8999 REM REVISED JUNE, 1972    ANDY ROTH  C.C.G.
9000 REM ****: CURFIT ****: MATHEMATICS PROGRAM *****
9001 REM ***** VERSION 1 ***** 7/31/69 ****:
9002 REM LEAST SQUARES CURVE FIR #1
9003 DIM X(200),Y(200),U(200),V(200),A(6),B(6),C(6),S(6),F(6)
9004 MAT F=CON
9005 INPUT"HOW MANY DATA PAIRS";N
9006 PRINT
9007 FOR I=1 TO N
9008 PRINT"DATA PAIR #";I;:INPUTX(I),Y(I)
9009 NEXT I
9010 PRINT
9011 PRINT
9012 PRINT " ","LEAST SQUARES CURVES FIT"
9013 PRINT
9014 PRINT "CURVE TYPE","  INDEX OF ","   A","   B"
9015 PRINT " ","DETERMINATION"
9016 PRINT
9017 FOR I=1 TO 6
9018 MAT S=ZER
9019 GOSUB 9120
9020 IF (I-5)*(I-6)=0 THEN 9035
9021 IF (I-2)*(I-3)=0 THEN 9028
9022 FOR J=1 TO N
9023 LET V(J)=Y(J)
9024 GOSUB 9098
9025 NEXT J
9026 IF I=1 THEN 9045
9027 GOTO 9056
9028 FOR J=1 TO N
9029 IF Y(J) <= 0 THEN 9042
9030 LET V(J)=LOG(Y(J))
9031 GOSUB 9098
9032 NEXT J
9033 IF I=3 THEN 9050
9034 GOTO 9045
9035 FOR J=1 TO N
9036 IF Y(J)=0 THEN 9042
9037 LET V(J)=1/Y(J)
9038 GOSUB 9098
9039 NEXT J
9040 IF I=6 THEN 9056
9041 GOTO 9045
9042 PRINT "CAN'T FIT"
9043 LET F(I)=0
9044 GOTO 9063
9045 FOR J=1 TO N
9046 LET U(J)=X(J)
9047 GOSUB 9101
9048 NEXT J
9049 GOTO 9061
9050 FOR J=1 TO N
9051 IF X(J) <= 0 THEN 9042
9052 LET U(J)=LOG(U(J))
9053 GOSUB 9101
9054 NEXT J
9055 GOTO 9061
9056 FOR J=1 TO N
9057 IF X(J)=0 THEN 9042
9058 LET U(J)=1/X(J)
9059 GOSUB 9101
9060 NEXT J
9061 GOSUB 9161
9062 PRINT C(I),A(I),B(I)
9063 NEXT I
9064 GOSUB 9105
9065 PRINT
9066 PRINT
9067 PRINT
9068 PRINT"DETAILS FOR CURVE TYPE [0 TO TERMINATE]";
9069 INPUT I
9070 IF I=0 THEN 9999
9071 LET K=I
9072 IF F(I)=1 THEN 9076
9073 GOSUB 9120
9074 PRINT " COULD NOT BE FIT."
9075 GOTO 9065
9076 GOSUB 9138
9077 IF (I-1)*(I-5)*(I-6)<>0 THEN 9087
9078 FOR J=1 TO N
9079 LET Y=A(I)+B(I)*X(J)
9080 IF I=1 THEN 9084
9081 LET Y=1/Y
9082 IF I=5 THEN 9094
9083 LET Y=X(J)*Y
9084 GOSUB 9176
9085 NEXT J
9086 GOTO 9065
9087 FOR J=1 TO N
9088 IF I=2 THEN 9094
9089 IF I=3 THEN 9092
9090 LET Y=A(4)+B(4)/X(J)
9091 GOTO 9095
9092 LET Y=A(3)*(X(J)^B(3))
9093 GOTO 9095
9094 LET Y=A(2)*EXP(B(2)*X(J))
9095 GOSUB 9176
9096 NEXT J
9097 GOTO 9065
9098 LET S(5)=S(5)+V(J)^2
9099 LET S(3)=S(3)+V(J)
9100 RETURN
9101 LET S(1)=S(1)+U(J)
9102 LET S(2)=S(2)+U(J)^2
9103 LET S(4)=S(4)+U(J)*V(J)
9104 RETURN
9105 FOR I=1 TO N-1
9106 LET M=I
9107 FOR J=I+1 TO N
9108 IF X(M) <= X(J) THEN 9110
9109 LET M=J
9110 NEXT J
9111 IF M=I THEN 9118
9112 LET P=X(M)
9113 LET Q=Y(M)
9114 LET S(M)=X(I)
9115 LET Y(M)=Y(I)
9116 LET X(I)=P
9117 LET Y(I)=Q
9118 NEXT I
9119 RETURN
9120 LET K=I
9121 IF K=1 THEN 9136
9122 IF K=2 THEN 9134
9123 IF K=3 THEN 9132
9124 IF K=4 THEN 9130
9125 IF K=5 THEN 9128
9126 PRINT "6. Y=X/(A+B*X) ";
9127 RETURN
9128 PRINT "5. Y=1/(A+B*X) ";
9129 RETURN
9130 PRINT "4. Y=A+(B/X)",
9131 RETURN
9132 PRINT "3. Y=A*(X^B)",
9133 RETURN
9134 PRINT "2. Y=AEXP(B*X)";
9135 RETURN
9136 PRINT"1. Y=A+(B*X)",
9137 RETURN
9138 PRINT "   ";
9139 GOSUB 9121
9140 PRINT " IS A";
9141 IF K=1 THEN 9146
9142 IF K=2 THEN 9148
9143 IF K=3 THEN 9150
9144 PRINT " HYPERBOLIC";
9145 GOTO 9151
9146 PRINT " LINERAR";
9147 GOTO 9151
9148 PRINT "N EXPONENTIAL";
9149 GOT O 9151
9150 PRINT " POWER";
9151 PRINT " FUNCTION.  THEN RESULTS"
9152 IF K=1 THEN 9154
9153 PRINT "     OF A LEAST-SQUARES FIT OF ITS LINEAR TRANSFORM"
9154 PRINT "     (SORTED IN ORDER OF ASCENDING VALUES OF X)"
9155 PRINT "     ARE AS FOLLOWS:"
9156 PRINT
9157 PRINT "X-ACTUAL","Y-ACTUAL","Y-CALC","PCT DIFFER"
9158 PRINT
9159 RETURN
9160 PRINT
9161 LET B=(N*S(4)-S(1)*S(3))/(N*S(2)-(S(1)^2))
9162 LET A=(S(3)-B*S(1))/N
9163 LET S1=S(5)-(S(3)^2)/N
9164 LET S2=(B^2)*(S(2)-(S(1)^2)/N)
9165 LET C(I)=S2/S1
9166 IF (I-1)*(I-4)*(I-5)=0 THEN 9173
9167 IF (I-2)*(I-3)=0 THEN 9171
9168 LET A(6)=B
9169 LET B(6)=A
9170 RETURN
9171 LET A(I)=EXP(A)
9172 GOTO 9174
9173 LET A(I)=A
9174 LET B(I)=B
9175 RETURN
9176 PRINT X(J),Y(J),Y,
9177 LET D=Y(J)-Y
9178 LET D=.1*SGN(D)*INT(1000*ABS(D/Y))
9179 IF D<0 THEN 9184
9180 IF D>0 THEN 9183
9181 PRINT "     0"
9182 RETURN
9183 PRINT "      ";
9184 PRINT D
9185 RETURN
9999 END