'****************************************************
'*   Linear Least Squares Demonstration Program     *
'* ------------------------------------------------ *
'* Reference: BASIC Scientific Subroutines, Vol. II *
'*   By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981   *
'*   [BIBLI 01].                                    *
'* ------------------------------------------------ *
'* SAMPLE RUN:                                      *
'*                                                  *
'* This program calculates a linear                 *
'* least squares fit to a given data set.           *
'*                                                  *
'* INSTRUCTIONS                                     *
'* ------------                                     *
'*                                                  *
'* The number of data coordinates provided must be  *
'* greater than two. Otherwise, a divide by zero    *
'* error may result.                                *
'*                                                  *
'* Number of data points : 4                        *
'*                                                  *
'* There are two input options:                     *
'* 1. input coordinate pairs                        *
'* 2. first input the independant variable values,  *
'*    then input dependant ones.                    *
'*    Your choice (1 or 2): 1                       *
'*                                                  *
'* ? 1 1                                            *
'* ? 2 2                                            *
'* ? 3 3                                            *
'* ? 5 5.01                                         *
'*                                                  *
'* Fitted equation is:                              *
'*   Y = -4.573E-003 + 1.002571 X                   *
'*                                                  *
'* Standard deviation of fit: 2.9E-003              *
'*                                                  *
'****************************************************
defint i-n
defdbl a-h,o-z
10 CLS
PRINT
PRINT " This program calculates a linear      "
PRINT " least squares fit to a given data set."
PRINT
PRINT " INSTRUCTIONS"
PRINT " ------------"
PRINT
PRINT " The number of data coordinates provided"
PRINT " must be greater than two. Otherwise, a"
PRINT " divide by zero error may result."
PRINT
INPUT " Number of data points : ", n
IF n < 3 THEN GOTO 10
DIM x(n + 1), y(n + 1)
20 PRINT
PRINT " There are two input options:"
PRINT " 1. input coordinate pairs"
PRINT " 2. first input the independant variable values, then input dependant ones."
INPUT " Your choice (1 or 2) : ", iz
PRINT
IF iz < 1 THEN GOTO 20
IF iz > 2 THEN GOTO 20
IF iz = 1 THEN GOTO 30
FOR m = 0 TO n - 1
  PRINT m + 1; : INPUT x(m)
NEXT
PRINT
FOR m = 0 TO n - 1
  PRINT m + 1; : INPUT y(m)
NEXT
GOTO 50
30 FOR m = 0 TO n - 1
  PRINT m + 1; : INPUT x(m), y(m)
NEXT
'Call linear least squares subroutine
50 GOSUB 1000
PRINT
PRINT " Fitted equation is:"
PRINT "   Y = "; INT(1000000 * a) / 1000000; " ";
IF b > 0 THEN PRINT "+";
PRINT INT(1000000 * b) / 1000000; "X"
PRINT
PRINT " Standard deviation of fit: "; INT(10000 * d) / 10000
PRINT
END

'***************************************************
'*        Linear least squares subroutine          *
'* ----------------------------------------------- *
'* The input data set is X(m), Y(m). The number of *
'* data points is n (n must be > 2). The returned  *
'* parameters are: a,b, coefficients of equation   *
'* Y = a + b X, and d, standard deviation of fit.  *
'***************************************************
1000 a1 = 0: a2 = 0: b0 = 0: b1 = 0
FOR m = 0 TO n - 1
  a1 = a1 + x(m)
  a2 = a2 + x(m) * x(m)
  b0 = b0 + y(m)
  b1 = b1 + y(m) * x(m)
NEXT m%
a1 = a1 / n: a2 = a2 / n: b0 = b0 / n: b1 = b1 / n
d = a1 * a1 - a2
a = a1 * b1 - a2 * b0: a = a / d
b = a1 * b0 - b1: b = b / d
'Evaluation of standard deviation d (unbiased estimate)
d = 0
FOR m = 0 TO n - 1
  d1 = y(m) - a - b * x(m)
  d = d + d1 * d1
NEXT
d = SQR(d / (n - 2))
RETURN

'End of file Lstsqr1.bas