Solving Two Equations using MATRIX
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Suppose we have a 6X6 correlation matrix. I have two equations I need to solve. The following is GIVEN: COMPUTE r11 = 1. COMPUTE r12 = .20. COMPUTE r13 = .25. COMPUTE r14 = .85. COMPUTE r15 = .30. COMPUTE r16 = .15. COMPUTE r21 = .20. COMPUTE r22 = 1. COMPUTE r23 = .10. COMPUTE r24 = .05. COMPUTE r25 = .70. COMPUTE r26 = .30. COMPUTE r31 = .25. COMPUTE r32 = .10. COMPUTE r33 = 1. COMPUTE r34 = .35. COMPUTE r35 = .40. COMPUTE r36 = .80. COMPUTE r41 = .85. COMPUTE r42 = .05. COMPUTE r43 = .35. COMPUTE r44 = 1. COMPUTE r45 = .50. COMPUTE r46 = .45. COMPUTE r51 = .30. COMPUTE r52 = .70. COMPUTE r53 = .40. COMPUTE r54 = .50. COMPUTE r55 = 1. COMPUTE r56 = .55. COMPUTE r61 = .15. COMPUTE r62 = .30. COMPUTE r63 = .80. COMPUTE r64 = .45. COMPUTE r65 = .55. COMPUTE r66 = 1. COMPUTE wjk14 = 2. COMPUTE wjk15 = -1. COMPUTE wjk16 = -1. COMPUTE wjk24 = -1. COMPUTE wjk25 = 2. COMPUTE wjk26 = -1. COMPUTE wjk34 = -1. COMPUTE wjk35 = -1. COMPUTE wjk36 = 2. FIRST EQUATION: Sum[{j=1,3},{k=4,6}: w[j,k]*r[j,k]] COMPUTE x = wjk14*r14 + wjk15*r15 + wjk16*r16 + wjk24*r24 + wjk25*r25 + wjk26*r26 + wjk34*r34 + wjk35*r35 + wjk36*r36. While x is easy to solve outside of MATRIX, I'm curious how x could be solved more efficiently in MATRIX. Suppose the following is GIVEN as well: COMPUTE whm14 = 2. COMPUTE whm15 = -1. COMPUTE whm16 = -1. COMPUTE whm24 = -1. COMPUTE whm25 = 2. COMPUTE whm26 = -1. COMPUTE whm34 = -1. COMPUTE whm35 = -1. COMPUTE whm36 = 2. SECOND EQUATION: y = Sqrt[(.5/(N-1))*Sum[{j=1,3},{k=4,6},{h=1,3},{m=4,6}: w[j,k]*w[h,m]*( (r[j,h]-r[j,k]*r[k,h])*(r[k,m]-r[k,h]*r[h,m]) + (r[j,m]-r[j,h]*r[h,m])*(r[k,h]-r[k,j]*r[j,h]) + (r[j,h]-r[j,m]*r[m,h])*(r[k,m]-r[k,j]*r[j,m]) + (r[j,m]-r[j,k]*r[k,m])*(r[k,h]-r[k,m]*r[m,h]))]] As you can see, y is far more tedious to solve outside of MATRIX. The first of 81 "Sum[{..." terms could be solved using COMPUTE as follows: COMPUTE jk14_hm14 = wjk14*whm14*((r11-r14*r41)*(r44-r41*r14)+(r14-r11*r14)*(r41-r41*r11)+(r11-r14*r41)*(r44-r41*r14)+(r14-r14*r44)*(r41-r44*r41)). but then I'd have to work it out for the following 80 terms: compute jk15_hm14 = . compute jk16_hm14 = . compute jk24_hm14 = . compute jk25_hm14 = . compute jk26_hm14 = . compute jk34_hm14 = . compute jk35_hm14 = . compute jk36_hm14 = . compute jk14_hm24 = . compute jk15_hm24 = . compute jk16_hm24 = . compute jk24_hm24 = . compute jk25_hm24 = . compute jk26_hm24 = . compute jk34_hm24 = . compute jk35_hm24 = . compute jk36_hm24 = . compute jk14_hm34 = . compute jk15_hm34 = . compute jk16_hm34 = . compute jk24_hm34 = . compute jk25_hm34 = . compute jk26_hm34 = . compute jk34_hm34 = . compute jk35_hm34 = . compute jk36_hm34 = . compute jk14_hm15 = . compute jk15_hm15 = . compute jk16_hm15 = . compute jk24_hm15 = . compute jk25_hm15 = . compute jk26_hm15 = . compute jk34_hm15 = . compute jk35_hm15 = . compute jk36_hm15 = . compute jk14_hm16 = . compute jk15_hm16 = . compute jk16_hm16 = . compute jk24_hm16 = . compute jk25_hm16 = . compute jk26_hm16 = . compute jk34_hm16 = . compute jk35_hm16 = . compute jk36_hm16 = . compute jk14_hm25 = . compute jk15_hm25 = . compute jk16_hm25 = . compute jk24_hm25 = . compute jk25_hm25 = . compute jk26_hm25 = . compute jk34_hm25 = . compute jk35_hm25 = . compute jk36_hm25 = . compute jk14_hm26 = . compute jk15_hm26 = . compute jk16_hm26 = . compute jk24_hm26 = . compute jk25_hm26 = . compute jk26_hm26 = . compute jk34_hm26 = . compute jk35_hm26 = . compute jk36_hm26 = . compute jk14_hm35 = . compute jk15_hm35 = . compute jk16_hm35 = . compute jk24_hm35 = . compute jk25_hm35 = . compute jk26_hm35 = . compute jk34_hm35 = . compute jk35_hm35 = . compute jk36_hm35 = . compute jk14_hm36 = . compute jk15_hm36 = . compute jk16_hm36 = . compute jk24_hm36 = . compute jk25_hm36 = . compute jk26_hm36 = . compute jk34_hm36 = . compute jk35_hm36 = . compute jk36_hm36 = . and then sum the 81 terms and multiply by Sqrt[(.5/(N-1)). Any tips would be most appreciated. Thanks, Ryan |
Re: Solving Two Equations using MATRIX
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Hi Ryan,
Good to see you here! Here is a simple MATRIX program. Please verify that I haven't dropped a stitch. Curious as to what this is calculating. Could it be related to the Determinant of a matrix? If so there is the DET operator . MATRIX. COMPUTE R={1.00, .20, .25, .85, .30, .15; .20,1.00, .10, .05, .70, .30; .25, .10,1.00, .35, .40, .80; .85, .05, .35,1.00, .50, .45; .30, .70, .40, .50,1.00, .55; .15, .30, .80, .45, .55, 1.00}. COMPUTE W={0,0,0, 2,-1,-1; 0,0,0,-1, 2,-1; 0,0,0,-1,-1, 2; 0,0,0, 0, 0, 0; 0,0,0, 0, 0, 0; 0,0,0, 0, 0, 0}. COMPUTE X=MSUM(R&*W). COMPUTE y=0. LOOP j=1 TO 3. LOOP k=4 TO 6. LOOP h=1 TO 3. LOOP m=4 TO 6. COMPUTE y=y +w(j,k)*w(h,m) * (r(j,h)-r(j,k)*r(k,h))*(r(k,m)-r(k,h)*r(h,m)) + (r(j,m)-r(j,h)*r(h,m))*(r(k,h)-r(k,j)*r(j,h)) + (r(j,h)-r(j,m)*r(m,h))*(r(k,m)-r(k,j)*r(j,m)) + (r(j,m)-r(j,k)*r(k,m))*(r(k,h)-r(k,m)*r(m,h)) . END LOOP. END LOOP. END LOOP. END LOOP. COMPUTE y=SQRT(.5/??? -1) * y. END MATRIX.
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Those desiring my consulting or training services please feel free to email me. --- "Nolite dare sanctum canibus neque mittatis margaritas vestras ante porcos ne forte conculcent eas pedibus suis." Cum es damnatorum possederunt porcos iens ut salire off sanguinum cliff in abyssum?" |
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Thanks for the help, David! This is great!!! The code just needs two modifications.... COMPUTE y=y +w(j,k)*w(h,m) * (r(j,h)-r(j,k)*r(k,h))*(r(k,m)-r(k,h)*r(h,m)) + (r(j,m)-r(j,h)*r(h,m))*(r(k,h)-r(k,j)*r(j,h)) + (r(j,h)-r(j,m)*r(m,h))*(r(k,m)-r(k,j)*r(j,m)) + (r(j,m)-r(j,k)*r(k,m))*(r(k,h)-r(k,m)*r(m,h)) . should be COMPUTE y=y +w(j,k)*w(h,m) * ((r(j,h)-r(j,k)*r(k,h))*(r(k,m)-r(k,h)*r(h,m)) + (r(j,m)-r(j,h)*r(h,m))*(r(k,h)-r(k,j)*r(j,h)) + (r(j,h)-r(j,m)*r(m,h))*(r(k,m)-r(k,j)*r(j,m)) + (r(j,m)-r(j,k)*r(k,m))*(r(k,h)-r(k,m)*r(m,h))) . and COMPUTE y=SQRT(.5/??? -1) * y. should be COMPUTE y=SQRT(.5/(??? -1)) * y. x / y = z where, y is the estimated standard error and z is approximately standard normal which tests: Null Hypothesis: M[rho14,rho25,rho36] = M[rho15,rho16,rho24,rho26,rho34,rho35] Thanks again! Ryan p.s., thanks to Ray Koopman for referring me to the appropriate 1980 Steiger article which assisted me in constructing the test, and for providing additional guidance / confirmation along the way On Sun, Jul 19, 2015 at 11:37 PM, David Marso <[hidden email]> wrote: Hi Ryan, END LOOP. |
Re: Solving Two Equations using MATRIX
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Ryan, am I correct in assuming that in your statement of the null hypothesis, M[] represents the mean of the (population) correlations inside the square brackets? Thanks for clarifying.
p.s. - Ray's great, isn't he. If I ever start thinking that I'm getting to know quite a bit about statistics & data analysis, I just take a look at Ray, and invariably come away in a humbled condition. ;-)
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
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Hi Bruce,
Yes to your question. And I couldn't agree more about Ray. I'm very fortunate and grateful to have him as a resource. Best, Ryan Sent from my iPhone > On Jul 21, 2015, at 6:17 PM, Bruce Weaver <[hidden email]> wrote: > > Ryan, am I correct in assuming that in your statement of the null hypothesis, > M[] represents the *mean* of the (population) correlations inside the square > brackets? Thanks for clarifying. > > p.s. - Ray's great, isn't he. If I ever start thinking that I'm getting to > know quite a bit about statistics & data analysis, I just take a look at > Ray, and invariably come away in a humbled condition. ;-) > > > > Ryan Black wrote >> Thanks for the help, David! This is great!!! >> >> The code just needs two modifications.... >> >> COMPUTE y=y +w(j,k)*w(h,m) * >> (r(j,h)-r(j,k)*r(k,h))*(r(k,m)-r(k,h)*r(h,m)) + >> (r(j,m)-r(j,h)*r(h,m))*(r(k,h)-r(k,j)*r(j,h)) + >> (r(j,h)-r(j,m)*r(m,h))*(r(k,m)-r(k,j)*r(j,m)) + >> (r(j,m)-r(j,k)*r(k,m))*(r(k,h)-r(k,m)*r(m,h)) . >> >> should be >> >> COMPUTE y=y +w(j,k)*w(h,m) * >> ((r(j,h)-r(j,k)*r(k,h))*(r(k,m)-r(k,h)*r(h,m)) + >> (r(j,m)-r(j,h)*r(h,m))*(r(k,h)-r(k,j)*r(j,h)) + >> (r(j,h)-r(j,m)*r(m,h))*(r(k,m)-r(k,j)*r(j,m)) + >> (r(j,m)-r(j,k)*r(k,m))*(r(k,h)-r(k,m)*r(m,h))) . >> >> and >> >> COMPUTE y=SQRT(.5/??? -1) * y. >> >> should be >> >> COMPUTE y=SQRT(.5/(??? -1)) * y. >> >> x / y = z >> >> where, >> >> y is the estimated standard error and z is approximately standard normal >> which tests: >> >> Null Hypothesis: M[rho14,rho25,rho36] = >> M[rho15,rho16,rho24,rho26,rho34,rho35] >> >> Thanks again! >> >> Ryan >> >> p.s., thanks to Ray Koopman for referring me to the appropriate 1980 >> Steiger article which assisted me in constructing the test, and for >> providing additional guidance / confirmation along the way >> >> On Sun, Jul 19, 2015 at 11:37 PM, David Marso < > >> david.marso@ > >> > wrote: >> >>> Hi Ryan, >>> Good to see you here! >>> Here is a simple MATRIX program. >>> Please verify that I haven't dropped a stitch. >>> Curious as to what this is calculating. >>> Could it be related to the Determinant of a matrix? >>> If so there is the DET operator . >>> >>> MATRIX. >>> COMPUTE R={1.00, .20, .25, .85, .30, .15; >>> .20,1.00, .10, .05, .70, .30; >>> .25, .10,1.00, .35, .40, .80; >>> .85, .05, .35,1.00, .50, .45; >>> .30, .70, .40, .50,1.00, .55; >>> .15, .30, .80, .45, .55, 1.00}. >>> COMPUTE W={0,0,0, 2,-1,-1; >>> 0,0,0,-1, 2,-1; >>> 0,0,0,-1,-1, 2; >>> 0,0,0, 0, 0, 0; >>> 0,0,0, 0, 0, 0; >>> 0,0,0, 0, 0, 0}. >>> >>> COMPUTE X=MSUM(R&*W). >>> COMPUTE y=0. >>> LOOP j=1 TO 3. >>> LOOP k=4 TO 6. >>> LOOP h=1 TO 3. >>> LOOP m=4 TO 6. >>> COMPUTE y=y +w(j,k)*w(h,m) * >>> (r(j,h)-r(j,k)*r(k,h))*(r(k,m)-r(k,h)*r(h,m)) + >>> (r(j,m)-r(j,h)*r(h,m))*(r(k,h)-r(k,j)*r(j,h)) + >>> (r(j,h)-r(j,m)*r(m,h))*(r(k,m)-r(k,j)*r(j,m)) + >>> (r(j,m)-r(j,k)*r(k,m))*(r(k,h)-r(k,m)*r(m,h)) . >> >> END LOOP. >>> END LOOP. >>> END LOOP. >>> END LOOP. >>> COMPUTE y=SQRT(.5/??? -1) * y. >>> END MATRIX. >>> >>> >>> >>> >>> Ryan Black wrote >>>> Dear SPSS-L, >>>> >>>> Suppose we have a 6X6 correlation matrix. I have two equations I need >>> to >>>> solve. >>>> >>>> The following is GIVEN: >>>> >>>> COMPUTE r11 = 1. >>>> COMPUTE r12 = .20. >>>> COMPUTE r13 = .25. >>>> COMPUTE r14 = .85. >>>> COMPUTE r15 = .30. >>>> COMPUTE r16 = .15. >>>> COMPUTE r21 = .20. >>>> COMPUTE r22 = 1. >>>> COMPUTE r23 = .10. >>>> COMPUTE r24 = .05. >>>> COMPUTE r25 = .70. >>>> COMPUTE r26 = .30. >>>> COMPUTE r31 = .25. >>>> COMPUTE r32 = .10. >>>> COMPUTE r33 = 1. >>>> COMPUTE r34 = .35. >>>> COMPUTE r35 = .40. >>>> COMPUTE r36 = .80. >>>> COMPUTE r41 = .85. >>>> COMPUTE r42 = .05. >>>> COMPUTE r43 = .35. >>>> COMPUTE r44 = 1. >>>> COMPUTE r45 = .50. >>>> COMPUTE r46 = .45. >>>> COMPUTE r51 = .30. >>>> COMPUTE r52 = .70. >>>> COMPUTE r53 = .40. >>>> COMPUTE r54 = .50. >>>> COMPUTE r55 = 1. >>>> COMPUTE r56 = .55. >>>> COMPUTE r61 = .15. >>>> COMPUTE r62 = .30. >>>> COMPUTE r63 = .80. >>>> COMPUTE r64 = .45. >>>> COMPUTE r65 = .55. >>>> COMPUTE r66 = 1. >>>> >>>> COMPUTE wjk14 = 2. >>>> COMPUTE wjk15 = -1. >>>> COMPUTE wjk16 = -1. >>>> COMPUTE wjk24 = -1. >>>> COMPUTE wjk25 = 2. >>>> COMPUTE wjk26 = -1. >>>> COMPUTE wjk34 = -1. >>>> COMPUTE wjk35 = -1. >>>> COMPUTE wjk36 = 2. >>>> >>>> FIRST EQUATION: >>>> >>>> Sum[{j=1,3},{k=4,6}: w[j,k]*r[j,k]] >>>> >>>> COMPUTE x = wjk14*r14 + wjk15*r15 + wjk16*r16 + >>>> wjk24*r24 + wjk25*r25 + wjk26*r26 + >>>> wjk34*r34 + wjk35*r35 + wjk36*r36. >>>> >>>> While x is easy to solve outside of MATRIX, I'm curious how x could be >>>> solved more efficiently in MATRIX. >>>> >>>> Suppose the following is GIVEN as well: >>>> >>>> COMPUTE whm14 = 2. >>>> COMPUTE whm15 = -1. >>>> COMPUTE whm16 = -1. >>>> COMPUTE whm24 = -1. >>>> COMPUTE whm25 = 2. >>>> COMPUTE whm26 = -1. >>>> COMPUTE whm34 = -1. >>>> COMPUTE whm35 = -1. >>>> COMPUTE whm36 = 2. >>>> >>>> SECOND EQUATION: >>>> >>>> y = Sqrt[(.5/(N-1))*Sum[{j=1,3},{k=4,6},{h=1,3},{m=4,6}: >>>> w[j,k]*w[h,m]*( >>>> >>>> (r[j,h]-r[j,k]*r[k,h])*(r[k,m]-r[k,h]*r[h,m]) + >>>> >>>> (r[j,m]-r[j,h]*r[h,m])*(r[k,h]-r[k,j]*r[j,h]) + >>>> >>>> (r[j,h]-r[j,m]*r[m,h])*(r[k,m]-r[k,j]*r[j,m]) + >>>> >>>> (r[j,m]-r[j,k]*r[k,m])*(r[k,h]-r[k,m]*r[m,h]))]] >>>> >>>> As you can see, y is far more tedious to solve outside of MATRIX. The >>>> first >>>> of 81 "Sum[{..." terms could be solved using COMPUTE as follows: >>>> >>>> COMPUTE jk14_hm14 = >>> wjk14*whm14*((r11-r14*r41)*(r44-r41*r14)+(r14-r11*r14)*(r41-r41*r11)+(r11-r14*r41)*(r44-r41*r14)+(r14-r14*r44)*(r41-r44*r41)). >>>> >>>> but then I'd have to work it out for the following 80 terms: >>>> >>>> compute jk15_hm14 = . >>>> compute jk16_hm14 = . >>>> compute jk24_hm14 = . >>>> compute jk25_hm14 = . >>>> compute jk26_hm14 = . >>>> compute jk34_hm14 = . >>>> compute jk35_hm14 = . >>>> compute jk36_hm14 = . >>>> >>>> compute jk14_hm24 = . >>>> compute jk15_hm24 = . >>>> compute jk16_hm24 = . >>>> compute jk24_hm24 = . >>>> compute jk25_hm24 = . >>>> compute jk26_hm24 = . >>>> compute jk34_hm24 = . >>>> compute jk35_hm24 = . >>>> compute jk36_hm24 = . >>>> >>>> compute jk14_hm34 = . >>>> compute jk15_hm34 = . >>>> compute jk16_hm34 = . >>>> compute jk24_hm34 = . >>>> compute jk25_hm34 = . >>>> compute jk26_hm34 = . >>>> compute jk34_hm34 = . >>>> compute jk35_hm34 = . >>>> compute jk36_hm34 = . >>>> >>>> compute jk14_hm15 = . >>>> compute jk15_hm15 = . >>>> compute jk16_hm15 = . >>>> compute jk24_hm15 = . >>>> compute jk25_hm15 = . >>>> compute jk26_hm15 = . >>>> compute jk34_hm15 = . >>>> compute jk35_hm15 = . >>>> compute jk36_hm15 = . >>>> >>>> compute jk14_hm16 = . >>>> compute jk15_hm16 = . >>>> compute jk16_hm16 = . >>>> compute jk24_hm16 = . >>>> compute jk25_hm16 = . >>>> compute jk26_hm16 = . >>>> compute jk34_hm16 = . >>>> compute jk35_hm16 = . >>>> compute jk36_hm16 = . >>>> >>>> compute jk14_hm25 = . >>>> compute jk15_hm25 = . >>>> compute jk16_hm25 = . >>>> compute jk24_hm25 = . >>>> compute jk25_hm25 = . >>>> compute jk26_hm25 = . >>>> compute jk34_hm25 = . >>>> compute jk35_hm25 = . >>>> compute jk36_hm25 = . >>>> >>>> compute jk14_hm26 = . >>>> compute jk15_hm26 = . >>>> compute jk16_hm26 = . >>>> compute jk24_hm26 = . >>>> compute jk25_hm26 = . >>>> compute jk26_hm26 = . >>>> compute jk34_hm26 = . >>>> compute jk35_hm26 = . >>>> compute jk36_hm26 = . >>>> >>>> compute jk14_hm35 = . >>>> compute jk15_hm35 = . >>>> compute jk16_hm35 = . >>>> compute jk24_hm35 = . >>>> compute jk25_hm35 = . >>>> compute jk26_hm35 = . >>>> compute jk34_hm35 = . >>>> compute jk35_hm35 = . >>>> compute jk36_hm35 = . >>>> >>>> compute jk14_hm36 = . >>>> compute jk15_hm36 = . >>>> compute jk16_hm36 = . >>>> compute jk24_hm36 = . >>>> compute jk25_hm36 = . >>>> compute jk26_hm36 = . >>>> compute jk34_hm36 = . >>>> compute jk35_hm36 = . >>>> compute jk36_hm36 = . >>>> >>>> and then sum the 81 terms and multiply by Sqrt[(.5/(N-1)). >>>> >>>> Any tips would be most appreciated. >>>> >>>> Thanks, >>>> >>>> Ryan >>>> >>>> ===================== >>>> To manage your subscription to SPSSX-L, send a message to >>> >>>> LISTSERV@.UGA >>> >>>> (not to SPSSX-L), with no body text except the >>>> command. To leave the list, send the command >>>> SIGNOFF SPSSX-L >>>> For a list of commands to manage subscriptions, send the command >>>> INFO REFCARD >>> >>> >>> >>> >>> >>> ----- >>> Please reply to the list and not to my personal email. >>> Those desiring my consulting or training services please feel free to >>> email me. >>> --- >>> "Nolite dare sanctum canibus neque mittatis margaritas vestras ante >>> porcos >>> ne forte conculcent eas pedibus suis." >>> Cum es damnatorum possederunt porcos iens ut salire off sanguinum cliff >>> in >>> abyssum?" >>> -- >>> View this message in context: >>> http://spssx-discussion.1045642.n5.nabble.com/Solving-Two-Equations-using-MATRIX-tp5730174p5730175.html >>> Sent from the SPSSX Discussion mailing list archive at Nabble.com. >>> >>> ===================== >>> To manage your subscription to SPSSX-L, send a message to > >> LISTSERV@.UGA > >> (not to SPSSX-L), with no body text except the >>> command. To leave the list, send the command >>> SIGNOFF SPSSX-L >>> For a list of commands to manage subscriptions, send the command >>> INFO REFCARD >> >> ===================== >> To manage your subscription to SPSSX-L, send a message to > >> LISTSERV@.UGA > >> (not to SPSSX-L), with no body text except the >> command. To leave the list, send the command >> SIGNOFF SPSSX-L >> For a list of commands to manage subscriptions, send the command >> INFO REFCARD > > > > > > ----- > -- > Bruce Weaver > [hidden email] > http://sites.google.com/a/lakeheadu.ca/bweaver/ > > "When all else fails, RTFM." > > NOTE: My Hotmail account is not monitored regularly. > To send me an e-mail, please use the address shown above. > > -- > View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Solving-Two-Equations-using-MATRIX-tp5730174p5730214.html > Sent from the SPSSX Discussion mailing list archive at Nabble.com. > > ===================== > To manage your subscription to SPSSX-L, send a message to > [hidden email] (not to SPSSX-L), with no body text except the > command. To leave the list, send the command > SIGNOFF SPSSX-L > For a list of commands to manage subscriptions, send the command > INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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