rem Nth Order Regression
cls
print
print "Nth Order Regression"
print "will fit data to a curve"
print "y=c+a1*x+a2*x^2...+an*x^n"
print

dim a(13)
dim r(7,8)
dim t(8)

rem data entry
input "degree of equation? ";d
input "number of points to input? ";n
a(1)=n
for i=1 to n
 print
 print "x(";i;")= ";
 input " ";x
 print "y(";i;")= ";
 input " ";y
 for j=2 to (2*d+1)
  a(j)=a(j)+x^(j-1)
 next j
 for k=1 to d+1
  r(k,d+2)=t(k)+y*x^(k-1)
  t(k)=t(k)+y*x^(k-1)
 next k
 t(d+2)=t(d+2)+y^2
next i

for j=1 to d+1
 for k=1 to d+1
  r(j,k)=a(j+k-1)
 next k
next j

for j=1 to d+1
 k=j
 [cleap]
 if r(k,j)<>0 then
  goto [aleap]
 end if
 k=k+1
 if k<=d+1 then
  goto cleap
 end if
 print
 print "SORRY, NO UNIQUE SOLUTION!"
 end
[aleap]
 for i=1 to d+2
  s=r(j,i)
  r(j,i)=r(k,i)
  r(k,i)=s
 next i
 z=1/r(j,j)
 for i=1 to d+2
  r(j,i)=z*r(j,i)
 next i
 for k=1 to d+1
  if k=j then
   goto [bleap]
  end if
  z= -1*r(k,j)
  for i=1 to d+2
   r(k,i)=r(k,i)+z*r(j,i)
  next i
[bleap]
 next k
next j

print
print "constant= ";r(1,d+2)
for j=1 to d
 print "degree ";j;" coefficient= ";r(j+1,d+2)
next j
print

p=0
for j=2 to d+1
 p=p+r(j,d+2)*(t(j)-a(j)*t(1)/n)
next j
q=t(d+2)-t(1)^2/n
z=q-p
i=n-d-1
j=p/q
print "coeff of determination (r^2)= ";j
print "coeff of correlation= ";j^.5
if i>0 then
 print "standard error estimate= ";(z/i)^.5
end if
print

rem "estimate y coordinate"
[again]
p=r(1,d+2)
print
print "Interpolation (enter x=q to end program) ";
input "x= ";x$
if x$="q" then
 end
end if
x=val(x$)
for j=1 to d
 p=p+r(j+1,d+2)*x^j
next j
print "y= ";p
goto [again]