Write a MATLAB program to fine the line of best fit. Your program consists of a LS$.$m to find the the line of best fit. In this function, the input parameters include

the data points $($xp$,$ yp$),$ and n the power of the line of best fit. A skeleton code for this problem will be below The use of the skeleton code is not mandatory.

The outputs printouts consist of the coefficient an of the polynomial.

program by the work you done above. Plot the first $3$ polynomials in the same plot together with your data set. Titleand labels are required.

function $[$an$]=$ myLS$2136($xp$,$ yp$,$ n$,$ noplot$)$

$\%\%$ least$\_$squares$($x$,$ y$,$ m$)$ fits a least$-$squares polynomial of degree m through

$\%$ a set of data where x and y are the coordinates.

$\%$ the set of coefficients c$0,$ c$1,...,$cm

$\%$ for the least$-$square polynomial Pm$($x$)=$ c$0+$ c$1*$x $+$ c$2*$x$^2+...+$ cm$*$x$^$m

$\%$ Input:

$\%$ xp $-$ x coordinates

$\%$ yp $-$ y coordinates

$\%$ n $-$ maximum power of the polynomial

$\%$ Example:

$\%[$an$]=$ myLeastSquares$($xp$,$ yp$,$ n$)$

$\%$

$\%$ Date: $30/05/2019$

$\%$ Author: Dr$.$ Hien Nguyen

$\%$ RMIT University

$\%--------------------------------------------------------------------------$

m $=$ size$($xp$,1)$; $\%$ checking the size of dataset

if m $==1$

m $=$ size$($xp$,2)$;

end

disp$(\text{'}\text{'})$;

disp$(\text{'}$ LEAST$-$SQUARES METHOD'$)$;

disp$(\text{'}---------------------------\text{'})$;

$\%$ fill in display Number of sample points is m$+1$

$\%$ fill in display Number of polynomial degree is n

if $($n$>=$ m$)$

$\%$ what happen if n$>=$ m$?$

end

$\%\%$ compute coefficients.

b $=$ zeros$($n$+1,1)$; $\%$ right$-$hand side column vector

for i $=1$:m

for j $=1$:n$+1$

$\%$ fill in your code

end

end

V $=$ zeros$($m$,$n$+1)$; $\%$ V matrix

for i $=1$:m

for j $=1$:n$+1$

$\%$ fill in your code

end

end

$\%$ fill in your code $\%$ S matrix

an $=$ S$\backslash$b; $\%$ solve for coefficient

$\%$ Using symbol tool box to display the resulted polynomial

syms x

$\%$ fill in your code

$\%$ format short

$\%\%$ Display output

disp$(\text{'}------------------------\text{'})$;

fprintf$(\text{'}$ a$\_$n$($x$)$:

$\text{'})$

disp$($an$)$;

disp$(\text{'}------------------------\text{'})$;

disp$($y$)$;

$\%\%$ creating an x$-$axis and evaluating the least$-$ssquare polynomial

if $($noplot $==1)$

$\%$ fill in your code to plot the polynomial

end

end