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+// example 4.36

+// method of least squares to fit the data to the curve P(x)=c0*X+c1/squrt(X)

+

+x=[.2 .3 .5 1 2];

+f=[16 14 11 6 3];

+

+// I(c0,c1)= summation of (f(x)-(c0*X+c1/sqrt(X)))^2 

+

+// hence on parcially derivating the summation,

+

+n=length(x);m=length(f);

+if m<>n then 

+   error('linreg - Vectors x and f are not of the same length.');

+   abort;

+end;

+

+s1=0;                        // s1= summation of x(i)*f(i)

+s2=0;                        // s2= summation of f(i)/sqrt(x(i))

+s3=0;

+for i=1:n

+    s1=s1+x(i)*f(i);

+    s2=s2+f(i)/sqrt(x(i));

+    s3=s3+1/x(i);

+end

+

+c0=det([s1 sum(sqrt(x));s2 s3])/det([sum(x^2) sum(sqrt(x));sum(sqrt(x)) s3])

+

+c1=det([sum(x^2) s1;sum(sqrt(x)) s2])/det([sum(x^2) sum(sqrt(x));sum(sqrt(x)) s3])

+X=poly(0,"X");

+P=c0*X+c1/X^1/2

+// hence  considering the polinomial  P(x)=7.5961*X^1/2-1.1836*X
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