rem Multiple Independent Variable Linera Regression
rem Using the form y=c+a1*x1+a2*x2+...+an*xn
cls
print
print "Multiple Independent Variable Linear Regression"
print "Using the form Y=C+C1*X1+C2*X2+...+Cn*Xn"
print

dim t(9)
dim x(9)
dim s(9)
dim a(9,10)

rem data entry
input "Number of independent variables? ";v
input "Number of points to input? ";n
[aleap]
input "Use keyboard (k) or read from data (d)? ";c$
print
if c$="k" then
 x(1)=1
 for i=1 to n
  print "Point ";i;":"
  for j=1 to v
   print " Independent Variable ";j;": ";
   input " ";x1
   x(j+1)=x1
  next j
  print " Dependent variable:";
  input " ";y1
  x(v+2)=y1
  for k=1 to v+1
   for l=1 to v+2
    a(k,l)=a(k,l)+x(k)*x(l)
    s(k)=a(k,v+2)
   next l
  next k
 s(v+2)=s(v+2)+x(v+2)^2
 next i
 goto [zleap]
end if
if c$="d" then
rem data must be in form 'data x1 x2 x3 ... xn y'
 x(1)=1
 for i=1 to n
  for j=1 to v
   read x1
   x(j+1)=x1
  next j
  read y1
  x(v+2)=y1
  for k=1 to v+1
   for l=1 to v+2
    a(k,l)=a(k,l)+x(k)*x(l)
    s(k)=a(k,v+2)
   next l
  next k
 s(v+2)=s(v+2)+x(v+2)^2
 next i
else
 goto [aleap]
end if

rem start calcs
[zleap]
for i=2 to v+1
 t(i)=a(1,i)
next i

for i=1 to v+1
 j=i
 [cleap]
 if a(j,i)<>0 then
  goto [bleap]
 end if
 j=j+1
 if j<=(v+1) then
  goto [cleap]
 else
  print
  print "Sorry, no unique solution..."
  end
 end if
 [bleap]
 for k=1 to v+2
  b=a(i,k)
  a(i,k)=a(j,k)
  a(j,k)=b
 next k
 z=1/a(i,i)
 for k=1 to v+2
  a(i,k)=z*a(i,k)
 next k
 for j=1 to v+1
  if j=i then
   goto [dleap]
  end if
  z=-1*a(j,i)
  for k=1 to v+2
   a(j,k)=a(j,k)+z*a(i,k)
  next k
  [dleap]
 next j
next i

rem print coefficients
print
print "Y=C+C1*X1+C2*X2+...+Cn*Xn"
print "C  = " ;a(1,v+2)
for i=2 to v+1
 print "C";i-1;" = ";a(i,v+2)
next i

rem calculation of fit parameters
p=0
for i=2 to v+1
 p=p+a(i,v+2)*(s(i)-t(i)*s(1)/n)
next i
r=s(v+2)-s(1)^2/n
z=r-p
l=n-v-1
i=p/r

rem print fit parameters
print
print "Coef. of Determination: ";i
print "Coef. mult. correlation: ";i^.5
print "Standard Error of est. : ";(abs(z/l))^.5

rem interpolation routine
print
print "Interpolation (enter x1=q to end program) "
[again]
p=a(1,v+2)
j=1
print
input "x1= ";x1$
if x1$="q" then
 end
else
 x=val(x1$)
end if
p=p+a(j+1,v+2)*x
for j=2 to v
 print "x";j;"=";
 input " ";x
 p=p+a(j+1,v+2)*x
next j
print "Y= ";p
goto [again]

data 8,48,59
data 9,49,55
data 6,44,50
data 10,59,80
data 8,55,61
data 9,51,75
data 9,55,67
data 7,50,58