~o|16
~?!i&32768
~o=295
~$>end_of_copyright
~/!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
~/Copyright (C) Heinz Spiess, CH-2558 Aegerten, 1994.  All rights reserved.
~/
~/The right to use this macro is granted to all EMME/2 users, provided the
~/following conditions are met:
~/   1) The macro cannot be sold for a fee (but it can be used and distributed
~/      without charge within consulting projects).
~/   2) The user is aware that this macro is not a part of the EMME/2 software
~/      licence and there is no explicit or implied warranty or support
~/      provided with this macro.
~/   3) The comments in this macros must not be removed and any additions or
~/      modification must be appropriately identified as such and give at least
~/      date, name and the reason of the modification.
~/!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
~:end_of_copyright
~/=============================================================================
~/MATREG 1.4 - (C) Heinz Spiess, EMME/2 Support Center, CH-2558 Aegerten, 1994
~/
~/Compute multiple linear regression Y=A*X0 + B*X1 [+C*X2 [+D*X3]]
~/using matrix data for dependent and independent variables.
~/
~/Usage:
~/  ~<matreg <cmat> <cint> <maty> [-x0 <matx0>] <matx1> [<matx2> [<matx3>]]
~/
~/where:
~/ <cmat>:       constraint matrix (/=none)
~/ <cint>:       constraint interval (/=none)
~/ <maty>:       matrix expression containing dependent variable Y
~/ -x0 <matx0>:  Option to redefine X0, which defaults to the constant 1 (opt.)
~/ <matx1>:      matrix expression containing first independent variable X1
~/ <matx2>:      matrix expr. containing second independent variable X2  (opt.)
~/ <matx3>:      matrix expr. containing third independent variable X3   (opt.)
~/
~/The scalars ms90 - ms99 are used to hold coefficients and statistics.
~/
~x=%0%
~?x>3   / check if enough parameters are provided
~$>start_macro
~t9=~*Do you want to see more detailed instructions?
~t9=%t9.1%
~?!t9=y
~$>end_of_macro
~/
~/Temporary scalars used for regression: Y = A*X0 + B*X1 + C*X2 + D*X3 + eps
~/
~/ms90: regression coefficient A      ms91: regression coefficient B
~/ms92: regression coefficient C      ms93: regression coefficient D
~/ms94: currently not used            ms95: sum of squares for treatment SST
~/ms96: sum of squares for error SSE  ms97: standard deviation SIGMA
~/ms98: R^2 value                     ms99: number of data points N
~/
~/Notes:
~/1) The type of matrix <cmat> must be that implied by the matrix expressions
~/2) The dependent and independent variables can be any valid matrix
~/   or matrix expression (such as e.g. "ln(mf15/mo15/md15)").
~/3) If constraint matrix and interval are provided, only the O-D pairs
~/   satisfying the constraint condition are used for the regression.
~/4) T-values for the coefficients are computed and displayed in result summary
~/5) This macro must be started at the level of the main menu.
~/6) This macro uses only the matrix calculator module 3.21.
~/7) This macro should be run with EMME/2 Release 7 or higher.
~/8) If switch 15 is ON, dialog suppression is turned on and macro is run
~/   in ``fallback-to-debug'' mode.
~/9) See the copyright notice in macro file for details regarding the right to
~/   use, copy and modify this macro.
~$>end_of_macro
~:start_macro
~t8=%t0%
~t1=%1%
~t2=%2%
~t3=%3%
~t4=%4%
~?!t4=-x0
~t0=%1% %2% %3% 1 %4% %5% %6%
~?t4=-x0
~t0=%1% %2% %3% %5% %6% %7% %8%
~x=%0%
~x-3
~/Constraint matrix:           %1%    interval:  %2%
~/Dependent variable Y:        %3%
~?t4=-x0
~/Independent variable X0:     %4%   (No implicit constant term!)
~?x>1
~/Independent variable X1:     %5%
~?x>2
~/Independent variable X2:     %6%
~?x>3
~/Independent variable X3:     %7%
~/
~p=50
~?p=7
~$>release_okay
~?p=8
~$>release_okay
~?p=9
~$>release_okay
~/Warning! This macro is intended for use with EMME/2 release 7, 8 or 9.
~t9=~*Current release level of data bank is %p%.  Continue anyway?
~t9=%t9.1%
~?!t9=y
~$>end_of_macro
~:release_okay
~y=%i%       / preserve state of switches in register y
on=22        / set switch 22 (engineering notation)
c='start macro: matreg %t8%'
3.21         / compute the various scalars
1            /----------------------------------------------------------------
y
ms99         / YY=sum(Y*Y)
y
YY 
~t9=matreg(%3%|%4%,%5%,%6%,%7%)
~t9=%t9.32%
YY %t9%
~?q=1
y

~$>end_expression_explanation
#  The matrix
#  
#           / sumX0*Y | sumX0*X0 sumX0*X1 sumX0*X2 sumX0*X2 \
#           | sumX1*Y | sumX1*X0 sumX1*X1 sumX0*X2 sumX0*X2 |
#  X'(Y|X)= | sumX2*Y | sumX2*X0 sumX2*X1 sumX0*X2 sumX0*X2 |
#           \ sumX3*Y | sumX3*X0 sumX3*X1 sumX0*X2 sumX0*X2 /
#  
#  is computed in the following expression using the put(get(..)) mechanism.
#  The element of the matrix are stored in get(I) as follows:
#  
#           /  get(2) |   get(3)   get(5)   get(8)  get(12) \
#           |  get(4) |   get(5)   get(6)   get(9)  get(13) |
#  X'(Y|X)= |  get(7) |   get(8)   get(9)  get(10)  get(14) |
#           \ get(11) |  get(12)  get(13)  get(14)  get(15) /
#  
#  Note that usually X0=1, i.e. X0 is used for the constant term in the
#  regression.  The above matrix is arranged in such a way that, depending
#  the number of independent variables, only a part starting from the upper
#  left corner is used.
#  
#  Once this matrix is computed from the matrix expressions, only
#  scalar computations are needed for the remaining computations.
#  
~:end_expression_explanation
(%3%)*(%3%) +0*(
 put(get(1)+1)
+put(get(2)+(%3%)*(%4%))
+put(get(3)+(%4%)*(%4%))
+put(get(4)+(%3%)*(%5%))
+put(get(5)+(%4%)*(%5%))
+put(get(6)+(%5%)*(%5%))
~?x<3
~$>end_of_expression
+put(get(7)+(%3%)*(%6%))
+put(get(8)+(%4%)*(%6%))
+put(get(9)+(%5%)*(%6%))
+put(get(10)+(%6%)*(%6%))
~?x<4
~$>end_of_expression
+put(get(11)+(%3%)*(%7%))
+put(get(12)+(%4%)*(%7%))
+put(get(13)+(%5%)*(%7%))
+put(get(14)+(%6%)*(%7%))
+put(get(15)+(%7%)*(%7%))
~:end_of_expression
)
 
~?!e
~$>expression_okay
~/
~/Erroneous matrix expression!
~/Check expressions for dependent and independent variables!
~/
q
~$>end_of_macro
~:expression_okay
%1%           / constraint matrix
~?!e
~$>constraint_matrix_okay
~/
~/Erroneous constraint matrix!
~/

q
~$>end_of_macro
~:constraint_matrix_okay
~?q=0
%2%           / constraint interval
~?!e
~$>constraint_interval_okay
~/
~/Erroneous constraint interval!
~/

q
~$>end_of_macro
~:constraint_interval_okay
~?q=1
no            / no submatrix
~?q=
+
~?q=0
+
~+|~?q=2|1|c
1            /----------------------------------------------------------------
y
ms98         / Determinant of matrix (X'X)
y
DET
DET  %t9%
~?q=1
y

~?x=2
(get(3)*get(6)-get(5)*get(5))
~?x=3
(get(3)*(get(6)*get(10)-get(9)*get(9))
~?x=3
-get(5)*(get(5)*get(10)-get(9)*get(8))+get(8)*(get(5)*get(9)-get(6)*get(8)))
~?!x=4
~$>end_DET4
(get(3)*(get(6)*(get(10)*get(15)-get(14)*get(14))-get(9)*(get(9)*get(15)
-get(14)*get(13))+get(13)*(get(9)*get(14)-get(10)*get(13)))-get(5)*(get(5)
*(get(10)*get(15)-get(14)*get(14))-get(8)*(get(9)*get(15)-get(14)*get(13))
+get(12)*(get(9)*get(14)-get(10)*get(13)))+get(8)*(get(5)*(get(9)*get(15)
-get(13)*get(14))-get(8)*(get(6)*get(15)-get(13)*get(13))+get(12)*(get(6)
*get(14)-get(9)*get(13)))-get(12)*(get(5)*(get(9)*get(14)-get(13)*get(10))
-get(8)*(get(6)*get(14)-get(13)*get(9))+get(12)*(get(6)*get(10)-get(9)*get(9))))
~:end_DET4
 

~+|~?q=2|1|c
~t2=%ms98%
~?!t2=0
~$>determinant_okay
~/
~/Zero determinant of (X'X)! 
~/Check for zero or colinear independent variables.
~/
q
~$>end_of_macro
~:determinant_okay
1            /----------------------------------------------------------------
~?!t2=0
y
ms90         / regression coefficient A
y
A
A  %t9%
~?q=1
y

~?x=2
(get(2)*get(6)-get(5)*get(4))/ms98
~?x=3
(get(2)*(get(6)*get(10)-get(9)*get(9))-get(5)*(get(4)*get(10)-get(9)*get(7))
~?x=3
+get(8)*(get(4)*get(9)-get(6)*get(7)))/ms98
~?!x=4
~$>end_A4
(get(2)*(get(6)*(get(10)*get(15)-get(14)*get(14))-get(9)*(get(9)*get(15)
-get(14)*get(13))+get(13)*(get(9)*get(14)-get(10)*get(13)))-get(4)*(get(5)
*(get(10)*get(15)-get(14)*get(14))-get(8)*(get(9)*get(15)-get(14)*get(13))
+get(12)*(get(9)*get(14)-get(10)*get(13)))+get(7)*(get(5)*(get(9)*get(15)
-get(13)*get(14))-get(8)*(get(6)*get(15)-get(13)*get(13))+get(12)*(get(6)
*get(14)-get(9)*get(13)))-get(11)*(get(5)*(get(9)*get(14)-get(13)*get(10))
-get(8)*(get(6)*get(14)-get(13)*get(9))+get(12)*(get(6)*get(10)-get(9)*get(9))))
/ms98
~:end_A4
 

~+|~?q=2|1|c
1            /----------------------------------------------------------------
y
ms91         / regression coefficient
y
B
B  %t9%
~?q=1
y

~?x=2
(get(3)*get(4)-get(2)*get(5))/ms98
~?x=3
(get(3)*(get(4)*get(10)-get(9)*get(7))-get(2)*(get(5)*get(10)-get(9)*get(8))
~?x=3
+get(8)*(get(5)*get(7)-get(4)*get(8)))/ms98
~?!x=4
~$>end_B4
(get(3)*(get(4)*(get(10)*get(15)-get(14)*get(14))-get(9)*(get(7)*get(15)
-get(14)*get(11))+get(13)*(get(7)*get(14)-get(10)*get(11)))-get(5)*(get(2)
*(get(10)*get(15)-get(14)*get(14))-get(8)*(get(7)*get(15)-get(14)*get(11))
+get(12)*(get(7)*get(14)-get(10)*get(11)))+get(8)*(get(2)*(get(9)*get(15)
-get(13)*get(14))-get(8)*(get(4)*get(15)-get(13)*get(11))+get(12)*(get(4)
*get(14)-get(9)*get(11)))-get(12)*(get(2)*(get(9)*get(14)-get(13)*get(10))
-get(8)*(get(4)*get(14)-get(13)*get(7))+get(12)*(get(4)*get(10)-get(9)*get(7))))
/ms98
~:end_B4
 

~+|~?q=2|1|c
~?x<3
~$>end_of_coefficients
1            /----------------------------------------------------------------
y
ms92         / C
y
C
C %t9%
~?q=1
y

~?x=3
(get(3)*(get(6)*get(7)-get(4)*get(9))-get(5)*(get(5)*get(7)-get(4)*get(8))
~?x=3
+get(2)*(get(5)*get(9)-get(6)*get(8)))/ms98
~?!x=4
~$>end_C4
(get(3)*(get(6)*(get(7)*get(15)-get(14)*get(11))-get(4)*(get(9)*get(15)
-get(14)*get(13))+get(13)*(get(9)*get(11)-get(7)*get(13)))-get(5)*(get(5)
*(get(7)*get(15)-get(14)*get(11))-get(2)*(get(9)*get(15)-get(14)*get(13))
+get(12)*(get(9)*get(11)-get(7)*get(13)))+get(8)*(get(5)*(get(4)*get(15)
-get(13)*get(11))-get(2)*(get(6)*get(15)-get(13)*get(13))+get(12)*(get(6)
*get(11)-get(4)*get(13)))-get(12)*(get(5)*(get(4)*get(14)-get(13)*get(7))
-get(2)*(get(6)*get(14)-get(13)*get(9))+get(12)*(get(6)*get(7)-get(4)*get(9))))
/ms98
~:end_C4
 

~+|~?q=2|1|c
~?x<4
~$>end_of_coefficients
1            /----------------------------------------------------------------
y
ms93         / D
y
D
D %t9%
~?q=1
y

(get(3)*(get(6)*(get(10)*get(11)-get(7)*get(14))-get(9)*(get(9)*get(11)
-get(7)*get(13))+get(4)*(get(9)*get(14)-get(10)*get(13)))-get(5)*(get(5)
*(get(10)*get(11)-get(7)*get(14))-get(8)*(get(9)*get(11)-get(7)*get(13))
+get(2)*(get(9)*get(14)-get(10)*get(13)))+get(8)*(get(5)*(get(9)*get(11)
-get(4)*get(14))-get(8)*(get(6)*get(11)-get(4)*get(13))+get(2)*(get(6)
*get(14)-get(9)*get(13)))-get(12)*(get(5)*(get(9)*get(7)-get(4)*get(10))
-get(8)*(get(6)*get(7)-get(4)*get(9))+get(2)*(get(6)*get(10)-get(9)*get(9))))
/ms98
 

~+|~?q=2|1|c
~:end_of_coefficients
1            /----------------------------------------------------------------
y
ms95         / SST
y
SST
SST %t9%
~?q=1
y

(ms99
~t1=%4%
~?t1=1
-get(2)*get(2)/get(1)
)
 

~+|~?q=2|1|c
1            /----------------------------------------------------------------
y
ms97         / SIGMA
y
SIGMA
SIGMA %t9%
~?q=1
y

sqrt((ms99
-ms90*get(2)
~?x>1
-ms91*get(4)
~?x>2
-ms92*get(7)
~?x>3
-ms93*get(11)
)/(get(1)-%x%))
 

~+|~?q=2|1|c
~?x>4
~$>end_t_values
1            /----------------------------------------------------------------
y
ms96         / T(A)
y
TA
TA %t9%
~?q=1
y

ms90/ms97/sqrt(
~?x=2
get(6) 
~?x=3
(get(6)*get(10)-get(9)*get(9))
~?x=4
(get(6)*(get(10)*get(15)-get(14)*get(14))-get(9)*(get(9)*get(15)
~?x=4
-get(14)*get(13))+get(13)*(get(9)*get(14)-get(10)*get(13)))
/ms98)


~+|~?q=2|1|c
~t4=(t=%ms96%)
1            /----------------------------------------------------------------
y
ms96         / T(B)
y
TB
TB %t9%
~?q=1
y

ms91/ms97/sqrt(
~?x=2
get(3) 
~?x=3
(get(3)*get(10)-get(8)*get(8))
~?x=4
(get(3)*(get(10)*get(15)-get(14)*get(14))-get(8)*(get(8)*get(15)
~?x=4
-get(14)*get(12))+get(12)*(get(8)*get(14)-get(10)*get(12)))
/ms98)


~+|~?q=2|1|c
~t5=(t=%ms96%)
~?x<3
~$>end_t_values
1            /----------------------------------------------------------------
y
ms96         / T(C)
y
TC
TC %t9%
~?q=1
y

ms92/ms97/sqrt(
~?x=3
(get(3)*get(6)-get(5)*get(5))
~?x=4
(get(3)*(get(6)*get(15)-get(13)*get(13))-get(5)*(get(5)*get(15)
~?x=4
-get(13)*get(12))+get(12)*(get(5)*get(13)-get(6)*get(12)))
/ms98)


~+|~?q=2|1|c
~t6=(t=%ms96%)
~?x<4
~$>end_t_values
1            /----------------------------------------------------------------
y
ms96         / T(D)
y
TD
TD %t9%
~?q=1
y

ms93/ms97/sqrt(
~?x=4
(get(3)*(get(6)*get(10)-get(9)*get(9))-get(5)*(get(5)*get(10)
~?x=4
-get(9)*get(8))+get(8)*(get(5)*get(9)-get(6)*get(8)))
/ms98)


~+|~?q=2|1|c
~t7=(t=%ms96%)
~:end_t_values
1            /----------------------------------------------------------------
y
ms96         / ^2
y
SSE
SSE %t9%
~?q=1
y

ms99
-ms90*get(2)
~?x>1
-ms91*get(4)
~?x>2
-ms92*get(7)
~?x>3
-ms93*get(11)
 

~+|~?q=2|1|c
1            /----------------------------------------------------------------
y
ms98         / R^2
y
R2
R2 %t9%
~?q=1
y

1-(ms99
-ms90*get(2)
~?x>1
-ms91*get(4)
~?x>2
-ms92*get(7)
~?x>3
-ms93*get(11)
)/(ms99
~t1=%4%
~?t1=1
-get(2)*get(2)/get(1)
)
 

~+|~?q=2|1|c
1            /----------------------------------------------------------------
y
ms99         / N
y
N
N %t9%
~?q=1
y

get(1)
 

~+|~?q=2|1|c
q
~/===========================================================================
~/
~/  ms90:      A = %ms90% 	%t4%
~/  ms91:      B = %ms91% 	%t5%
~?x>2
~/  ms92:      C = %ms92% 	%t6%
~?x>3
~/  ms93:      D = %ms93% 	%t7%
~z=%ms99%
~?t1=1
~z-1
~/  ms95:    SST = %ms95% 	(DF=%z%)
~z-%x%
~?t1=1
~z+1
~/  ms96:    SSE = %ms96% 	(DF=%z%)
~/  ms97:  SIGMA = %ms97%
~/  ms98:     R2 = %ms98%
~/  ms99:      N = %ms99%
~/
~/Regression done:
~t9=*(%4%)
~?t9=*(1)
~t9=
~?x=2
~/%3% ~= %ms90%%t9% + %ms91%*(%5%)
~?x=3
~/%3% ~= %ms90%%t9% + %ms91%*(%5%) + %ms92%*(%6%)
~?x=4
~/%3% ~= %ms90%%t9% + %ms91%*(%5%) + %ms92%*(%6%) + %ms93%*(%7%)
~:end_of_macro
~?!y&4194304  / reset switch 22 (engineering notation) if it was OFF
off=22
~/===========================================================================
~o=6