%*********************************************************************
%Csci 2031
%Assignment 6
%Problem 7
%Compare least squares difference of the four different approximants
%*********************************************************************

function[]=problem7

y=[ 111.98
113.54
112.89
110.69
113.62
114.35
118.77
121.19
118.40
121.33
122.67
123.64
124.07
124.49
120.19
120.38
117.50
118.75
120.50
125.09
123.66
121.55
123.90
123.00
122.34
119.65
121.89
120.56
122.04
122.04
121.26
127.17
132.75
132.30
130.33
132.35
132.39
134.07
137.73
138.10
138.91
138.12
140.00
143.75
143.70
134.89
137.26
146.00
143.85
141.43
131.76
135.00
136.49
131.85
135.25
135.03
134.01
126.39
125.00
127.79
124.03
119.90
117.05
122.06
122.22
127.57
132.51
];
%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)

end