coefficients that result in the least-squares fit for a second-order polynomial with a zero intercept. Compare this result to a quadratic curve fit that includes an intercept value, a0.

y = a0 + a1*x + a2*x^2

Note: Your function needs to be able to handle sample data sets of arbitrary size.

GIven Code Need Matlab function

function [F_fit,a0,a1,a2,r2] = Chapra_15p2(n,v_sample,F_sample,v_fit)

% Input

% n: number of terms in the curve fit (scalar)

% n=2 for zero intercept,

% n=3 includes an intercept

% v_sample: sample velocity values (vector)

% F_sample: experimental data of force for sample velocity values (vector)

% v_fit: velocity values to evaluate fit of Force (vector)

%

% Output

% F_fit: Value of polynomial fit for Force (vector)

% evaluated at given velocity, v_fit

% a0: coefficient for value of y-intercept (scalar)

% a1: coefficient for value of slope (scalar)

% a2: coefficient for value of quadratic term (scalar)

% r2: Coefficient of determination (scalar)

%

% Write your code here.

end