coefCI
Confidence intervals of coefficient estimates of nonlinear regression model
Description
Examples
Default Confidence Intervals
Create a nonlinear model for auto mileage based on the carbig
data. Then obtain confidence intervals for the resulting model coefficients.
Load the data and create a nonlinear model.
load carbig ds = dataset(Horsepower,Weight,MPG); modelfun = @(b,x)b(1) + b(2)*x(:,1) + ... b(3)*x(:,2) + b(4)*x(:,1).*x(:,2); beta0 = [1 1 1 1]; mdl = fitnlm(ds,modelfun,beta0)
mdl = Nonlinear regression model: MPG ~ b1 + b2*Horsepower + b3*Weight + b4*Horsepower*Weight Estimated Coefficients: Estimate SE tStat pValue __________ __________ _______ __________ b1 63.558 2.3429 27.127 1.2343e-91 b2 -0.25084 0.027279 -9.1952 2.3226e-18 b3 -0.010772 0.00077381 -13.921 5.1372e-36 b4 5.3554e-05 6.6491e-06 8.0542 9.9336e-15 Number of observations: 392, Error degrees of freedom: 388 Root Mean Squared Error: 3.93 R-Squared: 0.748, Adjusted R-Squared 0.746 F-statistic vs. constant model: 385, p-value = 7.26e-116
All the coefficients have extremely small -values. This means a confidence interval around the coefficients will not contain the point 0
, unless the confidence level is very high.
Find 95% confidence intervals for the coefficients of the model.
ci = coefCI(mdl)
ci = 4×2
58.9515 68.1644
-0.3045 -0.1972
-0.0123 -0.0093
0.0000 0.0001
The confidence interval for b4
seems to contain 0
. Examine it in more detail.
ci(4,:)
ans = 1×2
10-4 ×
0.4048 0.6663
As expected, the confidence interval does not contain the point 0
.
Input Arguments
mdl
— Nonlinear regression model object
NonLinearModel
object
Nonlinear regression model object, specified as a NonLinearModel
object created by using fitnlm
.
alpha
— Significance level
0.05 (default) | numeric value in the range [0,1]
Significance level for the confidence interval, specified as a numeric value in the
range [0,1]. The confidence level of ci
is equal to 100(1 – alpha
)%. alpha
is the probability that the confidence
interval does not contain the true value.
Example: 0.01
Data Types: single
| double
Output Arguments
ci
— Confidence intervals
numeric matrix
Confidence intervals, returned as a k-by-2 numeric matrix, where
k is the number of coefficients. The jth row
of ci
is the confidence interval of the jth
coefficient of mdl
. The name of coefficient j is
stored in the CoefficientNames
property of
mdl
.
Data Types: single
| double
More About
Confidence Interval
The coefficient confidence intervals provide a measure of precision for regression coefficient estimates.
A 100(1 – α)% confidence interval gives the range for the corresponding regression coefficient with 100(1 – α)% confidence, meaning that 100(1 – α)% of the intervals resulting from repeated experimentation will contain the true value of the coefficient.
The software finds confidence intervals using the Wald method. The 100(1 – α)% confidence intervals for regression coefficients are
where bi is the coefficient estimate, SE(bi) is the standard error of the coefficient estimate, and t(1–α/2,n–p) is the 100(1 – α/2) percentile of the t-distribution with n – p degrees of freedom. n is the number of observations and p is the number of regression coefficients.
Version History
Introduced in R2012a
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)