Numerical Analysis Programs Using Fortran 90 - University of ...

Problem:
Write a program to determine the parameters A & B so that
f ( x)
= A ln( x)
+ B , fits the following data in least squares sense.
X 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
y 0.27 0.72 1.48 2.66 4.48 7.26 11.43 17.64 26.78
program List_Square_Fitting
dimension x(20),y(20),f(20)
n=9
data (x(i), i=1,9)/.1,.2,.3,.4,.5,.6,.7,.8,.9/
data (y(i), i=1,9)/.27,.72,1.48,2.66,4.48,7.26,11.43,17.64,26.78/
sx=0; sxx=0;sy=0;sxy=0
do i=1,n
sx=sx+log(x(i))
sy=sy+y(i)
sxx=sxx+(log(x(i)))**2
sxy=sxy+log(x(i))*y(i)
enddo
print *,'sx=',sx
print *,'sxx=',sxx
print *,'sy=',sy
print *,'sxy=',sxy
d=n*sxx-sx**2
a1=(sxx*sy-sx*sxy)/d
a2=(n*sxy-sx*sy)/d
a=a2; b=a1
print*,'A=',a
print*,'B=',b
s=0
do i=1,n
f(i)=a*log(x(i))+b
s=s+(y(i)-f(i))**2
enddo
print*,'Standerd Deviation=',s
end
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
A=9.74113 B=16.66255
S=260.5141
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