Polynomial Regression and finding Standard Error

Please help me double check my work here ♥

x = [-4 7 -5 -9 2 -6 1 10];
y = [13 -3 -16 -19 -12 1 9 -5];


c1 = [length(x) sum(x) sum(x.^2) sum(x.^3) sum(x.^4) sum(x.^5)]';
c2 = [sum(x) sum(x.^2) sum(x.^3) sum(x.^4) sum(x.^5) sum(x.^6)]';
c3 = [sum(x.^2) sum(x.^3) sum(x.^4) sum(x.^5) sum(x.^6) sum(x.^7)]';
c4 = [sum(x.^3) sum(x.^4) sum(x.^5) sum(x.^6) sum(x.^7) sum(x.^8)]';
c5 = [sum(x.^4) sum(x.^5) sum(x.^6) sum(x.^7) sum(x.^8) sum(x.^9)]';
c6 = [sum(x.^5) sum(x.^6) sum(x.^7) sum(x.^8) sum(x.^9) sum(x.^10)]';

N = [c1 c2 c3 c4 c5 c6]

 
r = [sum(y) sum(x.*y) sum(x.^2.*y) sum(x.^3.*y) sum(x.^4.*y) sum(x.^5.*y)]'

%Solve
a = N\r

%Plotting
xx = linspace(-9,10,500);
yy = polyval(flipud(a),xx);
plot(x,y,'or',xx,yy,'-b')

[John wick]

My graph would be like this

Answer 1

[Duncan Carlsmith]

The following shows how. https://www.mathworks.com/matlabcentral/fileexchange/165941-polynomial-fit-explorer