Please solve all parts of the following problem. Not just some part. If you're only going to solve one part of the problem, please leave it up to someone else that can do all parts of the problem! Thank you very much.

Finding a model

Measurements in two columns (x,y):

1.9994026313426514 0.22084777003924433 2.3923277413772563 0.05974438833742985 3.3782985347758987 0.09586824640069871 4.288434217817152 0.31644888654622105 3.7762994087507082 0.3397284151174721 5.637537875796101 0.6458365604333939 6.609507346707895 0.36447804339157 7.641427401532939 0.693906249750492 8.519824018897943 0.6543278007339605 9.941954912366356 0.48781182406244383 9.677141770792247 0.6206253289344827 11.999197368748531 0.8316249739216012 14.463107363004816 0.6340368263800553 12.832101379128494 0.7466776299878759 13.639063209240526 0.6655960101107807 15.038358443503103 0.6992914291141503 15.764561820146088 0.6657599032836308 18.82900336135164 0.5845406472869716 19.777376081388777 0.7840302373357366 18.995826720773586 0.633579489720824 21.567934962749096 0.7448770701324401 24.17107571411403 0.35176292425686834 22.986223811117235 0.48063552583311653 23.4089215029184 0.5137356076209786 26.50786348097033 0.154095579343918 26.112459002529047 0.43954302039250903 26.992418739046233 0.2774342464967693 28.436725681848216 0.27615470253738633 28.623658451684907 0.09261292075069 30.349608650731184 -0.15371566236633086 29.987766632495322 0.06519753135375524 29.963858645558897 0.061174646089002374 33.020506671435385 -0.14169868515295966 33.36688796080034 -0.3212805113621837 34.32041281272065 -0.11382478858179398 37.315767246875204 -0.42256346037601883 36.195847065211694 -0.21079144618140794 38.61175996424642 -0.20557561413725495 41.23526060588138 -0.32664043621164673 40.679584007157985 -0.1521715747837823 41.41382942027407 -0.39362645567390814 44.17041143463551 -0.4329625529289662 43.88749772870937 -0.42523005201042013 43.167457651514276 -0.5868387938559823 43.098646239309204 -0.3363967374408377 46.2622507896608 -0.44184176257634333 45.84885242076878 -0.417215081823271 48.552332900541835 -0.31753326908670965 49.03231463352088 -0.2776624598471248 52.57783883098123 -0.18526091790437083 52.94200352389225 -0.03882254163204779 51.71137902549721 -0.30622583574125956 52.406011663217576 -0.21966124882978239 52.023605856296555 -0.17241891535455206 53.73389636709627 -0.34805878551820235 56.687459647042495 -0.2480907257041381 56.86571940927967 -0.21035534463611769 55.946216177758 -0.07127596972203823 59.75733158963875 -0.22024301757590947 60.01180973421057 -0.11115196204268533 60.388069219741695 -0.023885840040131792 60.874572768129546 0.108905754168225 63.42258308144638 -0.1157383895168862 63.190158545805346 0.029655345096346653 65.77852052749903 0.07904910047286444 66.22274426551266 0.07511232008421613 67.99170726723985 0.2710436847722348 69.11937064593825 0.24121172760255527 69.06717135154585 0.016573979528777052 71.24950744535178 0.2248360298438942 70.13174090525406 0.06786892869642111 72.22460462963484 0.3040591182124634 73.28304882558729 0.31652984009909696 71.50264626887684 0.30656885658272515 75.07948445103233 0.18370963524666795 76.9575399211764 0.032361584188426024 77.34419447701939 0.036696775872251675 77.62193985572408 0.3375927832874336 79.34263423724683 0.15916983481126035 81.72898062031415 0.2648606412269218 79.28707732766665 0.17781510881927637 83.6353107390435 0.2037256392074862 82.06857356631477 0.10609257516227014 83.20472029093449 0.0844815656732376 85.9998926900646 0.31222317475237366 86.67196352191415 0.2125207238338812 85.37009555750772 0.23123254126525844 86.78210998849983 0.07352904064342047 90.43764087094566 -0.08666728864169577 90.7482420674281 0.06143432640260728 90.93371541931954 0.10703975720309643 92.46087715225022 0.0865800994531277 92.84311613862103 -0.11164143308980577 93.51700658053436 0.10813269239636372 95.1352549241488 -0.1268722029092091 96.974251307876 0.03511757250674831 98.20507390441915 -0.05863962050130503 97.71439583216164 -0.1880940870664864 99.44127214317078 -0.012271639573986137 100.09317149272015 -0.25660679660415137

Prepare a python script, which load measurements. Try to find the model, which describes the dependence between x and y with a minimal set of parameters.

Try first with linear regression.

Then try different mathematical models and use scipy.optimize.curve_fit function.

Run the program and check if it works.

Submit the resulting python script and pictures of the graph of measurements (use symbols) and model (use curves). Report the values of parameters and their errors.