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

Problem:
Write a program to determine the parameters A & B so that
A
f ( x)
= + B , fits the following data in least squares sense.
x
X 0.5 2 3.5 4.1 5 6.2 7.5 9.2
y 3.3 2 1.4 1.2 1 0.8 0.64 0.5
program List_Square_Fitting
dimension x(20),y(20),f(20)
n=8
data (x(i), i=1,8)/.5,2,3.5,4.1,5,6.2,7.5,9.2/
data (y(i), i=1,8)/3.3,2,1.4,1.2,1,.8,.64,.5/
sx=0; sxx=0;sy=0;sxy=0
do i=1,n
sx=sx+1/x(i)
sy=sy+y(i)
sxx=sxx+(1/x(i))**2
sxy=sxy+y(i)*(1/x(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/x(i)+b
s=s+(y(i)-f(i))**2
enddo
print*,'Standerd Deviation=',s
end
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
A= 1.353131
B= .7405201
S=.7070401
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