#
# canola - canon canola 1614p emulator
# Copyright (C) 2011 Peter Miller
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License, version 3, as
# published by the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
# General Public License for more details.
#
# You should have received a copy of the GNU General Public License along
# with this program. If not, see <http://www.gnu.org/licenses/>.
#
; ------------------  Card-Pocket-Begin  -----------------------------------
; Title: ST-2: Linear Regression
; Color: green
; Style: blank
; ------------------  Card-Pocket-End  -------------------------------------
;
; How-to-Operate:
;     [START]
;  x1 [START] y1 [START]
;  x2 [START] y2 [START]
;  x3 [START] y3 [START]
;   :    :     :    :
;  xn [START] yn [START]
;     [START] => a
;                b
;  x  [START] => y      ; this repeats
;  :     :
;     [START]           ; no X entry means start again from beginning
;
; Example:
;    [START]
;  2 [START] 12 [START]
;  3 [START] 15 [START]
;  4 [START] 20 [START]
;    [START] => 3.66667 ; a
;               4.00000 ; b
;  1 [START] => 7.66667
;
; Equations:
;  y = a + b * x
;  a = (sigma(x**2) * sigma(y) - sigma(x) * sigma(x * y)) /
;      (n * sigma(x**2) - (sigma(x))**2)
;  b = (n * sigma(x * y) - sigma(x) * sigma(y)) /
;      (n * sigma(x**2) - (sigma(x))**2)
;
    CM14        ; sigma(x)
    CM13        ; sigma(x**2)
    CM12        ; sigma(y)
    CM11        ; sigma(x * y)
    CM10        ; n
    ENT
FJ $611
    M14
    *
    +=
    M13
    RV
    *
    ENT
    M12
    +=
    M11
    1
    M10
    RM10
    EJ $611     ; if more data, loop
    *
    RM13
    +=
    SM9         ; m9 = n * sigma(x**2)
    RM14
    *
    -=
    M9          ; m9 = n * sigma(x**2) - sigma(x) ** 2
    RM10
    *
    RM11
    +=
    SM10        ; m10 = n * sigma(x * y)
    RM14
    *
    RM12
    -=          ; - sigma(x) * sigma(y)
    RM10
    +=          ; n * sigma(x * y) - sigma(x) * sigma(y)
    /
    RM9
    ROUND 5
    +=
    SM10        ; b
    RM14
    *
    RM11
    -=          ; sigma(x) * sigma(x * y)
    SM14
    RM13
    *
    RM12        ; sigma(x**2) * sigma(y)
    +=
    RM14
    +=          ; sigma(x**2) * sigma(y) - sigma(x) * sigma(x * y)
    /
    RM9
    ROUND 5
    +=
    SM9         ; a
    PRINT
    RM10        ; b
    PRINT

    ENT         ; x
FJ $612
    *
    RM10
    +=
    RM9
    +=
    PRINT       ; a + b * x
    EJ $612