rem Polynomial Regression For Two Variables
cls
print
print "Polynomial Regression for Two Variables"
print
print "where x and y are the independent variables"
print "and d is the dependent variable"
print

dim d(50)
dim x(50)
dim y(50)
dim z(50)
dim a(9,10)

rem data entry
input "Number of points to input? ";n
[dleap]
input "Use keyboard (k) or read from data (d)? ";c$
if c$="k" then
 for i=1 to n
  print "x(";i;")= ";
  input " ";x1
  print "y(";i;")= ";
  input " ";y1
  print "d(";i;")= ";
  input " ";d1
  x(i)=x1
  y(i)=y1
  d(i)=d1
  print
 next i
end if
if c$="d" then
 for i=1 to n
  read x1,y1,d1
  x(i)=x1
  y(i)=y1
  d(i)=d1
  next i
else
 goto [dleap]
end if

rem zero the program variables
for k=1 to 50
 z(k)=0
next k
for k=1 to 9
 for l=1 to 10
  a(k,l)=0
 next l
next k

rem load matrix
for j=1 to n

 gosub [matrix]
 for k=1 to 9
  for l=1 to 9
   a(k,l)=a(k,l)+z(k)*z(l)
  next l
 next j

 rem solve for coefficients
 for k=1 to 9
  p=a(k,k)
  a(k,k)=1
  if p=0 then
   print "Zero Diagonal - no solution"
  end
  end if
  for l=k+1 to 10
   a(k,l)=a(k,l)/p
  next l
  m=1
  [bleap]
  if m=k then
   goto [aleap]
  end if
  r=a(m,k)
  for l=1 to 10
   a(m,l)=a(m,l)-r*a(k,l)
  next l
 a(m,k)=0
 [aleap]
 m=m+1
 if m=10 then
  goto [cleap]
 end if
  goto [bleap]
 [cleap]
next k

rem print coefficients
print
print "Coefficients a1 to a9 are:"
print
for k=1 to 9
 print "a(";k;")= ";a(k,10)
next k
print

rem Calculate the standard deviation
q=0
for j=1 to n
 gosub [matrix]
 dc=0
 for k=1 to 9
  dc=dc+a(k,10)*z(k)
 next k
 q=q+(dc-d(j))^2
next j
r=(q/n)^.5
print "standard deviation= ";r

rem estimate y coordinate
[again]
d=0
print
print "Interpolation (enter x=q to end program) ";
input "x= ";x1$
if x1$="q" then
 end
end if
input "y= ";y1
x1=val(x1$)
x(50)=x1
y(50)=y1
j=50
gosub [matrix]
for k=1 to 9
 d=d+a(k,10)*z(k)
next k
print "d= ";d
goto [again]

[matrix]
z(1)=1
z(2)=x(j)
z(3)=x(j)^2
z(4)=y(j)
z(5)=y(j)^2
z(6)=x(j)*y(j)
z(7)=z(3)*y(j)
z(8)=z(5)*x(j)
z(9)=z(3)*z(5)
return

data .8,1400,873
data .8,1600,877
data .8,1800,888
data .8,2000,904
data 1.2,1400,1076
data 1.2,1600,1072
data 1.2,1800,1070
data 1.2,2000,1076
data 1.6,1400,1253
data 1.6,1600,1245
data 1.6,1800,1239
data 1.6,2000,1235
data 2.0,1400,1409
data 2.0,1600,1399
data 2.0,1800,1391
data 2.0,2000,1386