Brief analyses of the two sereis of HW#5. There are many adequate models for a given time series. The model I obtained is not the only model available. (A) GDP series -- input yy,mm,dd,gdp. file 'gdp.txt' YY , A 235 BY 1 VARIABLE, IS STORED IN THE WORKSPACE ... GDP , A 235 BY 1 VARIABLE, IS STORED IN THE WORKSPACE -- x=ln(gdp) -- iarima x. THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 235 THE CRITICAL VALUE FOR SIGNIFICANCE TESTS OF ACF AND ESTIMATES IS 1.960 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- UTSMODEL ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED 1 X RANDOM ORIGINAL (1-B ) ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 CNST 1 0 NONE .0170 .0012 14.18 2 X D-AR 1 1 NONE .4607 .0581 7.93 TOTAL NUMBER OF OBSERVATIONS . . . . 235 EFFECTIVE NUMBER OF OBSERVATIONS . . 233 RESIDUAL STANDARD ERROR. . . . . . . 0.993144E-02 -- iden x. dfor 1. 1 DIFFERENCE ORDERS. . . . . . . . . . . (1-B ) NAME OF THE SERIES . . . . . . . . . . X TIME PERIOD ANALYZED . . . . . . . . . 1 TO 235 MEAN OF THE (DIFFERENCED) SERIES . . . 0.0170 STANDARD DEVIATION OF THE SERIES . . . 0.0112 T-VALUE OF MEAN (AGAINST ZERO) . . . . 23.2475 AUTOCORRELATIONS 1- 12 .46 .31 .06 -.03 -.15 -.05 .03 .05 .19 .22 .19 .04 ST.E. .07 .08 .08 .08 .08 .08 .08 .08 .08 .09 .09 .09 Q 50.3 73.0 73.9 74.1 79.5 80.1 80.3 80.9 89.8 101 110 111 13- 24 .03 .05 .06 .20 .20 .24 .16 .17 .03 .02 -.03 .03 ST.E. .09 .09 .09 .09 .09 .09 .10 .10 .10 .10 .10 .10 Q 111 112 113 123 133 149 155 162 162 163 163 163 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 +----+----+----+----+----+----+----+----+----+----+ I 1 0.46 + IXX+XXXXXXXXX 2 0.31 + IXXX+XXXX 3 0.06 + IXX + 4 -0.03 + XI + 5 -0.15 XXXXI + 6 -0.05 + XI + 7 0.03 + IX + 8 0.05 + IX + 9 0.19 + IXXX+X 10 0.22 + IXXX+X 11 0.19 + IXXX+X 12 0.04 + IX + 13 0.03 + IX + 14 0.05 + IX + 15 0.06 + IXX + 16 0.20 + IXXX+X 17 0.20 + IXXXXX 18 0.24 + IXXXX+X 19 0.16 + IXXXX+ 20 0.17 + IXXXX+ 21 0.03 + IX + 22 0.02 + IX + 23 -0.03 + XI + 24 0.03 + IX + PARTIAL AUTOCORRELATIONS 1- 12 .46 .12 -.15 -.05 -.11 .10 .10 -.03 .17 .08 .01 -.10 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 13- 24 .03 .16 .04 .17 .03 .08 .00 .04 -.02 .05 -.01 .04 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 +----+----+----+----+----+----+----+----+----+----+ I 1 0.46 + IXX+XXXXXXXXX 2 0.12 + IXXX 3 -0.15 X+XXI + 4 -0.05 + XI + 5 -0.11 XXXI + 6 0.10 + IXXX 7 0.10 + IXXX 8 -0.03 + XI + 9 0.17 + IXX+X 10 0.08 + IXX+ 11 0.01 + I + 12 -0.10 +XXI + 13 0.03 + IX + 14 0.16 + IXX+X 15 0.04 + IX + 16 0.17 + IXX+X 17 0.03 + IX + 18 0.08 + IXX+ 19 0.00 + I + 20 0.04 + IX + 21 -0.02 + I + 22 0.05 + IX + 23 -0.01 + I + 24 0.04 + IX + -- tsm m1. model (1,2,3)x(1)=c1+noise. -- estim m1. hold resi(r1). THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 235 NONLINEAR ESTIMATION TERMINATED DUE TO: RELATIVE CHANGE IN (OBJECTIVE FUNCTION)**0.5 LESS THAN 0.1000D-02 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- M1 ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED 1 X RANDOM ORIGINAL (1-B ) ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 C1 CNST 1 0 NONE .0092 .0014 6.58 2 X AR 1 1 NONE .4220 .0642 6.57 3 X AR 1 2 NONE .1885 .0688 2.74 4 X AR 1 3 NONE -.1553 .0642 -2.42 EFFECTIVE NUMBER OF OBSERVATIONS . . 231 R-SQUARE . . . . . . . . . . . . . . 1.000 RESIDUAL STANDARD ERROR. . . . . . . 0.966299E-02 -- acf r1. NAME OF THE SERIES . . . . . . . . . . R1 TIME PERIOD ANALYZED . . . . . . . . . 5 TO 235 MEAN OF THE (DIFFERENCED) SERIES . . . 0.0000 STANDARD DEVIATION OF THE SERIES . . . 0.0097 T-VALUE OF MEAN (AGAINST ZERO) . . . . -0.0006 AUTOCORRELATIONS 1- 12 -.00 -.01 .05 .03 -.13 .04 .06 -.05 .08 .14 .11 -.08 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 Q .0 .0 .6 .8 5.0 5.3 6.3 7.0 8.5 13.1 15.9 17.6 13- 24 -.01 .05 -.04 .14 .10 .13 .01 .11 -.02 .04 -.04 .03 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 Q 17.6 18.2 18.6 23.3 25.7 30.0 30.0 32.9 33.0 33.3 33.7 33.9 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 +----+----+----+----+----+----+----+----+----+----+ I 1 0.00 + I + 2 -0.01 + I + 3 0.05 + IX + 4 0.03 + IX + 5 -0.13 XXXI + 6 0.04 + IX + 7 0.06 + IXX+ 8 -0.05 + XI + 9 0.08 + IXX+ 10 0.14 + IXXX 11 0.11 + IXXX 12 -0.08 +XXI + 13 -0.01 + I + 14 0.05 + IX + 15 -0.04 + XI + 16 0.14 + IXXX 17 0.10 + IXX + 18 0.13 + IXXX+ 19 0.01 + I + 20 0.11 + IXXX+ 21 -0.02 + I + 22 0.04 + IX + 23 -0.04 + XI + 24 0.03 + IX + -- outlier m1. type ao,io,ls,tc. INITIAL RESIDUAL STANDARD ERROR = 0.96630E-02 TIME ESTIMATE T-VALUE TYPE 126 0.04 4.36 IO 96 -0.02 -3.80 AO 12 -0.03 -3.63 TC 15 0.03 3.70 IO 136 0.03 3.79 IO 9 -0.03 -3.85 IO 138 -0.02 -3.86 AO 45 -0.03 -3.68 LS 53 0.02 3.49 TC 44 -0.02 -3.35 IO 24 0.02 3.10 TC 56 -0.02 -3.11 LS ADJUSTED RESIDUAL STANDARD ERROR = 0.68510E-02 -- oestim m1. hold resi(r1). new v1,v2. THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 235 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- M1 ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED 1 X RANDOM ORIGINAL (1-B ) ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 C1 CNST 1 0 NONE .0088 .0012 7.45 2 X AR 1 1 NONE .4268 .0616 6.93 3 X AR 1 2 NONE .4010 .0626 6.40 4 X AR 1 3 NONE -.3695 .0616 -6.00 SUMMARY OF OUTLIER DETECTION AND ADJUSTMENT ------------------------------------- TIME ESTIMATE T-VALUE TYPE ------------------------------------- 9 -0.033 -5.62 LS 10 -0.022 -3.05 IO 13 0.025 3.67 IO 24 0.017 3.60 TC 44 -0.020 -3.02 IO 45 -0.028 -5.07 LS 50 0.015 4.41 AO 96 -0.021 -5.91 AO 100 -0.012 -3.53 AO 105 0.020 3.69 LS 115 0.022 3.27 IO 126 0.043 6.35 IO 136 0.041 6.92 LS 137 0.027 3.74 IO 141 -0.016 -4.55 AO ------------------------------------- TOTAL NUMBER OF OBSERVATIONS. . . . . . . . . . . . . . 235 EFFECTIVE NUMBER OF OBSERVATIONS. . . . . . . . . . . . 231 RESIDUAL STANDARD ERROR (WITHOUT OUTLIER ADJUSTMENT). . 0.998499E-02 RESIDUAL STANDARD ERROR (WITH OUTLIER ADJUSTMENT) . . . 0.672875E-02 -- acf v1. NAME OF THE SERIES . . . . . . . . . . V1 TIME PERIOD ANALYZED . . . . . . . . . 5 TO 235 MEAN OF THE (DIFFERENCED) SERIES . . . 0.0000 STANDARD DEVIATION OF THE SERIES . . . 0.0065 T-VALUE OF MEAN (AGAINST ZERO) . . . . -0.0548 AUTOCORRELATIONS 1- 12 .01 -.00 .01 .03 -.04 .04 -.01 .04 .03 .07 -.10 -.05 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 Q .0 .0 .0 .2 .7 1.0 1.0 1.4 1.7 2.9 5.3 5.8 13- 24 -.03 .03 .15 .06 -.02 .07 .00 .06 -.07 .02 .04 -.01 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 Q 6.1 6.4 12.1 12.8 12.9 14.2 14.2 15.1 16.5 16.6 17.1 17.1 -- (B) DPI series input yy,mm,dd,dpi. file 'dpi.txt' YY , A 235 BY 1 VARIABLE, IS STORED IN THE WORKSPACE .... DPI , A 235 BY 1 VARIABLE, IS STORED IN THE WORKSPACE -- y=ln(dpi) -- iarima y THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 235 THE CRITICAL VALUE FOR SIGNIFICANCE TESTS OF ACF AND ESTIMATES IS 1.960 SAMPLE ACF OF THE RESIDUALS (** SIGNIFICANT VALUES EXIST **) 1 - 12 -.01 -.00 .06 -.07 -.05 .11 .11 .00 .08 .21 .07 .02 T-VALUE -.22 -.05 .97-1.10 -.72 1.72 1.57 .03 1.18 3.11 1.02 .30 13 - 24 .09 -.01 .03 .08 .12 .10 .14 -.00 .05 .09 .03 -.01 T-VALUE 1.21 -.18 .38 1.18 1.60 1.33 1.88 -.06 .66 1.21 .42 -.20 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- UTSMODEL ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED 1 Y RANDOM ORIGINAL (1-B ) ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 CNST 1 0 NONE .0170 .0011 15.85 2 Y D-AR 1 1 NONE .1301 .0628 2.07 3 Y D-AR 1 2 NONE .2191 .0619 3.54 TOTAL NUMBER OF OBSERVATIONS . . . . 235 EFFECTIVE NUMBER OF OBSERVATIONS . . 232 RESIDUAL STANDARD ERROR. . . . . . . 0.106421E-01 -- iden y. dfor 1. 1 DIFFERENCE ORDERS. . . . . . . . . . . (1-B ) NAME OF THE SERIES . . . . . . . . . . Y TIME PERIOD ANALYZED . . . . . . . . . 1 TO 235 MEAN OF THE (DIFFERENCED) SERIES . . . 0.0170 STANDARD DEVIATION OF THE SERIES . . . 0.0114 T-VALUE OF MEAN (AGAINST ZERO) . . . . 22.9540 AUTOCORRELATIONS 1- 12 .12 .23 .12 .01 -.00 .11 .18 .13 .16 .32 .09 .15 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .08 .08 .08 Q 3.6 16.6 20.1 20.2 20.2 23.3 30.8 34.7 41.1 65.9 67.8 73.2 13- 24 .13 .06 .10 .13 .19 .15 .21 .10 .11 .11 .09 .03 ST.E. .08 .08 .08 .08 .09 .09 .09 .09 .09 .09 .09 .09 Q 77.4 78.5 81.1 85.1 94.7 101 112 114 117 121 123 123 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 +----+----+----+----+----+----+----+----+----+----+ I 1 0.12 + IXXX 2 0.23 + IXX+XXX 3 0.12 + IXXX 4 0.01 + I + 5 0.00 + I + 6 0.11 + IXXX 7 0.18 + IXXXX 8 0.13 + IXXX+ 9 0.16 + IXXXX 10 0.32 + IXXX+XXXX 11 0.09 + IXX + 12 0.15 + IXXXX 13 0.13 + IXXX+ 14 0.06 + IXX + 15 0.10 + IXXX+ 16 0.13 + IXXX+ 17 0.19 + IXXX+X 18 0.15 + IXXXX 19 0.21 + IXXX+X 20 0.10 + IXX + 21 0.11 + IXXX+ 22 0.11 + IXXX+ 23 0.09 + IXX + 24 0.03 + IX + PARTIAL AUTOCORRELATIONS 1- 12 .12 .22 .08 -.06 -.05 .13 .19 .06 .04 .27 .03 .02 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 13- 24 .05 .03 .06 .03 .09 .08 .08 -.08 .03 .06 .01 -.10 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 +----+----+----+----+----+----+----+----+----+----+ I 1 0.12 + IXXX 2 0.22 + IXX+XXX 3 0.08 + IXX+ 4 -0.06 +XXI + 5 -0.05 + XI + 6 0.13 + IXXX 7 0.19 + IXX+XX 8 0.06 + IX + 9 0.04 + IX + 10 0.27 + IXX+XXXX 11 0.03 + IX + 12 0.02 + I + 13 0.05 + IX + 14 0.03 + IX + 15 0.06 + IXX+ 16 0.03 + IX + 17 0.09 + IXX+ 18 0.08 + IXX+ 19 0.08 + IXX+ 20 -0.08 +XXI + 21 0.03 + IX + 22 0.06 + IXX+ 23 0.01 + I + 24 -0.10 +XXI + -- tsm m2. model (1,2)y(1)=c2+noise. -- estim m2. hold resi(r2) THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 235 NONLINEAR ESTIMATION TERMINATED DUE TO: RELATIVE CHANGE IN (OBJECTIVE FUNCTION)**0.5 LESS THAN 0.1000D-02 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- M2 ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED 1 Y RANDOM ORIGINAL (1-B ) ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 C2 CNST 1 0 NONE .0111 .0016 7.00 2 Y AR 1 1 NONE .1300 .0628 2.07 3 Y AR 1 2 NONE .2190 .0619 3.54 EFFECTIVE NUMBER OF OBSERVATIONS . . 232 R-SQUARE . . . . . . . . . . . . . . 1.000 RESIDUAL STANDARD ERROR. . . . . . . 0.106421E-01 -- acf r2. NAME OF THE SERIES . . . . . . . . . . R2 TIME PERIOD ANALYZED . . . . . . . . . 4 TO 235 MEAN OF THE (DIFFERENCED) SERIES . . . 0.0000 STANDARD DEVIATION OF THE SERIES . . . 0.0106 T-VALUE OF MEAN (AGAINST ZERO) . . . . -0.0005 AUTOCORRELATIONS 1- 12 -.01 -.00 .06 -.07 -.05 .11 .11 .00 .08 .21 .07 .02 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 Q .0 .1 1.0 2.3 2.8 6.0 8.7 8.7 10.2 21.3 22.6 22.7 13- 24 .09 -.01 .03 .08 .12 .10 .14 -.00 .05 .09 .03 -.01 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .08 .08 .08 Q 24.6 24.6 24.8 26.6 30.0 32.4 37.3 37.3 37.9 40.1 40.3 40.4 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 +----+----+----+----+----+----+----+----+----+----+ I 1 -0.01 + I + 2 0.00 + I + 3 0.06 + IXX+ 4 -0.07 +XXI + 5 -0.05 + XI + 6 0.11 + IXXX 7 0.11 + IXXX 8 0.00 + I + 9 0.08 + IXX+ 10 0.21 + IXX+XX 11 0.07 + IXX+ 12 0.02 + IX + 13 0.09 + IXX + 14 -0.01 + I + 15 0.03 + IX + 16 0.08 + IXX + 17 0.12 + IXXX+ 18 0.10 + IXX + 19 0.14 + IXXX+ 20 0.00 + I + 21 0.05 + IX + 22 0.09 + IXX + 23 0.03 + IX + 24 -0.01 + I + -- outlier m2. type ao,io,ls,tc. INITIAL RESIDUAL STANDARD ERROR = 0.10642E-01 TIME ESTIMATE T-VALUE TYPE 13 0.06 5.80 IO 9 -0.05 -4.98 IO 114 0.04 4.50 LS 220 -0.02 -3.54 AO 185 -0.03 -3.52 IO 136 0.03 3.51 LS 104 0.03 3.58 IO 14 -0.02 -3.37 TC 8 -0.03 -3.32 IO 232 0.02 3.12 AO ADJUSTED RESIDUAL STANDARD ERROR = 0.76004E-02 -- oestim m2. hold resi(r2). new w1,w2. THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 235 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- M2 ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED 1 Y RANDOM ORIGINAL (1-B ) ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 C2 CNST 1 0 NONE .0071 .0013 5.66 2 Y AR 1 1 NONE .3889 .0622 6.26 3 Y AR 1 2 NONE .1918 .0606 3.17 SUMMARY OF OUTLIER DETECTION AND ADJUSTMENT ------------------------------------- TIME ESTIMATE T-VALUE TYPE ------------------------------------- 8 -0.030 -4.07 IO 9 -0.042 -5.75 IO 13 0.060 8.21 IO 104 0.024 3.55 LS 114 0.027 6.47 AO 134 -0.026 -4.41 TC 139 0.021 3.12 LS 154 0.015 3.49 AO 162 -0.020 -3.49 TC 185 -0.030 -4.48 LS 189 -0.019 -3.27 TC 218 -0.013 -3.14 AO 220 -0.022 -5.30 AO 232 0.016 3.80 AO ------------------------------------- ** THE OUTLIER(S) AFTER TIME PERIOD 230 OCCURS WITHIN THE LAST FIVE OBSERVATIONS OF THE SERIES. THE IDENTIFIED TYPE ANS THE ESTIMATE OF THE OUTLIER(S) MAY NOT BE RELIABLE TOTAL NUMBER OF OBSERVATIONS. . . . . . . . . . . . . . 235 EFFECTIVE NUMBER OF OBSERVATIONS. . . . . . . . . . . . 232 RESIDUAL STANDARD ERROR (WITHOUT OUTLIER ADJUSTMENT). . 0.110247E-01 RESIDUAL STANDARD ERROR (WITH OUTLIER ADJUSTMENT) . . . 0.732574E-02 -- acf w1. NAME OF THE SERIES . . . . . . . . . . W1 TIME PERIOD ANALYZED . . . . . . . . . 4 TO 235 MEAN OF THE (DIFFERENCED) SERIES . . . 0.0000 STANDARD DEVIATION OF THE SERIES . . . 0.0071 T-VALUE OF MEAN (AGAINST ZERO) . . . . 0.0101 AUTOCORRELATIONS 1- 12 .02 -.07 .01 -.08 .05 .05 .13 .02 .07 .04 .05 .08 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 Q .1 1.1 1.2 2.5 3.1 3.7 7.6 7.7 8.7 9.1 9.6 11.2 13- 24 -.01 .09 .01 .14 .21 .03 -.06 .02 .00 .01 .09 -.00 ST.E. .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 .07 Q 11.3 13.3 13.3 18.2 29.4 29.6 30.5 30.5 30.5 30.5 32.9 32.9 -- ofore m2. nofs 5. RESIDUAL STANDARD ERROR (USES DATA UP TO THE FIRST FORECAST ORIGIN)=0.73257E-02 TIME ESTIMATE T-VALUE TYPE 8 -0.030 -4.07 IO 9 -0.042 -5.75 IO 13 0.060 8.21 IO 104 0.024 3.55 LS 114 0.027 6.47 AO 134 -0.026 -4.41 TC 139 0.021 3.12 LS 154 0.015 3.49 AO 162 -0.020 -3.49 TC 185 -0.030 -4.48 LS 189 -0.019 -3.27 TC 218 -0.013 -3.14 AO 220 -0.022 -5.30 AO 232 0.016 3.80 AO ---------------------------------- 5 FORECASTS, BEGINNING AT 235 ---------------------------------- TIME FORECAST STD. ERROR ACTUAL IF KNOWN 236 9.1248 0.0073 237 9.1378 0.0125 238 9.1523 0.0178 239 9.1675 0.0228 240 9.1833 0.0275