dear Ivan, I've not gone into residual analysis; but my observation is simple: I've checked the hist of both HF5 and HF6. There is not much difference. Also I've replaced all outliers. HF1 ~ (m/HF5 )+ 1 is getting fitted properly, but not HF1 ~ (m/HF6) + 1. The following are the actual values:
> HF1 Time Series: Start = 1 End = 800 Frequency = 1 [1] 1.0319256 0.9842066 1.0098243 1.0446384 0.9177308 1.0060822 0.9609599 1.0374124 1.0139675 0.9973329 0.9559346 0.9848896 [13] 0.9749513 1.0511627 0.9789968 1.0964832 0.9879833 0.9549759 0.9787043 1.0203225 0.9947078 0.9813439 1.0138056 0.9670097 [25] 0.9711946 0.9873085 1.0858024 1.0394149 0.9766102 0.9689002 1.0097453 1.0235376 0.9873976 0.9705998 1.0356838 1.0165155 [37] 0.9855907 1.0757638 1.0072182 1.0280799 0.9281543 0.9587241 1.1086856 1.0446199 1.0158398 0.9529567 1.0610853 0.9976204 [49] 0.9575143 0.9803208 1.1238821 1.0118991 1.0112989 0.9415333 1.0424331 0.9912462 1.0106361 0.9802978 1.0108935 1.0159902 [61] 0.9892313 0.9438749 1.0118004 0.9953912 0.9175923 0.9479009 1.0235502 1.0060517 0.9890903 0.9885812 0.9900430 1.0350717 [73] 1.0108698 1.0468498 1.0656555 1.0436655 0.9908752 0.9751098 1.0163194 0.9851445 0.9710072 0.9885114 1.0109649 1.0490736 [85] 0.9795251 1.0108749 1.0029784 1.0149087 0.9965277 0.9893746 0.9917926 1.0115123 1.0472170 1.0437206 1.0139089 1.0372349 [97] 1.0038352 0.9586151 1.0085806 1.0119048 1.0118624 0.9896469 1.0272961 1.0172400 1.0134005 0.9757968 0.9717420 1.0269058 [109] 1.0114416 0.9512890 1.0181753 1.0565599 1.0376291 0.9865798 1.0212159 1.0701965 1.0324734 0.9899814 0.9973403 1.0172419 [121] 1.0020050 0.9889063 1.0129236 1.0277797 0.9826509 0.9922282 1.0988522 1.0275115 1.0183555 0.9774303 1.0172997 1.0150803 [133] 0.9685015 0.9924186 0.9937192 1.0072210 0.9673327 1.0473338 1.0562761 0.9707440 0.9771936 0.9883559 1.0208805 0.9894798 [145] 1.0694593 0.9754638 1.0383527 1.0013232 0.9863309 0.8778824 1.0157532 1.0438316 1.0000022 0.9740199 1.0305441 1.0275372 [157] 0.9723386 0.9954525 1.0046082 0.9531964 0.9768512 0.9899314 1.0496263 1.0546074 0.9616430 1.0210772 0.9901334 1.0689765 [169] 1.0154938 0.8765444 0.9919604 1.0082690 0.9860675 0.9823378 0.9897682 1.0363582 0.9805102 0.9723787 1.0741545 1.0290322 [181] 0.9760903 0.9850951 1.0500385 0.9774908 0.9861186 0.9898369 0.9941887 1.0097938 1.0187774 1.0591694 1.0270933 1.0466363 [193] 1.0000043 0.9815685 1.0238718 0.9740055 0.9717232 1.0251001 0.9946316 1.0075567 0.9751129 0.9871612 1.0643235 1.0075491 [205] 0.9888058 0.9396797 1.0068366 0.9962325 1.0455487 1.0442334 1.0103938 1.0236919 0.9852552 0.9767037 1.0063593 1.0518584 [217] 0.9705860 0.9718808 1.0178662 1.0414515 0.9883699 0.9860597 1.0394941 1.0103630 0.9082023 0.9889798 0.9646139 1.0052705 [229] 0.9688456 1.0559528 1.0401153 0.9785603 1.0169463 0.9929363 0.9812825 0.9302532 1.0272447 1.0644704 1.0201468 1.0248872 [241] 0.9587034 0.9884793 1.0065787 1.0568458 1.0167972 0.9702934 1.0233577 1.0052691 0.9690838 0.9900543 1.0171212 1.0093782 [253] 0.9518359 0.8953816 1.1180924 1.0126421 0.9847542 0.9731075 0.9906067 1.0191311 0.9757062 0.9819144 1.0392988 1.0358210 [265] 0.9842700 1.0057314 1.0206313 1.0088607 0.9779384 0.9860996 0.9894232 1.0180867 1.0060215 0.9419578 1.0604701 1.0186874 [277] 0.9824626 0.9303484 1.0491317 1.0204767 0.9892820 0.9971268 1.0322837 1.0435960 1.0123649 0.9791956 0.9880841 1.0203823 [289] 0.9696436 0.9769832 1.0704628 1.0230000 0.9665417 0.8624573 1.0152342 1.0538081 0.9885551 0.9605257 1.0196322 1.0135050 [301] 1.0420189 0.9875982 1.0228686 1.0224319 0.9778704 0.9912653 1.0116106 1.0226598 0.9387455 0.9717815 1.0122788 0.9889690 [313] 1.0232488 1.0276606 1.0173681 1.0159885 0.9877074 0.9838069 1.0374707 1.0152624 0.9789677 0.9612178 1.0192874 1.0644549 [325] 0.9715407 0.9787567 0.9925342 0.9790322 0.9777879 0.9680505 1.0224064 1.0348370 0.9875051 0.9457753 0.9914921 0.9591109 [337] 0.9629202 0.9995519 1.0136481 1.0221348 1.0148608 0.9912785 1.0439862 1.0330749 0.9762325 0.9983923 0.9348918 1.0227065 [349] 0.9794121 0.9733227 1.0082373 1.0421889 0.9767361 0.9726911 1.0100370 0.9921361 0.9861159 0.9749961 1.0594331 1.0806732 [361] 1.0276992 1.0329190 1.0686383 1.0466639 0.9740776 0.9672371 1.0128714 0.9934691 0.9582222 0.9332858 1.0029784 1.0250300 [373] 1.0059249 0.9999445 1.0082015 1.0252359 0.9760324 0.9493543 0.9996351 1.0116540 0.9675301 0.9470141 1.0127507 1.0112527 [385] 0.9766712 0.9703953 1.0592567 1.0360448 0.9790881 0.9680051 0.9711350 1.0049626 0.9738689 0.9819661 1.0835125 0.9765333 [397] 0.9138484 1.0220322 1.0465788 1.0065803 1.0273082 0.9838126 1.0151329 1.0146824 0.9452442 0.9489901 0.9921946 1.0101152 [409] 0.9730738 0.9354592 0.9542558 0.9681532 0.9792620 1.0352246 1.0426173 1.0180344 0.9576323 0.9533448 0.9846387 1.0261479 [421] 0.9453757 0.9455791 1.0691109 1.0084141 0.9844405 0.9537970 1.0118840 1.0094733 1.1493009 0.9922558 0.9941628 1.0290179 [433] 1.0020050 0.9971342 1.0436267 1.0726863 1.0925811 1.1072580 1.0390200 1.0376942 1.0302470 0.9838505 1.0420336 0.9793092 [445] 0.9850191 1.0196805 1.0065491 1.0158645 1.0117730 0.9406381 1.0097070 0.9870108 0.9818856 1.0040046 0.9712323 0.9951345 [457] 1.0199816 1.0551752 1.0112867 1.0763534 1.0253155 1.0029784 1.0251464 1.0814414 0.9987183 0.9771628 0.9726044 1.0482059 [469] 1.0020050 0.8931139 1.0367775 1.0260033 0.9728766 1.0225689 0.9908196 1.0068729 0.9912127 0.9931128 1.0158280 1.0433496 [481] 1.0203120 1.0085496 0.9812741 1.0615742 1.0119223 0.9849236 0.9992032 0.9879929 0.9000571 0.9891419 1.0345521 1.0381184 [493] 0.9886766 0.9574869 1.0149106 1.0294410 0.9882982 1.0244778 0.9812230 1.0082813 0.9664091 1.0283733 1.0124268 0.9992115 [505] 0.9872004 0.9884649 1.0386713 0.9763343 0.9597727 0.9567414 1.0086152 1.0165768 0.9848861 0.9620526 1.0123326 1.0447678 [517] 0.9934084 0.9669690 1.0360421 0.9829837 0.9761610 0.9708850 1.0014170 1.0195497 0.9806560 0.9757284 1.0251931 1.0116233 [529] 0.9868054 0.9756085 1.0303624 1.0077517 1.0505017 0.9414114 1.0124536 1.0131595 0.9638660 0.9887363 1.0132553 1.0052792 [541] 0.9820370 0.9460134 1.0125483 1.0426700 0.9818528 0.9762532 0.9582658 0.9814603 0.9618717 0.9615659 0.9496436 0.9877108 [553] 0.9999971 1.0284677 1.0106125 1.0031898 0.9793703 0.9486161 1.0226473 1.0236002 0.9538295 0.9689285 1.0313897 1.0212912 [565] 0.9505638 0.9921170 1.0130086 1.0419494 1.0000323 0.9607922 1.0211809 1.0424671 0.9795343 0.9497697 1.0231071 1.0142700 [577] 0.9765539 0.9492815 1.0267628 1.0135138 0.9885966 0.9529603 1.0264062 1.0249176 0.9872525 0.9849608 0.9986306 1.0437033 [589] 1.0041780 0.9931204 1.0329029 0.9939742 0.9459785 0.9629758 0.9456565 0.9836949 0.9754926 0.9976241 1.0232742 1.0050830 [601] 0.9481952 0.9854969 1.0352188 1.0337062 0.9892019 0.9554122 1.0189333 0.9793607 0.9899167 0.9503345 1.0117583 1.0371750 [613] 1.0070349 0.9804208 1.0500940 1.0107281 1.0698735 0.9881469 1.0565684 1.0179031 0.9856278 1.0314952 1.0720689 1.0011222 [625] 0.9743944 1.0034468 0.9824861 1.0192735 0.9991494 0.9842630 1.0060971 1.0294506 0.9695057 0.9725408 1.0227924 1.0088150 [637] 0.9765886 0.9889828 1.0108903 1.0068109 0.9905286 0.9517037 1.0527706 1.0257783 0.9932039 1.0121870 1.0506565 0.9816386 [649] 0.9843450 0.9552800 1.0124886 1.0332463 1.0021401 0.9885442 1.0136001 1.0381933 0.9594773 1.0679251 0.9653448 0.9997715 [661] 0.9890589 0.9658054 1.0079124 1.1292276 0.9873225 0.9730770 1.0699042 1.0174021 1.0041981 1.0232245 1.0389181 0.9720513 [673] 0.8686271 0.9915428 0.9606290 1.0482094 0.9898013 0.9510998 0.9602020 0.9976802 1.1427011 0.9917742 0.9770992 0.8638270 [685] 0.9991782 1.0455336 1.1043633 1.0489159 1.0029784 0.9906192 1.0307161 1.0182152 0.9677313 1.0090984 0.9851279 0.9596324 [697] 0.9743092 0.9748568 1.0206321 1.0517142 0.9876535 0.9732838 1.0656093 1.0603864 0.9980164 0.9795437 0.9746766 0.9784871 [709] 0.9746066 1.0484975 1.0228157 1.0165735 0.9785301 1.0322862 1.0303562 1.0203352 0.9606113 1.0674109 1.0051598 1.0095761 [721] 1.0138837 0.9862772 1.0173451 0.9879873 0.9761662 0.9828150 0.9839169 0.9887962 0.9474475 0.9786754 1.0405266 1.0246702 [733] 0.9764242 0.9782060 1.0004626 1.0653315 1.1480925 0.9567859 1.0410088 1.0246378 1.0025964 0.9894414 1.0146759 1.0449204 [745] 0.9917509 0.9706269 1.0199806 1.0044524 0.9942750 1.0145927 0.9917488 1.0314604 0.9495737 1.0005564 0.9972033 0.9849848 [757] 0.9741118 0.9693319 1.0061280 0.9892915 0.9944768 1.0101943 1.0545997 1.0044063 1.0020050 1.0127975 1.0164313 1.0285558 [769] 1.0043574 0.9854983 1.0122655 1.0123857 0.9879603 0.9734764 0.9995228 1.0315182 0.9564373 1.0543879 1.0099970 0.9987432 [781] 0.9580883 0.9724853 1.0167722 1.0102822 0.9629902 0.9908875 0.9838395 0.9733901 1.0207349 0.9848377 1.0633785 1.0312998 [793] 1.0316422 1.0335433 0.9890110 1.0334082 0.9915590 0.9909167 1.0208474 0.9899497 > HF6 Time Series: Start = 1 End = 800 Frequency = 1 [1] 9.703261e-02 -3.302060e-01 5.100922e+00 1.932550e+00 -1.386912e-01 1.482268e-02 -1.137384e+00 3.732522e-01 2.506729e-01 [10] -2.919045e-01 -6.675508e-02 -1.267444e+00 -4.271286e-01 1.539651e-01 -1.424168e-01 2.632788e-01 -6.013491e-02 -5.743224e-02 [19] -1.955379e-01 7.423308e-01 -3.041726e-03 -2.667225e-02 2.409421e-01 -4.339732e-02 -2.372542e-01 -2.194143e-01 2.712374e-01 [28] 1.764577e+00 -1.583502e-01 -1.558412e-01 4.859185e+00 6.595212e-02 -6.227563e-02 -3.663468e-02 9.338089e-01 1.165410e+00 [37] -3.776054e-02 1.015936e+01 4.269841e+00 8.659153e-01 -1.045996e+00 -8.061952e-01 2.627137e-01 1.023131e-01 2.757644e-01 [46] -6.199723e-02 1.466399e-01 -3.353696e-01 -2.881873e-01 -1.560865e-01 2.946743e-01 1.825263e-01 6.075510e-01 -7.659018e-02 [55] 9.332004e-02 -7.924914e-01 -2.995696e+00 -2.625424e-01 6.959834e+00 2.882190e-01 -5.555718e-02 -3.191530e+00 -2.894247e+00 [64] -7.495410e-01 -5.698178e-01 -2.920025e-01 7.262345e-02 6.955618e-01 -7.509777e-01 -3.111461e-02 -1.757717e+00 9.583333e-02 [73] 2.022944e-01 1.481875e-01 3.709509e-01 3.297667e+00 -1.679928e-02 -6.633111e-01 3.081464e-01 -1.522342e-01 -2.697393e-01 [82] -2.474069e-01 1.267182e+00 2.990766e-01 -1.483910e-01 1.851073e-02 -3.320246e+00 5.365467e-01 3.685251e-02 -5.869044e-02 [91] -5.304953e-01 8.510204e-02 -1.943394e+00 6.796528e-01 8.707915e+00 5.339946e-01 3.334323e-01 -5.567989e-01 1.741750e-01 [100] 3.974109e-01 -1.180250e-01 -3.248193e-01 2.839601e-01 8.396776e-01 1.587400e+00 -1.052848e-01 -5.427561e-02 1.308345e+00 [109] -4.321102e+00 -2.114642e+00 2.545551e-01 2.608206e-01 2.468002e-01 -3.503397e-01 8.657229e-02 4.993098e-01 2.432785e+00 [118] -1.896142e-02 -2.014234e+00 2.029458e+00 6.079714e+00 -2.764164e-01 2.669853e-01 3.423891e+00 -5.324067e-01 -1.615363e-02 [127] 2.728479e+00 2.063365e+00 3.873700e-01 -9.717373e-01 2.802471e-01 3.221953e+00 -1.380415e+00 -2.251014e-01 -9.367013e-01 [136] 1.453974e-01 -9.212878e-01 6.660146e-01 2.698844e-01 -2.378487e-01 -1.841615e-01 -7.505472e-01 2.545551e-01 -1.904946e-02 [145] 2.825536e-01 -1.849939e-01 3.591260e-01 3.743418e-01 -2.778478e+00 -1.329060e+00 3.160122e-01 4.643313e-01 5.750524e-05 [154] -6.072878e-01 2.644429e-01 1.874244e+00 -2.695451e-01 -9.715273e-03 3.494761e-01 -9.281908e-02 -1.818026e-01 -3.065760e+00 [163] 1.745485e-01 4.058502e-01 -7.937648e-02 4.082885e-01 -5.328007e-02 5.173842e-01 3.014029e-01 -1.332769e+00 -1.525841e+00 [172] 1.278083e+00 -2.592115e+00 -5.447981e-02 -5.511966e-02 1.499697e-01 -7.537936e-01 -6.736513e-01 2.502264e-01 1.421474e+00 [181] -1.908278e-01 -2.629398e+00 3.030101e-01 -5.162059e-01 -2.154668e-01 1.774540e-03 -8.088480e-01 5.501430e-01 5.268684e-02 [190] 2.180616e-01 5.120812e-01 2.823400e-01 1.174173e-04 -3.871419e-02 3.158028e+00 -1.044852e+00 -2.686278e-01 7.454716e-01 [199] 7.658868e+00 1.125989e+00 -1.923856e-01 -2.441550e+00 5.024290e-01 2.290590e+00 -5.988608e-02 -7.947542e-01 4.383090e-01 [208] -6.176262e-03 2.480572e-01 6.266179e-01 3.552698e+00 7.503722e-01 -2.675535e-02 -5.389840e-01 8.622592e-01 1.991035e-01 [217] -2.189162e-01 -1.161234e+00 6.972145e-01 2.780796e-01 -6.312992e-02 -2.608414e+00 2.618422e+00 5.462640e+00 -1.142624e+00 [226] -8.490826e-01 -1.288512e-01 4.011994e-02 -2.048321e-01 3.272460e+00 6.866489e-01 -5.466328e-02 3.070392e-01 -9.886495e-01 [235] -1.569525e+00 -1.306696e-01 3.623149e+00 1.978161e-01 2.545551e-01 2.002372e+00 -5.400229e-01 -1.656640e-02 1.206290e-01 [244] 2.054049e-01 3.155210e-01 -1.744452e-01 2.545551e-01 7.412855e-01 -1.234508e-01 -1.718832e-02 7.214410e-01 6.076084e-01 [253] -1.024878e+01 -1.287062e+00 3.080408e+00 5.876054e-01 -2.777261e-01 -1.009898e+00 -5.856174e-01 6.067372e-02 -8.840570e-02 [262] -3.594392e-01 1.813739e+00 1.405564e-01 -3.372484e-02 8.371325e-01 3.424895e-01 1.493120e+00 -1.433819e+00 -4.222862e-01 [271] -6.719543e-02 3.063784e+00 1.282949e-01 -1.294272e-01 3.830982e-01 2.144883e+00 -8.491788e-02 -2.231544e+00 3.286810e-01 [280] 7.426660e-01 -6.825884e-02 -3.435546e-02 1.707858e+00 2.714363e-01 2.583534e-01 -1.856543e-01 -2.983154e-02 1.084806e+00 [289] -2.070454e+00 -1.513304e-01 2.514891e-01 1.531216e+00 -1.656472e+00 -1.337082e+00 3.243848e-01 1.715378e-01 -7.437379e-02 [298] -6.363805e-01 8.216420e-01 2.398677e+00 2.481079e-01 -1.493501e+00 1.788803e+00 4.053156e-01 -1.932145e-01 -1.698920e-01 [307] 3.829476e+00 1.608798e+00 -1.129716e-01 -1.141733e+00 1.621158e+00 -3.343241e-02 4.700237e+00 2.001713e+00 4.618576e+00 [316] 2.501457e+00 -7.836369e-02 -1.908722e-01 1.028320e+01 5.647405e-02 -1.710083e-01 -1.065351e+00 4.019061e-01 2.086564e-01 [325] -3.025440e-01 -9.047322e-02 -6.460067e-01 -6.844164e-01 -1.881830e-01 -8.318599e-02 3.826786e+00 9.766119e-01 -7.635718e-02 [334] -2.220902e-01 -3.856785e+00 -1.094635e+00 -7.540428e-02 3.058904e-02 9.137646e-01 3.775832e+00 2.989209e-01 -1.054544e-01 [343] 1.553016e-01 2.089815e+00 -1.232086e+00 -6.334727e-03 -7.148192e-01 1.619745e+00 -1.637780e-01 -2.134504e-01 1.515387e-01 [352] 2.434295e-01 -1.831071e-01 -9.457498e-01 2.459490e+00 -4.414135e-02 -8.114919e-02 -4.016494e-01 3.734457e-01 4.896307e-01 [361] 4.049245e+00 2.017318e+00 2.488363e-01 2.780003e-01 -1.550511e+00 -3.131615e+00 3.587101e+00 -8.323622e-02 -9.310946e-01 [370] -1.594693e-01 -6.449885e+00 8.850238e-01 2.298414e-01 2.548747e-02 3.259190e-01 3.200593e+00 -4.624236e-02 -3.353935e+00 [379] -9.192395e-03 1.659781e+00 -3.100714e-01 -2.432555e+00 2.493722e+00 6.676577e+00 -1.780416e-01 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5.556761e+00 -8.453119e-01 [739] 3.526444e-01 2.922084e+00 2.172985e-01 -1.469902e+00 1.632111e-01 3.493874e-01 -1.966893e-01 -2.924236e-01 1.102409e-01 [748] 6.462530e-02 -1.704171e-02 4.125223e-01 -2.080039e-01 2.607025e-01 -2.169992e-01 8.481024e-02 1.636632e-01 -5.962679e-01 [757] -3.093319e-01 -1.073459e-01 1.363464e+00 -1.401023e+00 -2.107503e-02 5.597599e-01 5.385795e-01 1.863389e+00 6.397418e+00 [766] 1.861240e+00 1.194237e+00 2.997435e-01 1.611484e-01 -5.484613e-01 1.189842e+00 3.837644e+00 -2.338096e-01 -5.737762e-01 [775] 2.413753e-03 3.455508e+00 -6.577547e-01 3.693522e-01 1.219843e-01 -2.947803e-02 -2.569075e-01 -1.664628e-01 2.123460e+00 [784] 4.798212e+00 -1.675385e-01 -7.847523e-02 -3.216411e-01 -2.386470e-01 2.017492e+00 -2.721515e-01 2.467115e+00 5.415200e-01 [793] 1.157133e+00 4.056428e-01 -2.823108e-01 4.366070e-01 -9.937483e-01 -6.383019e-02 2.599436e-01 -2.154435e-01 > HF5 Time Series: Start = 1 End = 800 Frequency = 1 [1] -0.053649858 0.473045129 -1.855791134 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2.044204651 -0.376951275 -0.256646314 -0.462593438 [460] -0.150378251 -0.036127900 -0.168221859 -0.250161833 -0.132990944 -0.092393191 0.017930849 -0.821142000 -0.045328381 [469] -0.156346755 0.251034593 -0.015115175 -0.049923585 9.808254454 -10.923406279 0.218855389 -3.481913209 2.269242277 [478] 1.618053635 -0.568450760 -0.100185900 -0.218372487 -0.533170368 -3.035492341 -0.018080448 -0.270147632 0.064100947 [487] -1.656390523 0.044406230 0.403815427 4.463785965 -0.242225219 -0.060562600 0.111633931 1.952214234 -1.702724573 [496] -2.321447242 7.091924992 -0.100624956 0.014795836 -0.127924982 2.603975673 -0.238145700 -0.206169571 -0.280573145 [505] 0.133267731 1.334596328 -0.080741903 1.136959798 0.103590046 0.382617191 -0.120816198 -10.255711630 4.959744726 [514] 0.203784749 -0.241718413 -0.418653153 7.263519760 0.175385478 -0.121027999 -0.921554800 0.014025795 0.812840365 [523] -0.033736823 -0.881201126 0.014024605 1.413383175 -0.084845152 -1.501412214 0.014026681 0.351134701 -0.105825219 [532] -0.190871159 -0.016198856 1.582199545 -0.355298930 -0.119154942 1.119952829 15.442702714 -0.526105476 0.254349129 [541] 0.182400471 0.290090107 -0.544720386 -0.704947881 0.182413507 0.415254298 0.478675043 0.337429554 0.015951895 [550] 0.579123775 0.276916517 0.336730820 0.166459998 -0.165019677 -0.170639297 -2.156172309 0.007015360 0.679413452 [559] -0.180776170 -0.412514852 1.919485711 0.564221261 -1.814078186 -0.523469370 0.850946856 0.654857991 -0.433715765 [568] -0.064963825 0.315600383 0.208368575 -1.362624306 -0.036163560 1.522171004 0.501262098 -2.957851936 0.041325375 [577] 0.792613097 0.461937482 -0.549182039 -0.201497868 0.559521219 2.330550367 -0.072344287 -0.696108042 0.255478720 [586] 1.414073413 -0.568775940 -0.324689599 0.489813834 -0.149345898 -0.083926323 12.669192340 0.395227403 0.575646109 [595] 0.969961408 0.139445941 0.028068230 0.961621369 -0.747248768 -1.600810860 1.075547238 0.420965386 -0.113631655 [604] -0.903460198 0.524895605 0.044527148 -0.461720956 -0.547639601 0.084186467 1.174865283 -1.097194604 -0.032498414 [613] 2.392118505 0.986643396 -0.162424173 -3.164451200 -0.769422900 -0.184600192 -0.197917436 -0.352329082 1.290558257 [622] -0.184791050 -0.076097183 -1.798061452 0.080099125 2.062484105 -0.348501142 -2.106705631 0.007017747 2.305538391 [631] -0.915838960 -0.220861746 0.077200047 0.610466280 -0.688401758 -0.207153770 0.049139553 22.362186197 -5.441551857 [640] -1.708605711 0.926299855 0.207035751 -0.106446657 -2.675294607 -0.404511023 -0.788943233 -0.048807464 -0.227614326 [649] -0.085333035 0.977385829 -16.826537503 -0.200423157 -0.051340705 6.499090143 -0.304213082 -0.065082852 0.048070630 [658] 0.666539778 -0.064016381 -0.109602571 0.533325153 0.528565621 -0.248317213 -3.473373955 1.272400022 1.711836935 [667] -0.228344960 -0.252753461 -0.488373752 -0.401594723 -0.030427542 -0.455079097 3.252051577 0.960391227 -0.256075733 [676] -0.136915862 0.098237444 1.674612416 0.044609980 -0.248469202 -0.298662830 1.173803660 -0.208363252 1.850645023 [685] 1.036270876 -0.152137097 -0.048105658 -1.277109207 0.059431246 0.064698690 -0.246801765 -0.196775000 0.533961473 [694] 0.220699810 -0.312873635 0.014867680 -0.241851486 0.032156787 -1.816522484 -0.167733410 4.158794025 2.099466739 [703] -0.030488507 0.112566051 0.075675048 0.302820106 -0.469476310 0.210115120 0.056139143 -0.030484607 -0.072570524 [712] -0.033886465 0.091219120 -0.248023454 -0.081455556 -0.203068185 0.054095543 -0.015255905 -3.701371648 -0.623879061 [721] 0.853410776 6.103753013 -1.341198580 1.247921308 0.751060465 0.781642884 0.379135477 1.145320110 0.313305428 [730] 0.112618403 -1.412256823 -0.103142715 -0.007113346 0.659901598 -2.519498558 -0.365995410 -0.184937991 0.897416670 [739] -0.518805259 -3.353209940 1.867572217 9.205127781 -0.187969046 -0.778383177 -0.042669664 0.806807477 -0.090799820 [748] -0.021826161 0.448223805 -0.164371146 -0.618774302 -0.244839681 0.194235170 1.570125546 1.754972837 0.500679719 [757] 0.870366653 0.433784961 -1.002863246 2.101960944 0.697030522 7.950881827 -0.061270167 -2.371332122 -0.142291873 [766] -1.729969712 -1.941166110 -0.245036824 -0.106730528 5.057757700 -1.038846526 -0.858866602 3.386084663 1.395573786 [775] -0.291650577 -2.212035645 0.856991031 -1.532383568 -0.185747818 -0.711396025 1.062315644 0.241829929 -1.838103065 [784] -12.577074634 1.735801542 0.484405184 0.013854970 0.416285923 -1.975226723 0.938110382 -0.647308291 -0.706063547 [793] -0.082810695 -0.054601369 -0.014973073 0.127614348 18.906618087 0.502810107 -0.152371107 -0.036187828 very many thanks for your time and effort.... Yours sincerely, AKSHAY M KULKARNI ________________________________ From: Ivan Krylov <krylov.r...@gmail.com> Sent: Thursday, March 21, 2019 9:06 PM To: r-help@r-project.org Cc: akshay kulkarni Subject: Re: [R] problem with nls.... One of the assumptions made by least squares method is that the residuals are independent and normally distributed with same parameters (or, in case of weighted regression, the standard deviation of the residual is known for every point). If this is the case, the parameters that minimize the sum of squared residuals are the maximum likelihood estimation of the true parameter values. The problem is, your data doesn't seem to adhere well to your formula. Have you tried plotting your HF1 - ((m/HF6) + 1) against HF6 (i.e. the residuals themselves)? With large residual values (outliers?), the loss function (i.e. sum of squared residuals) is disturbed and doesn't reflect the values you would expect to get otherwise. Try computing sum((HF1 - ((m/HF6) + 1))^2) for different values of m and see if changing m makes any difference. Try looking up "robust regression" (e.g. minimize sum of absolute residuals instead of squared residuals; a unique solution is not guaranteed, but it's be less disturbed by outliers). -- Best regards, Ivan [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.