How can I compute the standard error for coefficients returned from curve fitting functions in the Curve Fitting Toolbox?

Question

MathWorks Support Team 2013-10-18

2
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/153547-how-can-i-compute-the-standard-error-for-coefficients-returned-from-curve-fitting-functions-in-the-c

评论： Adam Danz 2019-8-29

I fit my data to a polynomial model using the FIT function from the Curve Fitting Toolbox as follows:

load census
[fitresult,gof1,out1] = fit(cdate,pop,'poly2');

The FIT function returns the following coefficients, along with confidence intervals:

 fitresult =
      Linear model Poly2:
        fit1(x) = p1*x^2 + p2*x + p3
      Coefficients (with 95% confidence bounds):
        p1 =    0.006541  (0.006124, 0.006958)
        p2 =      -23.51  (-25.09, -21.93)
        p3 =  2.113e+004  (1.964e+004, 2.262e+004)

I am interested in finding the standard error of the coefficients rather than the confidence interval.

请先登录，再回答此问题。

Answer 1

MathWorks Support Team 2019-8-29

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/153547-how-can-i-compute-the-standard-error-for-coefficients-returned-from-curve-fitting-functions-in-the-c#answer_150796

编辑：MathWorks Support Team 2019-8-28

在 MATLAB Online 中打开

The FIT function in the Curve Fitting Toolbox does not currently return the standard error or variance information on the estimated coefficients.

You can compute the standard errors from the confidence interval in the following manner.

Let "fitresult" be the result of calling "fit", and "df" be the degrees of freedom:

>> alpha = 0.95
>> ci = confint(fitresult, alpha) 
>> t = tinv((1+alpha)/2, df); 
>> se = (ci(2,:)-ci(1,:)) ./ (2*t) % Standard Error

Alternatively, models fitted using the Statistics Toolbox methods will have their coefficient-covariance matrices calculated and stored automatically as a model property. For example, you can access the coefficient-covariance matrix of a model "mdl" generated as output of the command "fitlm" by the command "mdl.Coefficient." See the following documentation link for more information:

https://www.mathworks.com/help/stats/linearmodel.html#bsz4dm2-1_sep_shared-Coefficients

You can also refer to the following discussion on MATLAB Answers:

https://www.mathworks.com/matlabcentral/answers/34234-how-to-obtain-std-of-coefficients-from-curve-fitting