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Best linear Fit to slope data with Fixed starting point/value.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63541] Best linear Fit to slope data with Fixed starting point/value.
  • From: "Lea Rebanks" <lrebanks at netvigator.com>
  • Date: Wed, 4 Jan 2006 03:17:20 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Given the list below, (quite large - 4516 points), is when plotted an
almost perfect straight line with noise.

I want to plot the best linear fit (i.e. m*x + b) to this data, however
I must retain the original first value (151.0993767999595).

Obviously I could do this manually, but was wondering if there was a
more accurate & efficient way using Mathematica.

Many thanks for your attention.

Best Regards - Lea Rebanks...


Data below:-

{151.0993767999595, 151.15815657519292, 151.21693635042635, 
 151.27571612565978, 151.33449590089322, 151.39327567612665, 
 151.45205545136008, 151.51083522659354, 151.56961500182697, 
 151.6283947770604, 151.68717455229384, 151.74595432752727, 
 151.8047341027607, 151.86351387799414, 151.92229365322757, 
 151.981073428461, 152.03985320369446, 152.0986329789279, 
 152.15741275416133, 152.21619252939476, 152.2749723046282, 
 152.33375207986163, 152.39253185509506, 152.4513116303285, 
 152.51009140556192, 152.56887118079536, 152.62765095602882, 
 152.68643073126225, 152.74521050649568, 152.8039902817291, 
 152.86277005696255, 152.92154983219598, 152.9803296074294, 
 153.03910938266284, 153.09788915789628, 153.15666893312974, 
 153.21544870836317, 153.2742284835966, 153.33300825883003, 
 153.39178803406347, 153.4505678092969, 153.50934758453033, 
 153.56812735976376, 153.6269071349972, 153.68568691023066, 
 153.7444666854641, 153.80324646069752, 153.86202623593095, 
 153.9208060111644, 153.97958578639782, 154.03836556163125, 
 154.09714533686468, 154.15592511209812, 154.21470488733158, 
 154.273484662565, 154.33226443779844, 154.39104421303188, 
 154.4498239882653, 154.50860376349874, 154.56738353873217, 
 154.6261633139656, 154.68494308919904, 154.7437228644325, 
 154.80250263966593, 154.86128241489936, 154.9200621901328, 
 154.97884196536623, 155.03762174059966, 155.0964015158331, 
 155.15518129106653, 155.21396106629996, 155.2727408415334, 
 155.33152061676685, 155.39030039200028, 155.44908016723372, 
 155.50785994246715, 155.56663971770058, 155.62541949293401, 
 155.68419926816745, 155.74297904340088, 155.8017588186343, 
 155.86053859386777, 155.9193183691012, 155.97809814433464, 
 156.03687791956807, 156.0956576948015, 156.15443747003494, 
 156.21321724526837, 156.2719970205018, 156.33077679573523, 
 156.3895565709687, 156.44833634620213, 156.50711612143556, 
 156.565895896669, 156.62467567190242, 156.68345544713586, 
 156.7422352223693, 156.80101499760272, 156.85979477283615, 
 156.9185745480696, 156.97735432330305, 157.03613409853648, 
 157.0949138737699, 157.15369364900334, 157.21247342423678, 
 157.2712531994702, 157.33003297470364, 157.38881274993707, 
 157.4475925251705, 157.50637230040397, 157.5651520756374, 
 157.62393185087083, 157.68271162610426, 157.7414914013377, 
 157.80027117657113, 157.85905095180456, 157.917830727038, 
 157.97661050227143, 158.0353902775049, 158.09417005273832, 
 158.15294982797175, 158.21172960320519, 158.27050937843862, 
 158.32928915367205, 158.38806892890548, 158.44684870413892, 
 158.50562847937235, 158.5644082546058, 158.62318802983924, 
 158.68196780507267, 158.7407475803061, 158.79952735553954, 
 158.85830713077297, 158.9170869060064, 158.97586668123984, 
 159.03464645647327, 159.09342623170673, 159.15220600694016, 
 159.2109857821736, 159.26976555740703, 159.32854533264046, 
 159.3873251078739, 159.44610488310732, 159.50488465834076, 
 159.5636644335742, 159.62244420880762, 159.68122398404108, 
 159.74000375927452, 159.79878353450795, 159.85756330974138, 
 159.9163430849748, 159.97512286020824, 160.03390263544168, 
 160.0926824106751, 160.15146218590854, 160.210241961142, 
 160.26902173637544, 160.32780151160887, 160.3865812868423, 
 160.44536106207573, 160.50414083730917, 160.5629206125426, 
 160.62170038777603, 160.68048016300946, 160.73925993824292, 
 160.79803971347636, 160.8568194887098, 160.91559926394322, 
 160.97437903917665, 161.0331588144101, 161.09193858964352, 
 161.15071836487695, 161.20949814011038, 161.26827791534384, 
 161.32705769057728, 161.3858374658107, 161.44461724104414, 
 161.50339701627757, 161.562176791511, 161.62095656674444, 
 161.67973634197787, 161.7385161172113, 161.79729589244474, 
 161.8560756676782, 161.91485544291163, 161.97363521814506, 
 162.0324149933785, 162.09119476861193, 162.14997454384536, 
 162.2087543190788, 162.26753409431223, 162.32631386954566, 
 162.38509364477912, 162.44387342001255, 162.50265319524598, 
 162.56143297047942, 162.62021274571285, 162.67899252094628, 
 162.7377722961797, 162.79655207141315, 162.85533184664658, 
 162.91411162188004, 162.97289139711347, 163.0316711723469, 
 163.09045094758034, 163.14923072281377, 163.2080104980472, 
 163.26679027328063, 163.32557004851407, 163.3843498237475, 
 163.44312959898096, 163.5019093742144, 163.56068914944782, 
 163.61946892468126, 163.6782486999147, 163.73702847514812, 
 163.79580825038155, 163.854588025615, 163.91336780084842, 
 163.97214757608185, 164.0309273513153, 164.08970712654875, 
 164.14848690178218, 164.2072666770156, 164.26604645224904, 
 164.32482622748248, 164.3836060027159, 164.44238577794934, 
 164.50116555318277, 164.55994532841623, 164.61872510364967, 
 164.6775048788831, 164.73628465411653, 164.79506442934996, 
 164.8538442045834, 164.91262397981683, 164.97140375505026, 
 165.0301835302837, 165.08896330551715, 165.1477430807506, 
 165.20652285598402, 165.26530263121745, 165.32408240645088, 
 165.38286218168432, 165.44164195691775, 165.50042173215118, 
 165.5592015073846, 165.61798128261808, 165.6767610578515, 
 165.73554083308494, 165.79432060831837, 165.8531003835518, 
 165.91188015878524, 165.97065993401867, 166.0294397092521, 
 166.08821948448553, 166.14699925971897, 166.20577903495243, 
 166.26455881018586, 166.3233385854193, 166.38211836065273, 
 166.44089813588616, 166.4996779111196, 166.55845768635302, 
 166.61723746158646, 166.6760172368199, 166.73479701205335, 
 166.79357678728678, 166.8523565625202, 166.91113633775365, 
 166.96991611298708, 167.0286958882205, 167.08747566345394, 
 167.14625543868738, 167.2050352139208, 167.26381498915427, 
 167.3225947643877, 167.38137453962113, 167.44015431485457, 
 167.498934090088, 167.55771386532143, 167.61649364055486, 
 167.6752734157883, 167.73405319102173, 167.7928329662552, 
 167.85161274148862, 167.91039251672206, 167.9691722919555, 
 168.02795206718892, 168.08673184242235, 168.14551161765579, 
 168.20429139288922, 168.26307116812265, 168.32185094335608, 
 168.38063071858954, 168.43941049382298, 168.4981902690564, 
 168.55697004428984, 168.61574981952327, 168.6745295947567, 
 168.73330936999014, 168.79208914522357, 168.850868920457, 
 168.90964869569046, 168.9684284709239, 169.02720824615733, 
 169.08598802139076, 169.1447677966242, 169.20354757185763, 
 169.26232734709106, 169.3211071223245, 169.37988689755792, 
 169.43866667279138, 169.49744644802482, 169.55622622325825, 
 169.61500599849168, 169.67378577372511, 169.73256554895855, 
 169.79134532419198, 169.8501250994254, 169.90890487465884, 
 169.9676846498923, 170.02646442512574, 170.08524420035917, 
 170.1440239755926, 170.20280375082604, 170.26158352605947, 
 170.3203633012929, 170.37914307652633, 170.43792285175977, 
 170.4967026269932, 170.55548240222666, 170.6142621774601, 
 170.67304195269352, 170.73182172792696, 170.7906015031604, 
 170.84938127839382, 170.90816105362725, 170.9669408288607, 
 171.02572060409412, 171.08450037932758, 171.143280154561, 
 171.20205992979444, 171.26083970502788, 171.3196194802613, 
 171.37839925549474, 171.43717903072817, 171.4959588059616, 
 171.55473858119504, 171.6135183564285, 171.67229813166193, 
 171.73107790689537, 171.7898576821288, 171.84863745736223, 
 171.90741723259566, 171.9661970078291, 172.02497678306253, 
 172.08375655829596, 172.14253633352942, 172.20131610876285, 
 172.26009588399629, 172.31887565922972, 172.37765543446315, 
 172.43643520969658, 172.49521498493002, 172.55399476016345, 
 172.61277453539688, 172.6715543106303, 172.73033408586377, 
 172.7891138610972, 172.84789363633064, 172.90667341156407, 
 172.9654531867975, 173.02423296203094, 173.08301273726437, 
 173.1417925124978, 173.20057228773123, 173.2593520629647, 
 173.31813183819813, 173.37691161343156, 173.435691388665, 
 173.49447116389842, 173.55325093913186, 173.6120307143653, 
 173.67081048959872, 173.72959026483215, 173.78837004006562, 
 173.84714981529905, 173.90592959053248, 173.9647093657659, 
 174.02348914099935, 174.08226891623278, 174.1410486914662, 
 174.19982846669964, 174.25860824193308, 174.31738801716654, 
 174.37616779239997, 174.4349475676334, 174.49372734286683, 
 174.55250711810027, 174.6112868933337, 174.67006666856713, 
 174.72884644380056, 174.787626219034, 174.84640599426743, 
 174.9051857695009, 174.96396554473432, 175.02274531996775, 
 175.0815250952012, 175.14030487043462, 175.19908464566805, 
 175.25786442090148, 175.31664419613492, 175.37542397136835, 
 175.4342037466018, 175.49298352183524, 175.55176329706867, 
 175.6105430723021, 175.66932284753554, 175.72810262276897, 
 175.7868823980024, 175.84566217323584, 175.90444194846927, 
 175.96322172370273, 176.02200149893616, 176.0807812741696, 
 176.13956104940303, 176.19834082463646, 176.2571205998699, 
 176.31590037510333, 176.37468015033676, 176.4334599255702, 
 176.49223970080365, 176.55101947603708, 176.60979925127052, 
 176.66857902650395, 176.72735880173738, 176.7861385769708, 
 176.84491835220425, 176.90369812743768, 176.9624779026711, 
 177.02125767790454, 177.080037453138, 177.13881722837144, 
 177.19759700360487, 177.2563767788383, 177.31515655407173, 
 177.37393632930517, 177.4327161045386, 177.49149587977203, 
 177.55027565500546, 177.60905543023893, 177.66783520547236, 
 177.7266149807058, 177.78539475593922, 177.84417453117265, 
 177.9029543064061, 177.96173408163952, 178.02051385687295, 
 178.07929363210638, 178.13807340733985, 178.19685318257328, 
 178.2556329578067, 178.31441273304014, 178.37319250827358, 
 178.431972283507, 178.49075205874044, 178.54953183397387, 
 178.6083116092073, 178.66709138444077, 178.7258711596742, 
 178.78465093490763, 178.84343071014106, 178.9022104853745, 
 178.96099026060793, 179.01977003584136, 179.0785498110748, 
 179.13732958630823, 179.19610936154166, 179.25488913677512, 
 179.31366891200855, 179.37244868724198, 179.43122846247542, 
 179.49000823770885, 179.54878801294228, 179.60756778817571, 
 179.66634756340915, 179.72512733864258, 179.78390711387604, 
 179.84268688910947, 179.9014666643429, 179.96024643957634, 
 180.01902621480977, 180.0778059900432, 180.13658576527664, 
 180.19536554051007, 180.2541453157435, 180.31292509097696, 
 180.3717048662104, 180.43048464144383, 180.48926441667726, 
 180.5480441919107, 180.60682396714412, 180.66560374237756, 
 180.724383517611, 180.78316329284442, 180.84194306807788, 
 180.9007228433113, 180.95950261854475, 181.01828239377818, 
 181.0770621690116, 181.13584194424504, 181.19462171947848, 
 181.2534014947119, 181.31218126994534, 181.37096104517877, 
 181.42974082041223, 181.48852059564567, 181.5473003708791, 
 181.60608014611253, 181.66485992134596, 181.7236396965794, 
 181.78241947181283, 181.84119924704626, 181.8999790222797, 
 181.95875879751316, 182.0175385727466, 182.07631834798002, 
 182.13509812321345, 182.19387789844689, 182.25265767368032, 
 182.31143744891375, 182.37021722414718, 182.42899699938062, 
 182.48777677461408, 182.5465565498475, 182.60533632508094, 
 182.66411610031437, 182.7228958755478, 182.78167565078124, 
 182.84045542601467, 182.8992352012481, 182.95801497648154, 
 183.016794751715, 183.07557452694843, 183.13435430218186, 
 183.1931340774153, 183.25191385264873, 183.31069362788216, 
 183.3694734031156, 183.42825317834902, 183.48703295358246, 
 183.5458127288159, 183.60459250404935, 183.66337227928278, 
 183.72215205451622, 183.78093182974965, 183.83971160498308, 
 183.8984913802165, 183.95727115544994, 184.01605093068338, 
 184.0748307059168, 184.13361048115027, 184.1923902563837, 
 184.25117003161714, 184.30994980685057, 184.368729582084, 
 184.42750935731743, 184.48628913255087, 184.5450689077843, 
 184.60384868301773, 184.6626284582512, 184.72140823348462, 
 184.78018800871806, 184.8389677839515, 184.89774755918492, 
 184.95652733441835, 185.0153071096518, 185.07408688488522, 
 185.13286666011865, 185.1916464353521, 185.25042621058554, 
 185.30920598581898, 185.3679857610524, 185.42676553628584, 
 185.48554531151927, 185.5443250867527, 185.60310486198614, 
 185.66188463721957, 185.720664412453, 185.77944418768647, 
 185.8382239629199, 185.89700373815333, 185.95578351338676, 
 186.0145632886202, 186.07334306385363, 186.13212283908706, 
 186.1909026143205, 186.24968238955393, 186.3084621647874, 
 186.36724194002082, 186.42602171525425, 186.48480149048768, 
 186.54358126572112, 186.60236104095455, 186.66114081618798, 
 186.7199205914214, 186.77870036665485, 186.8374801418883, 
 186.89625991712174, 186.95503969235517, 187.0138194675886, 
 187.07259924282204, 187.13137901805547, 187.1901587932889, 
 187.24893856852233, 187.30771834375577, 187.36649811898923, 
 187.42527789422266, 187.4840576694561, 187.54283744468952, 
 187.60161721992296, 187.6603969951564, 187.71917677038982, 
 187.77795654562325, 187.8367363208567, 187.89551609609012, 
 187.95429587132358, 188.013075646557, 188.07185542179045, 
 188.13063519702388, 188.1894149722573, 188.24819474749074, 
 188.30697452272418, 188.3657542979576, 188.42453407319104, 
 188.4833138484245, 188.54209362365793, 188.60087339889137, 
 188.6596531741248, 188.71843294935823, 188.77721272459166, 
 188.8359924998251, 188.89477227505853, 188.95355205029196, 
 189.01233182552542, 189.07111160075885, 189.1298913759923, 
 189.18867115122572, 189.24745092645915, 189.30623070169258, 
 189.36501047692602, 189.42379025215945, 189.48257002739288, 
 189.54134980262634, 189.60012957785978, 189.6589093530932, 
 189.71768912832664, 189.77646890356007, 189.8352486787935, 
 189.89402845402694, 189.95280822926037, 190.0115880044938, 
 190.07036777972726, 190.1291475549607, 190.18792733019413, 
 190.24670710542756, 190.305486880661, 190.36426665589443, 
 190.42304643112786, 190.4818262063613, 190.54060598159472, 
 190.59938575682816, 190.65816553206162, 190.71694530729505, 
 190.77572508252848, 190.8345048577619, 190.89328463299535, 
 190.95206440822878, 191.0108441834622, 191.06962395869564, 
 191.12840373392908, 191.18718350916254, 191.24596328439597, 
 191.3047430596294, 191.36352283486283, 191.42230261009627, 
 191.4810823853297, 191.53986216056313, 191.59864193579656, 
 191.65742171103, 191.71620148626346, 191.7749812614969, 
 191.83376103673032, 191.89254081196376, 191.9513205871972, 
 192.01010036243062, 192.06888013766405, 192.12765991289749, 
 192.18643968813092, 192.24521946336438, 192.3039992385978, 
 192.36277901383124, 192.42155878906468, 192.4803385642981, 
 192.53911833953154, 192.59789811476497, 192.6566778899984, 
 192.71545766523184, 192.77423744046527, 192.83301721569873, 
 192.89179699093216, 192.9505767661656, 193.00935654139903, 
 193.06813631663246, 193.1269160918659, 193.18569586709933, 
 193.24447564233276, 193.3032554175662, 193.36203519279965, 
 193.42081496803308, 193.47959474326652, 193.53837451849995, 
 193.59715429373338, 193.65593406896681, 193.71471384420025, 
 193.77349361943368, 193.8322733946671, 193.89105316990057, 
 193.949832945134, 194.00861272036744, 194.06739249560087, 
 194.1261722708343, 194.18495204606774, 194.24373182130117, 
 194.3025115965346, 194.36129137176803, 194.4200711470015, 
 194.47885092223493, 194.53763069746836, 194.5964104727018, 
 194.65519024793522, 194.71397002316866, 194.7727497984021, 
 194.83152957363552, 194.89030934886895, 194.9490891241024, 
 195.00786889933585, 195.06664867456928, 195.1254284498027, 
 195.18420822503614, 195.24298800026958, 195.301767775503, 
 195.36054755073644, 195.41932732596987, 195.4781071012033, 
 195.53688687643677, 195.5956666516702, 195.65444642690363, 
 195.71322620213707, 195.7720059773705, 195.83078575260393, 
 195.88956552783736, 195.9483453030708, 196.00712507830423, 
 196.0659048535377, 196.12468462877112, 196.18346440400455, 
 196.24224417923799, 196.30102395447142, 196.35980372970485, 
 196.41858350493828, 196.47736328017172, 196.53614305540515, 
 196.5949228306386, 196.65370260587204, 196.71248238110547, 
 196.7712621563389, 196.83004193157234, 196.88882170680577, 
 196.9476014820392, 197.00638125727264, 197.06516103250607, 
 197.1239408077395, 197.18272058297296, 197.2415003582064, 
 197.30028013343983, 197.35905990867326, 197.4178396839067, 
 197.47661945914012, 197.53539923437356, 197.594179009607, 
 197.65295878484042, 197.71173856007388, 197.77051833530732, 
 197.82929811054075, 197.88807788577418, 197.9468576610076, 
 198.00563743624105, 198.06441721147448, 198.1231969867079, 
 198.18197676194134, 198.2407565371748, 198.29953631240824, 
 198.35831608764167, 198.4170958628751, 198.47587563810853, 
 198.53465541334197, 198.5934351885754, 198.65221496380883, 
 198.71099473904226, 198.76977451427572, 198.82855428950916, 
 198.8873340647426, 198.94611383997602, 199.00489361520945, 
 199.0636733904429, 199.12245316567632, 199.18123294090975, 
 199.24001271614318, 199.29879249137662, 199.35757226661008, 
 199.4163520418435, 199.47513181707694, 199.53391159231037, 
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