%*********************************************************************
%Csci 2031
%Assignment 6
%Problem 7
%Compare least squares difference of the four different approximants
%*********************************************************************
function[]=problem7
%transpose of stock information
yData=y';
xData=1:1:67;
 
%Least Squares
F1=polyfit(xData, yData,1); %linear
F2=polyfit(xData, yData,3); %cubic
F3=polyfit(xData, yData, 8);%degree 8
 
%Cubic Spline approx.
counter=1;
yData2=zeros(1,12);
%extract every 6 element out of the original data array
for i=1:6:67
    yData2(counter)=yData(i);
    counter=counter+1;
end
xData2=1:6:67;
tt=1:0.1:67;
 
Fs= spline(xData2,yData2);
Ys= ppval(Fs, xData2);
 
%Evaluate at xData points
Y1= polyval(F1, xData);
Y2= polyval(F2, xData);
Y3= polyval(F3, xData);
 
%Error sums
e1 = sum ( (Y1-yData).^2)
e2 = sum( (Y2-yData).^2)
e3 = sum( (Y3-yData).^2)
es = sum((Ys-yData2).^2)
fprintf('Error using linear approximant %d\n', e1);
fprintf('Error using cubic approximant %d\n', e2);
fprintf('Error using degree 8 approximant %d\n', e3);
fprintf('Error using Cubic Spline approximant %d\n', es);

end

Output:
Error using linear approximant 3.267055e+003
Error using cubic approximant 1.443410e+003
Error using degree 8 approximant 4.412313e+002
Error using Cubic Spline approximant 0