MATLAB: Fitting a Custom Sigmoid

curve fittingsigmoid

Hello,

I have a set of data that decays in a sigmoidal fashion. I believe it should be a good fit to a function of the form shown in the first screenshot, but when I use the Custom Fit feature in the Curvefitting App matlab gives a -Rsq so something is clearly going wrong. I have attached a screenshot of the attempted fit and result as well. I would really appreciate any advice or input as to why this may not be working and alternatives I could try.

Thank you!

Best Answer

Hi，if the fitting function is：

1：y=a1*exp(-a2*exp(x))

Root of Mean Square Error (RMSE): 0.291990919479646
Sum of Squared Residual: 2.81353700293277
Correlation Coef. (R): 0.943693599341358
R-Square: 0.890557609437848
Adjusted R-Square: 0.883261450067038
Parameter	Best Estimate
----------	-------------
a1	7.58840204504645
a2	1.16352684388827E-7

2：y=a1*exp(-a2*exp(x))+a3

Root of Mean Square Error (RMSE): 0.111213914229836
Sum of Squared Residual: 0.408161645704602
Correlation Coef. (R): 0.991993546182226
R-Square: 0.984051195667188
Adjusted R-Square: 0.982987942045001
Parameter	Best Estimate
----------	-------------
a1	3.31691483854775
a2	6.92191293955397E-7
a3	4.93177045354278

3：y=a1*exp(-a2*exp(a4*x))+a3

Root of Mean Square Error (RMSE): 0.00643423581192002
Sum of Squared Residual: 0.001366179885952
Correlation Coef. (R): 0.999973308091645
R-Square: 0.999946616895747
Adjusted R-Square: 0.999943058022131
Parameter	Best Estimate
----------	-------------
a1	2.46665608498939
a2	4.05630590375969E-12
a4	1.85195743324274
a3	5.25959927640292

Related Solutions

MATLAB: How to solve the equation quickly

try 'fsolve'

fplot('(47.457/b1)-(76.3792)+(3.0499)-(((2.7272^b1)*(1.0033)+(1.59^b1)*(0.46376)+(2.4506^b1)*(0.89632)+(2.6129^b1)*(0.96046)+(1.367^b1)*(0.31264)+(0.39284^b1)*(-0.93436)+(1.5651^b1)*(0.44795)+(1.5083^b1)*(0.41096)+(0.81499^b1)*(-0.20458)+(1.6526^b1)*(0.50236)+(1.7819^b1)*(0.5777)+(2.4563^b1)*(0.89867)+(0.88014^b1)*(-0.12768)+(2.5081^b1)*(0.91954)+(2.741^b1)*(1.0083)+(1.8194^b1)*(0.59851)+(2.033^b1)*(0.70951)+(1.6526^b1)*(0.50236)+(2.4283^b1)*(0.88718)+(1.2561^b1)*(0.22802)+(0.67065^b1)*(-0.39951)+(1.4447^b1)*(0.36793)+(0.49793^b1)*(-0.69729)+(1.2089^b1)*(0.18969)+(2.3449^b1)*(0.85226)+(0.49793^b1)*(-0.69729)+(0.39284^b1)*(-0.93436)+(0.49793^b1)*(-0.69729)+(1.8122^b1)*(0.59453)+(0.12951^b1)*(-2.044)+(0.58896^b1)*(-0.5294)+(2.6787^b1)*(0.98533)+(0.39284^b1)*(-0.93436)+(2.7946^b1)*(1.0277)+(1.7509^b1)*(0.56012)+(1.9784^b1)*(0.68228)+(2.4229^b1)*(0.88499)+(1.2561^b1)*(0.22802)+(1.742^b1)*(0.55506)+(2.0081^b1)*(0.69717)+(1.2864^b1)*(0.25188)+(2.3003^b1)*(0.83305)+(0.19421^b1)*(-1.6388)+(1.616^b1)*(0.47995)+(2.521^b1)*(0.92467)+(0.88014^b1)*(-0.12768)+(1.5459^b1)*(0.43562)+(2.0526^b1)*(0.7191)+(0.74549^b1)*(-0.29371)+(2.505^b1)*(0.91829)+(1.8026^b1)*(0.58922)+(1.671^b1)*(0.51344)+(2.0037^b1)*(0.69501)+(2.5104^b1)*(0.92042)+(1.6863^b1)*(0.52251)+(0.74549^b1)*(-0.29371)+(1.4695^b1)*(0.38492)+(1.719^b1)*(0.54174)+(1.9258^b1)*(0.65532)+(1.8122^b1)*(0.59453)+(0.39284^b1)*(-0.93436)+(0.49793^b1)*(-0.69729)+(2.2284^b1)*(0.80128)+(2.2822^b1)*(0.82514)+(1.3017^b1)*(0.26365)+(2.0761^b1)*(0.73051)+(2.4563^b1)*(0.89867)+(2.7046^b1)*(0.99495)+(1.6818^b1)*(0.51988)+(0.26185^b1)*(-1.34)+(0.39284^b1)*(-0.93436)+(0.39284^b1)*(-0.93436)+(0.12951^b1)*(-2.044)+(0.74549^b1)*(-0.29371)+(0.39284^b1)*(-0.93436)+(0.58896^b1)*(-0.5294)+(0.19421^b1)*(-1.6388)+(0.88014^b1)*(-0.12768)+(0.58896^b1)*(-0.5294)+(0.26185^b1)*(-1.34)+(0.26185^b1)*(-1.34)+(0.26185^b1)*(-1.34)+(0.39284^b1)*(-0.93436)+(0.26185^b1)*(-1.34)+(2.794^b1)*(1.0275)+(1.8122^b1)*(0.59453)+(0.26185^b1)*(-1.34)+(0.39284^b1)*(-0.93436)+(0.26185^b1)*(-1.34)+(0.67065^b1)*(-0.39951)+(1.1598^b1)*(0.14828)+(0.74549^b1)*(-0.29371)+(1.2561^b1)*(0.22802)+(0.58896^b1)*(-0.5294)+(1^b1)*(0)+(0.26185^b1)*(-1.34)+(2.0761^b1)*(0.73051)+(1^b1)*(0)+(1.3017^b1)*(0.26365)+(1.0556^b1)*(0.054134)+0)/(5^(b1*47.457)))+((((2.7272^b1)+(1.59^b1)+(2.4506^b1)+(2.6129^b1)+(1.367^b1)+(0.39284^b1)+(1.5651^b1)+(1.5083^b1)+(0.81499^b1)+(1.6526^b1)+(1.7819^b1)+(2.4563^b1)+(0.88014^b1)+(2.5081^b1)+(2.741^b1)+(1.8194^b1)+(2.033^b1)+(1.6526^b1)+(2.4283^b1)+(1.2561^b1)+(0.67065^b1)+(1.4447^b1)+(0.49793^b1)+(1.2089^b1)+(2.3449^b1)+(0.49793^b1)+(0.39284^b1)+(0.49793^b1)+(1.8122^b1)+(0.12951^b1)+(0.58896^b1)+(2.6787^b1)+(0.39284^b1)+(2.7946^b1)+(1.7509^b1)+(1.9784^b1)+(2.4229^b1)+(1.2561^b1)+(1.742^b1)+(2.0081^b1)+(1.2864^b1)+(2.3003^b1)+(0.19421^b1)+(1.616^b1)+(2.521^b1)+(0.88014^b1)+(1.5459^b1)+(2.0526^b1)+(0.74549^b1)+(2.505^b1)+(1.8026^b1)+(1.671^b1)+(2.0037^b1)+(2.5104^b1)+(1.6863^b1)+(0.74549^b1)+(1.4695^b1)+(1.719^b1)+(1.9258^b1)+(1.8122^b1)+(0.39284^b1)+(0.49793^b1)+(2.2284^b1)+(2.2822^b1)+(1.3017^b1)+(2.0761^b1)+(2.4563^b1)+(2.7046^b1)+(1.6818^b1)+(0.26185^b1)+(0.39284^b1)+(0.39284^b1)+(0.12951^b1)+(0.74549^b1)+(0.39284^b1)+(0.58896^b1)+(0.19421^b1)+(0.88014^b1)+(0.58896^b1)+(0.26185^b1)+(0.26185^b1)+(0.26185^b1)+(0.39284^b1)+(0.26185^b1)+(2.794^b1)+(1.8122^b1)+(0.26185^b1)+(0.39284^b1)+(0.26185^b1)+(0.67065^b1)+(1.1598^b1)+(0.74549^b1)+(1.2561^b1)+(0.58896^b1)+(1^b1)+(0.26185^b1)+(2.0761^b1)+(1^b1)+(1.3017^b1)+(1.0556^b1)+0)*76.3792)/(5^(b1*47.457)))',[0 100]);

fsolve(@(b1)(47.457/b1)-(76.3792)+(3.0499)-(((2.7272^b1)*(1.0033)+(1.59^b1)*(0.46376)+(2.4506^b1)*(0.89632)+(2.6129^b1)*(0.96046)+(1.367^b1)*(0.31264)+(0.39284^b1)*(-0.93436)+(1.5651^b1)*(0.44795)+(1.5083^b1)*(0.41096)+(0.81499^b1)*(-0.20458)+(1.6526^b1)*(0.50236)+(1.7819^b1)*(0.5777)+(2.4563^b1)*(0.89867)+(0.88014^b1)*(-0.12768)+(2.5081^b1)*(0.91954)+(2.741^b1)*(1.0083)+(1.8194^b1)*(0.59851)+(2.033^b1)*(0.70951)+(1.6526^b1)*(0.50236)+(2.4283^b1)*(0.88718)+(1.2561^b1)*(0.22802)+(0.67065^b1)*(-0.39951)+(1.4447^b1)*(0.36793)+(0.49793^b1)*(-0.69729)+(1.2089^b1)*(0.18969)+(2.3449^b1)*(0.85226)+(0.49793^b1)*(-0.69729)+(0.39284^b1)*(-0.93436)+(0.49793^b1)*(-0.69729)+(1.8122^b1)*(0.59453)+(0.12951^b1)*(-2.044)+(0.58896^b1)*(-0.5294)+(2.6787^b1)*(0.98533)+(0.39284^b1)*(-0.93436)+(2.7946^b1)*(1.0277)+(1.7509^b1)*(0.56012)+(1.9784^b1)*(0.68228)+(2.4229^b1)*(0.88499)+(1.2561^b1)*(0.22802)+(1.742^b1)*(0.55506)+(2.0081^b1)*(0.69717)+(1.2864^b1)*(0.25188)+(2.3003^b1)*(0.83305)+(0.19421^b1)*(-1.6388)+(1.616^b1)*(0.47995)+(2.521^b1)*(0.92467)+(0.88014^b1)*(-0.12768)+(1.5459^b1)*(0.43562)+(2.0526^b1)*(0.7191)+(0.74549^b1)*(-0.29371)+(2.505^b1)*(0.91829)+(1.8026^b1)*(0.58922)+(1.671^b1)*(0.51344)+(2.0037^b1)*(0.69501)+(2.5104^b1)*(0.92042)+(1.6863^b1)*(0.52251)+(0.74549^b1)*(-0.29371)+(1.4695^b1)*(0.38492)+(1.719^b1)*(0.54174)+(1.9258^b1)*(0.65532)+(1.8122^b1)*(0.59453)+(0.39284^b1)*(-0.93436)+(0.49793^b1)*(-0.69729)+(2.2284^b1)*(0.80128)+(2.2822^b1)*(0.82514)+(1.3017^b1)*(0.26365)+(2.0761^b1)*(0.73051)+(2.4563^b1)*(0.89867)+(2.7046^b1)*(0.99495)+(1.6818^b1)*(0.51988)+(0.26185^b1)*(-1.34)+(0.39284^b1)*(-0.93436)+(0.39284^b1)*(-0.93436)+(0.12951^b1)*(-2.044)+(0.74549^b1)*(-0.29371)+(0.39284^b1)*(-0.93436)+(0.58896^b1)*(-0.5294)+(0.19421^b1)*(-1.6388)+(0.88014^b1)*(-0.12768)+(0.58896^b1)*(-0.5294)+(0.26185^b1)*(-1.34)+(0.26185^b1)*(-1.34)+(0.26185^b1)*(-1.34)+(0.39284^b1)*(-0.93436)+(0.26185^b1)*(-1.34)+(2.794^b1)*(1.0275)+(1.8122^b1)*(0.59453)+(0.26185^b1)*(-1.34)+(0.39284^b1)*(-0.93436)+(0.26185^b1)*(-1.34)+(0.67065^b1)*(-0.39951)+(1.1598^b1)*(0.14828)+(0.74549^b1)*(-0.29371)+(1.2561^b1)*(0.22802)+(0.58896^b1)*(-0.5294)+(1^b1)*(0)+(0.26185^b1)*(-1.34)+(2.0761^b1)*(0.73051)+(1^b1)*(0)+(1.3017^b1)*(0.26365)+(1.0556^b1)*(0.054134)+0)/(5^(b1*47.457)))+((((2.7272^b1)+(1.59^b1)+(2.4506^b1)+(2.6129^b1)+(1.367^b1)+(0.39284^b1)+(1.5651^b1)+(1.5083^b1)+(0.81499^b1)+(1.6526^b1)+(1.7819^b1)+(2.4563^b1)+(0.88014^b1)+(2.5081^b1)+(2.741^b1)+(1.8194^b1)+(2.033^b1)+(1.6526^b1)+(2.4283^b1)+(1.2561^b1)+(0.67065^b1)+(1.4447^b1)+(0.49793^b1)+(1.2089^b1)+(2.3449^b1)+(0.49793^b1)+(0.39284^b1)+(0.49793^b1)+(1.8122^b1)+(0.12951^b1)+(0.58896^b1)+(2.6787^b1)+(0.39284^b1)+(2.7946^b1)+(1.7509^b1)+(1.9784^b1)+(2.4229^b1)+(1.2561^b1)+(1.742^b1)+(2.0081^b1)+(1.2864^b1)+(2.3003^b1)+(0.19421^b1)+(1.616^b1)+(2.521^b1)+(0.88014^b1)+(1.5459^b1)+(2.0526^b1)+(0.74549^b1)+(2.505^b1)+(1.8026^b1)+(1.671^b1)+(2.0037^b1)+(2.5104^b1)+(1.6863^b1)+(0.74549^b1)+(1.4695^b1)+(1.719^b1)+(1.9258^b1)+(1.8122^b1)+(0.39284^b1)+(0.49793^b1)+(2.2284^b1)+(2.2822^b1)+(1.3017^b1)+(2.0761^b1)+(2.4563^b1)+(2.7046^b1)+(1.6818^b1)+(0.26185^b1)+(0.39284^b1)+(0.39284^b1)+(0.12951^b1)+(0.74549^b1)+(0.39284^b1)+(0.58896^b1)+(0.19421^b1)+(0.88014^b1)+(0.58896^b1)+(0.26185^b1)+(0.26185^b1)+(0.26185^b1)+(0.39284^b1)+(0.26185^b1)+(2.794^b1)+(1.8122^b1)+(0.26185^b1)+(0.39284^b1)+(0.26185^b1)+(0.67065^b1)+(1.1598^b1)+(0.74549^b1)+(1.2561^b1)+(0.58896^b1)+(1^b1)+(0.26185^b1)+(2.0761^b1)+(1^b1)+(1.3017^b1)+(1.0556^b1)+0)*76.3792)/(5^(b1*47.457))),1)

MATLAB: Exponential curve fitting with custom equation

Your model does not provide enough degree of freedom to fit all the points. Change the model to

mymodel=@(a,b,c,x) (b+c*exp(-x/a));

Best Answer

Related Solutions

MATLAB: How to solve the equation quickly

MATLAB: Exponential curve fitting with custom equation

Related Question