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//clc()
x = [0,1,2,3,4,5];
y = [2.1,7.7,13.6,27.2,40.9,61.1];
sumy = 0;
sumx = 0;
m = 2;
n = 6;
xsqsum = 0;
xcsum = 0;
x4sum = 0;
xysum = 0;
x2ysum = 0;
rsum = 0;
usum = 0;
for i=1:6
sumy = sumy+y(i);
sumx = sumx+x(i);
r(i) = (y(i) - s/n)^2;
xsqsum = xsqsum + x(i)^2;
xcsum = xcsum +x(i)^3;
x4sum = x4sum + x(i)^4;
xysum = xysum + x(i)*y(i);
x2ysum = x2ysum + y(i)*x(i)^2;
rsum = r(i) + rsum;
end
disp(sumy,"sum y =")
disp(sumx,"sum x =")
xavg = sumx/n;
yavg = sumy/n;
disp(xavg,"xavg = ")
disp(yavg,"yavg = ")
disp(xsqsum,"sum x^2 =")
disp(xcsum,"sum x^3 =")
disp(x4sum,"sum x^4 =")
disp(xysum,"sum x*y =")
disp(x2ysum,"sum x^2 * y =")
J = [n,sumx,xsqsum;sumx,xsqsum,xcsum;xsqsum,xcsum,x4sum];
I = [sumy;xysum;x2ysum];
X = inv(J) * I;
a0 = det(X(1,1));
a1 = det(X(2,1));
a2 = det(X(3,1));
for i=1:6
u(i) = (y(i) - a0 - a1*x(i) - a2*x(i)^2)^2;
usum = usum + u(i);
end
disp(r,"(yi - yavg)^2 = ")
disp(u,"(yi - a0 - a1*x - a2*x^2)^2 = ")
plot(x,y);
xtitle('x vs y','x','y');
syx = (usum/(n-3))^0,5;
disp(syx,"The standard error of the estimate based on regression polynomial =")
R2 = (rsum - usum)/(rsum);
disp("%",R2*100,"Percentage of original uncertainty that has been explained by the model = ")
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