Meta tags:
keywords= adjusted r square, ANOVA table, BestFitParameters, confidence region, error variance, FitCurvatureTable, hat matrix, MeanPredictionConfidenceIntervals, mean squares, nonlinear regression, parameter confidence intervals, parameter errors, parameter table, prediction bands, p-values, RSquared, single prediction confidence interval table, StandardizedResiduals;
description=NonlinearModelFit attempts to model the input data using a general mathematical formula with free parameters.;

Headings (most frequently used words):

for, data, educational, wolfram, options, science, technology, education, programs, of, initiatives, properties, examples, tech, products, finance, business, engineering, get, started, grow, your, skills, work, with, us, adults, youth, read, diagnostics, measures, nonlinearmodelfit, details, and, see, also, notes, related, guides, history, alpha, ai, core, technologies, additional, deployment, more, learning, support, resources, events, basic, scope, 17, generalizations, extensions, 14, applications, relations, possible, issues, constraints, confidencelevel, evaluationmonitor, gradient, maxiterations, method, stepmonitor, varianceestimatorfunction, weights, workingprecision, fitted, functions, residuals, sums, squares, parameter, estimation, curvature, influence, prediction, values, goodness, fit, text, cms, apa, bibtex, biblatex,

Text of the page (most frequently used words):
wolfram (301), language (189), the (182), data (173), code (163), nonlinearmodelfit (97), nlm (81), for (72), model (64), fit (60), and (53), exp (33), #method (33), log (32), with (32), #values (29), all (26), weights (24), function (22), analysis (22), table (21), use (21), variance (20), nonlinear (20), parameter (20), form (20), normal (18), properties (18), optimization (17), randomreal (17), from (16), listplot (16), confidence (16), science (15), statistical (15), automatic (15), show (14), using (14), plot (14), obtain (13), contact (12), nminimize (12), point (12), fitted (12), more (12), gradient (12), based (11), alpha (11), one (11), matrix (11), residuals (11), are (11), bands (11), response (11), curvature (11), cloud (11), support (10), resources (10), learning (10), scientific (10), tech (10), can (10), seedrandom (10), that (10), mean (10), confidencelevel (10), error (10), list (10), repository (9), options (9), products (9), research (9), computation (9), models (9), related (9), fitting (9), fitresiduals (9), aic (9), around (9), parameters (9), include (9), com (8), reference (8), tabular (8), numerical (8), findfit (8), plotrange (8), subscript (8), newton (8), solutions (8), diagnostics (8), school (8), about (7), educational (7), programs (7), documentation (7), mathematica (7), 2025 (7), time (7), unconstrained (7), constrained (7), fittedmodel (7), linearmodelfit (7), also (7), parameterestimates (7), params (7), responses (7), information (7), maxiterations (7), independent (7), varianceestimatorfunction (7), default (7), measures (7), prediction (7), extract (7), constructs (7), blog (6), your (6), math (6), fast (6), introduction (6), consulting (6), system (6), https (6), ref (6), html (6), modeling (6), minimization (6), guides (6), notes (6), see (6), points (6), property (6), meanpredictionbands (6), some (6), bestfit (6), best (6), workingprecision (6), estimates (6), uncertainty (6), number (6), intervals (6), single (6), input (6), education (6), engineering (6), community (5), events (5), account (5), books (5), students (5), notebook (5), player (5), engine (5), compute (5), 2008 (5), center (5), image (5), microscopy (5), supervised (5), machine (5), series (5), processing (5), curve (5), findminimum (5), findformula (5), timeseriesmodelfit (5), generalizedlinearmodelfit (5), ts1 (5), variables (5), bestfitparameters (5), fits (5), distributed (5), filling (5), visualize (5), get (5), high (5), convergence (5), used (5), estimatedvariance (5), search (5), specify (5), constraints (5), squares (5), value (5), predicted (5), column (5), 2026 (4), youtube (4), access (4), computational (4), programmers (4), give (4), history (4), centralized (4), possible (4), bic (4), check (4), find (4), sqrt (4), transpose (4), not (4), normally (4), additional (4), errors (4), precision (4), algorithm (4), standard (4), stepmonitor (4), randomsearch (4), when (4), sinc (4), formula (4), count (4), evaluationmonitor (4), confidenceinterval (4), goodness (4), influence (4), each (4), fitcurvature (4), 100 (4), between (4), expression (4), evaluate (4), examples (4), local (4), cons (4), connect (4), follow (4), stephen (4), foundation (4), initiatives (4), student (4), faqs (4), schools (4), core (4), intro (4), universities (4), technology (4), finance (4), apis (4), mcp (4), app (4), company (3), user (3), portal (3), media (3), mathworld (3), demonstrations (3), project (3), adventures (3), computer (3), challenges (3), problem (3), generator (3), server (3), deployment (3), licensing (3), mobile (3), apps (3), edition (3), modeler (3), services (3), online (3), updated (3), this (3), defined (3), rsquared (3), coefficient (3), determination (3), contains (3), constraint (3), loglike (3), aicc (3), estimation (3), errorsumofsquares (3), total (3), variancemle (3), temporaldata (3), 1724 (3), 3968817536402 (3), 5903 (3), 697723461762 (3), 19468 (3), 09340765025 (3), false (3), ts2 (3), will (3), true (3), range (3), assuming (3), bands90 (3), specific (3), findroot (3), estimate (3), steps (3), epilog (3), global (3), singularity (3), symbolic (3), problems (3), 112 (3), set (3), plotstyle (3), orange (3), numberq (3), singlepredictions (3), elements (3), effects (3), anova (3), sums (3), estimated (3), sr1 (3), sr2 (3), stem (3), original (3), close (3), measure (3), predictions (3), maximum (3), computed (3), specified (3), setting (3), where (3), real (3), vars (3), free (3), learn (3), complex (3), systems (3), insights (3), computing (3), privacy (2), policy (2), legal (2), linkedin (2), twitch (2), facebook (2), organization (2), drop (2), top (2), wolfram_2026_nonlinearmodelfit (2), title (2), year (2), url (2), note (2), accessed (2), october (2), cite (2), logplot (2), fit2 (2), listlogplot (2), proportional (2), first (2), assumptions (2), issues (2), against (2), length (2), 102448341846048 (2), 331833897009389 (2), 5843632999043455 (2), 59969789743589 (2), 76273258351092 (2), 150 (2), 00729051003992 (2), 644 (2), 7367359379259 (2), continuous (2), discrete (2), resamplingmethod (2), interpolation (2), interpolationorder (2), times (2), stamps (2), timeseries (2), nm2 (2), probitmodelfit (2), same (2), logitmodelfit (2), assumes (2), equivalent (2), linear (2), relations (2), bands95 (2), bands99 (2), bands999 (2), applications (2), computations (2), fixedpoint (2), 500 (2), option (2), settings (2), equal (2), squared (2), known (2), how (2), 123 (2), taken (2), initial (2), submethod (2), perform (2), methods (2), interiorpoint (2), interior (2), step (2), least (2), 1000 (2), reached (2), iterations (2), block (2), increasing (2), may (2), finite (2), differences (2), avoid (2), removable (2), since (2), given (2), level (2), gives (2), particular (2), integrate (2), mathematical (2), functional (2), parametricndsolvevalue (2), generalizations (2), extensions (2), adjustedrsquared (2), meanpredictions (2), predictedresponse (2), observed (2), frame (2), hatdiagonal (2), diagonal (2), hat (2), singledeletionvariances (2), deletion (2), max (2), flatten (2), standardizedresiduals (2), studentizedresiduals (2), pure (2), functions (2), nlmd (2), thick (2), starting (2), effectively (2), 011 (2), rule (2), rules (2), variable (2), scope (2), basic (2), prop (2), singlepredictionbands (2), bestfitdataaround (2), bestfitaround (2), criterion (2), observations (2), region (2), asymptotic (2), divided (2), approximate (2), such (2), any (2), found (2), tutorial (2), common (2), res (2), whenever (2), none (2), sought (2), object (2), name (2), forms (2), val (2), pars (2), details (2), subject (2), depends (2), ais (2), person (2), livestreams (2), mathematics (2), writings (2), read (2), program (2), middle (2), camp (2), youth (2), winter (2), summer (2), adults (2), jobs (2), opportunities (2), startups (2), ambassador (2), initiative (2), work (2), sites (2), career (2), daily (2), study (2), groups (2), highlighted (2), areas (2), software (2), developers (2), news (2), views (2), solve (2), share (2), ideas (2), courses (2), life (2), grow (2), skills (2), started (2), next (2), gen (2), edtech (2), colleges (2), teaching (2), social (2), behavioral (2), sciences (2), quantum (2), food (2), environmental (2), biosciences (2), agtech (2), sustainable (2), energy (2), automotive (2), civil (2), estate (2), healthcare (2), artificial (2), intelligence (2), business (2), organizational (2), group (2), wstpserver (2), wolframscript (2), web (2), linguistic (2), understanding (2), notebooks (2), computable (2), technologies (2), cag (2), component (2), agent (2), api (2), tool (2), ecosystem (2), website (2), enterprise (2), private (2), application (2), platform (2), technical (2), english, wolframcloud, wolframalpha, careers, faq, product, downloads, store, customer, publishing, thinking, public, webinars, training, github, archive, example, prompt, neural, net, paclet, repositories, volume, site, pro, introductory, book, feedback, biblatex, misc, author, howpublished, bibtex, retrieved, apa, last, modified, cms, text, 2024, 2023, introduced, multinonlinearmodelfit, addressed, inversely, but, shows, significant, deviations, scale, exponential, might, appear, correct, glance, 5randomreal, spans, over, multiple, orders, magnitude, sometimes, direct, calculation, calculated, uncorrected, here, interval, violate, distributional, upon, compare, 2pi, principles, 1024483418, 7359379259, 2111111111111111, acts, pathwise, multipath, timeseriesrescale, rescale, again, erf, identical, binomially, allows, extraction, plotlegends, various, levels, 999, blockrandom, 12345, simulate, reduce, after, higher, dampingfactor, tolerance, low, damping, factor, reach, cases, root, finding, handles, variates, does, converge, both, were, different, explicit, assume, unbiased, red, evolve, during, reap, sow, 107, 139, 159, 152, 191, 201, 207, 200, experiment, rate, enzymatic, reaction, space, michaelis, menten, experimental, searchpoints, 250, exhaustive, stepcontrol, linesearch, brent, configure, control, minimizing, objective, before, 33c, 7818074748209513b, 47a, 6686926778600345b, 32b, 46a, 8311998722869463b, 21b, 44a, slow, allow, finitedifference, has, there, derivatives, fails, derivative, generic, 70exp, 126, 125, 120, 119, 118, 116, 115, 114, 113, 111, 110, evaluations, within, instead, predictor, nintegrate, symbolically, numerically, other, operations, clear, make, much, faster, caching, differential, equation, module, ndsolvevalue, operation, grid, alignment, left, location, results, framelabel, axes, assess, variances, impact, removing, containing, extreme, selectfirst, type, numeric, tstatistic, statistic, formatted, sumofsquares, 2log, absolute, standardized, studentized, map, scaled, plots, raw, examine, plot3d, graphics3d, pointsize, 025, link, together, ensure, well, available, chop, 001, 002, 045, 215, 259, 206, 044, far, 0010978759544942, 8949819317774829, 6851122183910994, 7639434166108392, 3567934196980815, 18537374908770277, than, integer, two, open, called, these, bayesian, sample, corrected, akaike, adjusted, omitted, maxparametereffectscurvature, intrinsic, maxintrinsiccurvature, curvatureconfidenceregion, ellipsoidal, parameterconfidenceregion, bias, parameterbias, covariance, covariancematrix, correlation, correlationmatrix, sum, residual, difference, actual, types, design, vector, normality, valid, generated, along, warning, message, they, algorithms, take, suboptions, opts, quasi, bfgs, quasinewton, gauss, levenbergmarquardt, descent, conjugate, conjugategradient, treated, measurement, only, uncertainties, propagated, through, resulting, added, internally, self, consistent, solution, according, fasano, vio, aroundreplace, exact, assumed, probability, internal, estimating, precisiongoal, components, evaluated, digits, accuracy, accuracygoal, takes, following, numbers, multivariate, coordinates, should, starts, result, returns, represent, obtained, produces, under, assumption, deviation, attempts, general, built, symbol, page, enable, javascript, interact, content, submit, websites, navigation, menu, deliver, era, combining, driven, deep, expertise, multidomain, simulation, environment, definitive, experience, construct,

Text of the page (random words):
drandom 0 data table x exp 2x sqrt x randomreal 0 0 5 x randomreal 100 100 wolfram language code nlm nonlinearmodelfit data exp a x sqrt b x a b x wolfram language code nlm parameterestimates extract the column of statistic values wolfram language code nlm parameterestimates all tstatistic normal curvature diagnostics 1 fit a nonlinear model to some data wolfram language code data 8 76 7 73 0 17 5 34 3 05 1 16 7 65 1 98 0 95 1 21 6 7 0 42 2 04 1 12 0 42 3 13 3 78 0 71 2 93 0 21 0 9 6 05 2 71 1 14 7 67 3 88 0 61 7 26 9 11 0 72 0 88 3 84 0 61 5 32 4 53 0 69 6 46 0 79 0 83 4 5 0 44 0 46 1 1 9 64 0 2 nlm nonlinearmodelfit data a x b y c x 2 a b c x y obtain a table of curvature measures for the fitted model wolfram language code nlm fitcurvature extract the list of numeric values from the table wolfram language code nlm fitcurvature all curvature normal extract the max parameter effects curvature value wolfram language code nlm fitcurvature selectfirst type max parameter effects curvature influence measures 1 fit some data containing extreme values to a nonlinear model wolfram language code data 2 2 33 3 1 02 4 2 42 5 1 25 6 3 36 7 1 04 8 2 9 1 39 10 1 73 11 2 34 12 1 37 13 2 45 14 1 8 15 1 45 16 5 82 17 2 61 18 2 81 19 2 12 20 1 55 nlm nonlinearmodelfit data exp a x b x 3 c x a b c x use single deletion variances to check the impact on the error variance of removing each point wolfram language code listplot nlm singledeletionvariances plotrange 0 all filling 0 check the diagonal elements of the hat matrix to assess influence of points on the fitting wolfram language code listplot nlm hatdiagonal plotrange 0 all filling 0 prediction values 1 fit a nonlinear model wolfram language code data 2 8 9 1 3 5 14 8 4 4 24 1 3 9 19 2 7 7 9 2 9 10 6 0 6 1 3 0 7 1 6 0 2 3 2 3 9 18 3 nlm nonlinearmodelfit data a exp b x 2 c x a b c x plot the predicted values against the observed values wolfram language code listplot transpose nlm response predictedresponse framelabel observed predicted frame true axes false obtain tabular results for mean and single prediction confidence intervals wolfram language code nlm meanpredictions wolfram language code nlm singlepredictions get the single prediction intervals from the table wolfram language code nlm singlepredictions all confidenceinterval normal extract 99 mean prediction bands wolfram language code nlm meanpredictionbands confidencelevel 99 compute the 99 mean prediction bands at a specific location wolfram language code nlm meanpredictionbands 3 5 confidencelevel 99 goodness of fit measures 1 obtain a table of goodness of fit measures for a nonlinear model wolfram language code data 6 6 9 4 14 4 0 1 5 6 11 1 0 1 3 1 6 5 9 5 4 7 11 1 6 6 2 6 8 7 6 2 11 1 7 6 9 12 4 7 1 5 8 9 6 6 0 2 8 6 6 6 2 1 11 4 6 6 9 3 11 8 9 5 2 5 10 9 wolfram language code nlm nonlinearmodelfit data exp a x b y c a b c x y wolfram language code grid transpose nlm adjustedrsquared aic bic rsquared alignment left generalizations extensions 2 fit data to a model defined by a numerical operation wolfram language code data 6 47 3 65 7 43 3 45 3 9 2 94 4 8 1 29 2 48 0 35 6 32 3 16 2 59 1 19 9 13 2 3 81 3 04 3 33 2 68 wolfram language code model a_ numberq b_ numberq c_ numberq module y x ndsolvevalue y x a y x 0 y 0 b y 0 c y x 0 10 wolfram language code nlm nonlinearmodelfit data model a b c x a b c x method gradient wolfram language code show listplot data plot nlm x x 0 10 plotstyle orange use parametricndsolvevalue to make the computation much faster by caching solutions of the differential equation wolfram language code clear model model parametricndsolvevalue y x a y x 0 y 0 b y 0 c y x 0 10 a b c wolfram language code nlm nonlinearmodelfit data model a b c x a b c x method gradient perform other mathematical operations on the functional form of the model wolfram language code seedrandom 0 data exp range 10 randomreal 1 10 nlm nonlinearmodelfit data exp a b x a b x integrate symbolically and numerically wolfram language code integrate nlm x x wolfram language code nintegrate nlm x x 1 5 find a predictor value that gives a particular value for the model wolfram language code findroot nlm x 10 x 1 options 14 confidencelevel 1 the default gives 95 confidence intervals wolfram language code data 0 1 1 0 3 2 5 4 wolfram language code nlm nonlinearmodelfit data log a b x 2 a b x wolfram language code nlm parameterestimates all confidenceinterval normal use 99 intervals instead wolfram language code nlm nonlinearmodelfit data log a b x 2 a b x confidencelevel 99 wolfram language code nlm parameterestimates all confidenceinterval normal set the level to 90 within fittedmodel wolfram language code nlm parameterestimates confidencelevel 9 all confidenceinterval normal evaluationmonitor 1 count evaluations of the model with numerical values of the parameters wolfram language code data 4 00 126 5 00 125 7 00 123 12 0 120 14 0 119 16 0 118 20 0 116 24 0 115 28 0 114 31 0 113 34 0 112 37 5 111 41 0 110 wolfram language code block count 0 nonlinearmodelfit data 60 70exp a x a x evaluationmonitor count count gradient 1 specify the model gradient to avoid problems with a removable singularity wolfram language code data 0 1 2 2 5 5 6 4 1 0 2 0 with symbolic derivatives nonlinearmodelfit fails since the derivative for sinc is given as a generic formula wolfram language code nonlinearmodelfit data a sinc ω x x0 a ω x0 x the gradient has a singularity when since there is a point in the data with wolfram language code d a sinc ω x x0 a ω x0 specify finite differences to avoid the removable singularity wolfram language code fit nonlinearmodelfit data a sinc ω x x0 a ω x0 x gradient finitedifference show the data with the fit wolfram language code show listplot data plot fit x x 0 2 maxiterations 1 when convergence is slow increasing maxiterations may allow convergence to the best fit wolfram language code model x_ d 33c 0 7818074748209513b 4b 2 47a 2x π 2 0 6686926778600345b 32b 2 46a 2x π 2 0 8311998722869463b 21b 2 44a 2x π 2 xv randomreal 1 500 data block a 2 b 3 c 4 d 5 transpose xv model xv with the default convergence is not reached wolfram language code nonlinearmodelfit data model x a 2 3 b 3 2 c 3 9 d 4 9 x convergence is reached before 1000 iterations are used wolfram language code nonlinearmodelfit data model x a 2 3 b 3 2 c 3 9 d 4 9 x maxiterations 1000 method 3 use the default method for minimizing the least squares objective function wolfram language code nonlinearmodelfit 0 1 1 0 3 2 5 4 log a b x 2 a b x use newton s method for optimization wolfram language code nonlinearmodelfit 0 1 1 0 3 2 5 4 log a b x 2 a b x method newton configure the step control method for newton s algorithm wolfram language code nonlinearmodelfit 0 1 1 0 3 2 5 4 log a b x 2 a b x method newton stepcontrol linesearch method brent use the interior point method with constraints wolfram language code nonlinearmodelfit 0 1 1 0 3 2 5 4 log a b x 2 a 0 b 0 a b x method interiorpoint perform a more exhaustive search with the global optimization methods from nminimize wolfram language code nonlinearmodelfit 0 1 1 0 3 2 5 4 log a b x 2 a 0 b 0 a b x method nminimize use the submethod randomsearch wolfram language code nonlinearmodelfit 0 1 1 0 3 2 5 4 log a b x 2 a 0 b 0 a b x method nminimize method randomsearch specify the number of initial search points for the randomsearch algorithm wolfram language code nonlinearmodelfit 0 1 1 0 3 2 5 4 log a b x 2 a 0 b 0 a b x method nminimize method randomsearch searchpoints 250 stepmonitor 1 show steps taken in parameter space to fit the michaelis menten model to experimental data wolfram language code model subscript θ 1 x subscript θ 2 x data from an experiment on the rate of an enzymatic reaction wolfram language code data 0 02 76 0 02 47 0 06 97 0 06 107 0 11 123 0 11 139 0 22 159 0 22 152 0 56 191 0 56 201 1 1 207 1 1 200 wolfram language code fit steps reap nonlinearmodelfit data model subscript θ 1 subscript θ 2 x stepmonitor sow subscript θ 1 subscript θ 2 wolfram language code fit bestfitparameters show how the parameters evolve during the search wolfram language code listplot steps epilog red point subscript θ 1 subscript θ 2 fit bestfitparameters varianceestimatorfunction 1 use the default unbiased estimate of error variance wolfram language code data 0 1 1 0 3 2 5 4 wolfram language code nlm nonlinearmodelfit data log a b x 2 a b x wolfram language code nlm estimatedvariance assume a known error variance wolfram language code nlm estimatedvariance varianceestimatorfunction 1 estimate the variance by the mean squared error wolfram language code nlm estimatedvariance varianceestimatorfunction mean 2 weights 4 fit a model using equal weights wolfram language code data 0 1 1 0 3 2 5 4 wolfram language code nonlinearmodelfit data log a b x 2 a b x normal give explicit weights for the data points wolfram language code nonlinearmodelfit data log a b x 2 a b x weights 1 1 2 1 3 1 4 normal use around values to give different weights to data points wolfram language code data around 1 0 2 around 2 0 1 around 4 2 fit nonlinearmodelfit data log a b x 2 a b x weights automatic wolfram language code show plot fit x x 0 3 listplot data plotrange all find the weights that were used to account for the uncertainty in the data wolfram language code fit weights use around values in both the independent values and responses wolfram language code seedrandom 1 data table around x randomreal 0 25 around log 2 3 x 2 randomreal 0 25 randomreal 0 25 x 0 3 0 2 fit nonlinearmodelfit data log a b x 2 a b x wolfram language code show plot fit x x 0 3 listplot data plotrange all in some cases the root finding algorithm that handles uncertainty in the independent variates does not converge using the standard option settings wolfram language code data nonlinearmodelfit data exp a x b y a b x y weights automatic method findroot use the fixedpoint algorithm with a low damping factor and high maxiterations to reach convergence wolfram language code nonlinearmodelfit data exp a x b y a b x y weights automatic method fixedpoint maxiterations 500 dampingfactor 0 25 tolerance 10 10 workingprecision 1 use workingprecision to get higher precision in parameter estimates wolfram language code data table x x 2 x 10 wolfram language code nlm nonlinearmodelfit data exp a x a x workingprecision 50 obtain the fitted function wolfram language code nlm bestfit reduce the precision in property computations after the fitting wolfram language code nlm bestfit workingprecision 20 obtain the best fit at a specific point wolfram language code nlm bestfit 3 5 applications 1 simulate some data wolfram language code data blockrandom seedrandom 12345 table x exp 2 3 x 11 4 x x 2 randomreal 5 5 x randomreal 1 15 20 fit a nonlinear model to the data wolfram language code nlm nonlinearmodelfit data exp a x b c x a b c x obtain and visualize 90 confidence bands for the fit wolfram language code bands90 x_ nlm meanpredictionbands confidencelevel 9 show listplot data plot nlm x bands90 x x 1 15 filling 2 1 obtain 95 99 and 99 9 confidence bands wolfram language code bands95 x_ bands99 x_ bands999 x_ table nlm meanpredictionbands confidencelevel cl cl 95 99 999 visualize the confidence bands for the various levels wolfram language code show listplot data plot nlm x bands90 x bands95 x bands99 x bands999 x x 1 15 filling 2 1 3 2 4 3 5 4 plotlegends model 90 confidence bands 95 confidence bands 99 confidence bands 99 9 confidence bands properties relations 6 nonlinearmodelfit fits linear and nonlinear models assuming normally distributed errors wolfram language code data table i i i 10 wolfram language code nonlinearmodelfit data a b x 2 a b x normal wolfram language code nonlinearmodelfit data exp sqrt a x b a b x normal linearmodelfit fits linear models assuming normally distributed errors wolfram language code linearmodelfit range 10 x 2 x normal findfit and nonlinearmodelfit fit equivalent models wolfram language code seedrandom 0 data table i exp randomreal i 1 i i 10 wolfram language code findfit data exp a x a x wolfram language code nlm nonlinearmodelfit data exp a x a x wolfram language code nlm bestfitparameters nonlinearmodelfit allows for extraction of additional information about the fitting wolfram language code nlm fitresiduals nonlinearmodelfit assumes normally distributed responses wolfram language code seedrandom 0 data table i randomreal i 1 i 10 i 10 wolfram language code nm nonlinearmodelfit data 1 1 exp a b x a b x logitmodelfit assumes binomially distributed responses wolfram language code lm logitmodelfit data x x the fits are not identical wolfram language code normal lm normal nm wolfram language code plot lm x nm x x 1 5 the same is true for probitmodelfit wolfram language code pm probitmodelfit data x x wolfram language code nm2 nonlinearmodelfit data 1 2 1 erf a b x sqrt 2 transpose a b pm bestfitparameters x wolfram language code normal pm normal nm2 nonlinearmodelfit will use the time stamps of a timeseries as variables wolfram language code ts1 temporaldata timeseries 1 102448341846048 6 331833897009389 7 5843632999043455 44 59969789743589 98 76273258351092 150 00729051003992 644 7367359379259 1724 3968817536402 5903 697723461762 19468 09340765025 0 9 1 1 continuous 1 discrete 1 1 resamplingmethod interpolation interpolationorder 1 false 10 1 wolfram language code ts1 times wolfram language code nonlinearmodelfit ts1 exp a b x a b x rescale the time stamps and fit again wolfram language code ts2 timeseriesrescale ts1 1 2 wolfram language code ts2 times wolfram language code nonlinearmodelfit ts2 exp a b x a b x find fit for the values wolfram language code nonlinearmodelfit ts1 values exp a b x a b x nonlinearmodelfit acts pathwise on a multipath temporaldata wolfram language code nonlinearmodelfit temporaldata automatic 1 102448341846048 6 331833897009389 7 5843632999043455 44 59969789743589 98 76273258351092 150 00729051003992 644 7367359379259 1724 3968817536402 5903 697723461762 19468 09340765025 1 1024483418 7359379259 1724 3968817536402 5903 697723461762 19468 09340765025 0 9 1 0 1 2 0 2111111111111111 2 continuous 2 discrete 2 1 resamplingmethod interpolation interpolationorder 1 false 10 1 exp a b x a b x compute the aic from first principles wolfram language code data 0 1 1 0 3 2 5 4 6 4 7 5 n length data params a b k length params 1 1 for the estimation of the variance nlm nonlinearmodelfit data log a b x 2 params x errorsumofsquares total nlm fitresiduals 2 variancemle errorsumofsquares n loglike 1 2 n log 2pi variancemle errorsumofsquares variancemle aic 2 k 2 loglike compare against the aic property wolfram language code nlm aic aic check the aicc property wolfram language code nlm aicc aic 2k k 1 n k 1 check the bic property wolfram language code nlm bic log n k 2 loglike possible issues 3 distributional assumptions are based upon an unconstrained model wolfram language code data 1 0 75 2 0 89 3 0 42 4 0 99 5 0 84 6 0 34 ...