LABEL 0000000000XXXXXX0010000001 $ CARD LIST BEGIN SRAN 1 COMMENT BIVARIATE CORRELATION AND REGRESSION ANALYSIS. THE LONG SRAN 2 METHOD OF DIFFERENCES FROM THE AVERAGE IS USED SRAN 3 RATHER THAN THE SHORT-CUT SUM OF SQUARES. BOTH SRAN 4 Y = AX + B AND X = A"Y + B" ARE FITTED. THE LINE MAY BE SRAN 5 FORCED THROUGH THE ORIGIN ; SRAN 6 BEGIN SRAN 7 INTEGER J, N, NAME ; SRAN 8 BOOLEAN S, SWF, SWP ; SRAN 9 REAL IJ, DJ, ESTIMATE, RESIDUAL, SUMX, SUMY, SUMXY, SUMX2, SRAN 10 SUMY2, DXY, DX2, DY2, AVERAGEX, AVERAGEY, DIFFX, DIFFY, SRAN 11 VARIANCEX, VARIANCEY, SE, SA, SB, TA, TB, R2, SRAN 12 R, A, B, VARIANCE ; SRAN 13 FILE IN CARD1 (1,10) ; SRAN 14 FORMAT IN CARD2 (X10, 2E20.11), SRAN 15 CARD3 (X10, 4I5) ; SRAN 16 LIST SIZES (SWF, SWP, NAME, N) ; SRAN 17 FILE OUT PAPER (1,15) ; SRAN 18 FORMAT OUT HEAD (X45, "SIMPLE REGRESSION ANALYSIS" //), SRAN 19 FORM (X43, "CASE NO.", I11 // X40, "DATA POINTS", I11 // SRAN 20 X47, "CONSTANT TERM", //), SRAN 21 AVERAGEF (X25, "AVERAGE X", E16.8, X10, SRAN 22 "AVERAGE Y", E16.8, //), SRAN 23 VARIANCEF (X25, "VARIANCE X", E16.8, X9, SRAN 24 "VARIANCE Y", E16.8, //), SRAN 25 RF (X10, "CORRELATION COEFFICIENT", E16.8, SRAN 26 X10, "FRACTION OF VARIANCE REMOVED", E16.8, //), SRAN 27 HEAD1 (X47, "Y = AX + B" //), SRAN 28 AF(X5, "SLOPE", E16.8, X10, "SLOPE ERROR", SRAN 29 E16.8, X10, "SLOPE T-VALUE", E16.8, //), SRAN 30 BF ("INTERCEPT", E16.8, X10, "INTERCEPT ERROR", E16.8, SRAN 31 X10, "INTERCEPT T-VALUE", E16.8, //), SRAN 32 ERRORF (X18, "VARIANCE OF FIT", E16.8, X10, SRAN 33 "STANDARD ERROR OF ESTIMATE", E16.8, //), SRAN 34 HEAD2 (X47, "X = AY + B" //), SRAN 35 RESIDUALS (// // X23, "INDEPENDENT", X11, "DEPENDENT", SRAN 36 X13, "ESTIMATE", X13, "RESIDUAL" //), SRAN 37 RESF (X20, 4(E16.8, X5)), SRAN 38 FORCE (/ X45, "NO CONSTANT TERM" //), SRAN 39 TITLE1 (X49, "Y = AX" //), SRAN 40 TITLE2 (X49, "X = AY" //) ; SRAN 41 LIST CASE (NAME, N), SRAN 42 AVERAGEO (AVERAGEX, AVERAGEY), SRAN 43 VARIANCEO (VARIANCEX, VARIANCEY), SRAN 44 RO (R, R | R), SRAN 45 AO (A, SA, TA), SRAN 46 BO (B, SB, TB), SRAN 47 ERRORO (VARIANCE, SE), SRAN 48 RESO (IJ, DJ, ESTIMATE, RESIDUAL), SRAN 49 RFOO (R, R2) ; SRAN 50 LABEL START ; SRAN 51 START : READ (CARD1, CARD3, SIZES) ; SRAN 52 WRITE (PAPER, HEAD) ; SRAN 53 WRITE (PAPER, FORM, CASE) ; SRAN 54 SUMX ~ SUMY ~ SUMXY ~ SUMX2 ~ SUMY2 ~ SRAN 55 DXY ~ DX2 ~ DY2 ~ 0 ; SRAN 56 BEGIN SRAN 57 REAL ARRAY X[0:N], Y[0:N] ; SRAN 58 COMMENT THE PROCEDURE PRINTDIFF COMPUTES THE RESIDUALS AND PRINTS SRAN 59 THEM ALONG WITH THE CORRESPONDING DATA ; SRAN 60 PROCEDURE PRINTDIFF ; SRAN 61 BEGIN SRAN 62 WRITE (PAPER, RESIDUALS) ; SRAN 63 FOR J ~ 1 STEP 1 UNTIL N DO SRAN 64 BEGIN SRAN 65 IF S THEN SRAN 66 BEGIN SRAN 67 IJ ~ X[J] ; DJ ~ Y[J] SRAN 68 END SRAN 69 ELSE SRAN 70 BEGIN SRAN 71 IJ ~ Y[J] ; DJ ~ X[J] SRAN 72 END ; SRAN 73 ESTIMATE ~ A | IJ + B ; SRAN 74 RESIDUAL ~ DJ - ESTIMATE ; SRAN 75 WRITE (PAPER, RESF, RESO) SRAN 76 END ; SRAN 77 WRITE (PAPER [PAGE], RESF) SRAN 78 END PRINTDIFF ; SRAN 79 LIST DATA (X[J], Y[J]) ; SRAN 80 LABEL FORCELINE ; SRAN 81 FOR J ~ 1 STEP 1 UNTIL N DO SRAN 82 BEGIN SRAN 83 READ (CARD1, CARD2, DATA) ; SRAN 84 IJ ~ X[J] ; DJ ~ Y[J] ; SRAN 85 SUMX ~ IJ + SUMX ; SRAN 86 SUMY ~ DJ + SUMY ; SRAN 87 SUMXY ~ IJ | DJ + SUMXY ; SRAN 88 SUMX2 ~ IJ * 2 + SUMX2 ; SRAN 89 SUMY2 ~ DJ * 2 + SUMY2 SRAN 90 END ; SRAN 91 AVERAGEX ~ SUMX / N ; SRAN 92 AVERAGEY ~ SUMY / N ; SRAN 93 WRITE (PAPER, AVERAGEF, AVERAGEO) ; SRAN 94 FOR J ~ 1 STEP 1 UNTIL N DO SRAN 95 BEGIN SRAN 96 DIFFX ~ AVERAGEX - X[J] ; SRAN 97 DIFFY ~ AVERAGEY - Y[J] ; SRAN 98 DXY ~ DIFFX | DIFFY + DXY ; SRAN 99 DX2 ~ DIFFX * 2 + DX2 ; SRAN 100 DY2 ~ DIFFY * 2 + DY2 SRAN 101 END ; SRAN 102 VARIANCEX ~ DX2 / (N-1) ; SRAN 103 VARIANCEY ~ DY2 / (N-1) ; SRAN 104 WRITE (PAPER, VARIANCEF, VARIANCEO) ; SRAN 105 COMMENT COMPUTE THE CORRELATION COEFFICIENT ; SRAN 106 R ~ DXY / SQRT (DX2 | DY2) ; SRAN 107 WRITE (PAPER, RF, RO) ; SRAN 108 COMMENT COMPUTE REGRESSION COEFFICIENTS FOR Y = F(X) AND X = F(Y) SRAN 109 ALONG WITH OTHER RELATED DATA ; SRAN 110 WRITE (PAPER, HEAD1) ; SRAN 111 A ~ DXY / DX2 ; SRAN 112 B ~ (SUMY - A | SUMX) / N ; SRAN 113 VARIANCE ~ (DY2 - A | DXY) / (N-2) ; SRAN 114 SE ~ SQRT (VARIANCE) ; SRAN 115 SA ~ SE / SQRT (DX2) ; SRAN 116 TA ~ A / SA ; SRAN 117 WRITE (PAPER, AF, AO) ; SRAN 118 SB ~ SE | SQRT (SUMX2 / (N | DX2)) ; SRAN 119 TB ~ B/SB ; SRAN 120 WRITE (PAPER, BF, BO) ; SRAN 121 WRITE (PAPER, ERRORF, ERRORO) ; SRAN 122 IF SWP THEN SRAN 123 BEGIN SRAN 124 S ~ TRUE ; PRINTDIFF SRAN 125 END ; SRAN 126 WRITE (PAPER, HEAD2) ; SRAN 127 A ~ DXY / DY2 ; SRAN 128 B ~ (SUMX - A | SUMY) / N ; SRAN 129 VARIANCE ~ (DX2 - A | DXY) / (N-2) ; SRAN 130 SE ~ SQRT (VARIANCE) ; SRAN 131 SA ~ SE / SQRT (DY2) ; SRAN 132 TA ~ A / SA ; SRAN 133 WRITE (PAPER, AF, AO) ; SRAN 134 SB ~ SE | SQRT (SUMY2 / (N | DY2)) ; SRAN 135 TB ~ B / SB ; SRAN 136 WRITE (PAPER, BF, BO) ; SRAN 137 WRITE (PAPER, ERRORF, ERRORO) ; SRAN 138 IF SWP THEN SRAN 139 BEGIN SRAN 140 S ~ FALSE ; PRINTDIFF SRAN 141 END ; SRAN 142 IF NOT SWF THEN GO TO START ; SRAN 143 FORCELINE : WRITE (PAPER, FORCE) ; SRAN 144 B ~ R ~ 0 ; SRAN 145 A ~ SUMXY / SUMX2 ; SRAN 146 R2 ~ (A | SUMXY - SUMY | SUMY / N) / DY2 ; SRAN 147 WRITE (PAPER, TITLE1) ; SRAN 148 WRITE (PAPER, RF, RFOO) ; SRAN 149 VARIANCE ~ (SUMY2 - A | SUMXY) / (N-1) ; SRAN 150 SE ~ SQRT (VARIANCE) ; SRAN 151 SA ~ SE / SQRT (SUMX2) ; SRAN 152 TA ~ A / SA ; SRAN 153 WRITE (PAPER, AF, AO) ; SRAN 154 WRITE (PAPER, ERRORF, ERRORO) ; SRAN 155 IF SWP THEN SRAN 156 BEGIN SRAN 157 S ~ TRUE ; PRINTDIFF SRAN 158 END ; SRAN 159 WRITE (PAPER, TITLE2) ; SRAN 160 A ~ SUMXY / SUMY2 ; SRAN 161 R2 ~ (A | SUMXY - SUMX | SUMX / N) / DX2 ; SRAN 162 WRITE (PAPER, RF, RFOO) ; SRAN 163 VARIANCE ~ (SUMX2 - A | SUMXY) / (N-1) ; SRAN 164 SE ~ SQRT (VARIANCE) ; SRAN 165 SA ~ SE / SQRT (SUMY2) ; SRAN 166 TA ~ A / SA ; SRAN 167 WRITE (PAPER, AF, AO) ; SRAN 168 WRITE (PAPER, ERRORF, ERRORO) ; SRAN 169 IF SWP THEN SRAN 170 BEGIN SRAN 171 S ~ FALSE ; PRINTDIFF SRAN 172 END ; SRAN 173 GO TO START SRAN 174 END SRAN 175 END BIVARIATE ; SRAN 176 END . SRAN 177 LABEL 000000000II 0010000001 1 1 11 16 1.1 @ 0.109 @ 2 1.8 @ 0.1145 @ 2 2.5 @ 0.12 @ 2 2.2 @ 0.121 @ 2 3.1 @ 0.1245 @ 2 2.7 @ 0.123 @ 2 2.6 @ 0.1235 @ 2 3.5 @ 0.129 @ 2 2.4 @ 0.1185 @ 2 2.6 @ 0.12 @ 2 2.5 @ 0.1225 @ 2 2.1 @ 0.1175 @ 2 0.9 @ 0.109 @ 2 1.9 @ 0.116 @ 2 2.8 @ 0.1215 @ 2 1.8 @ 0.1145 @ 2