Polynomial Regression: Method of Least Squares

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. $(14\mathrm{.}15)$ and $(14\mathrm{.}16),$ derive the least$-$squares fit of the following model:

$y=a{1}^{**}x+a{2}^{**}{x}^2$

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, $a0.$

$y=a0+a{1}^{**}x+a{2}^{**}{x}^2$

Note: Your function needs to be able to handle sample data sets of arbitrary size. You may use the built$-$in MATLAB functions polyfit and polval for the quadratic curve fit that

includes an intercept value, a$0.($You may not use polyfit and polyval for the fit that does not include a$0.)$

Function $$