# coefCI

Class: NonLinearModel

Confidence intervals of coefficient estimates of nonlinear regression model

## Syntax

```ci = coefCI(mdl) ci = coefCI(mdl,alpha) ```

## Description

`ci = coefCI(mdl)` returns confidence intervals for the coefficients in `mdl`.

`ci = coefCI(mdl,alpha)` returns confidence intervals with confidence level `1 - alpha`.

## Input Arguments

 `mdl` Nonlinear regression model, constructed by `fitnlm`. `alpha` Scalar from 0 to 1, the probability that the confidence interval does not contain the true value. Default: 0.05

## Output Arguments

 `ci` `k`-by-`2` matrix of confidence intervals. The `j`th row of `ci` is the confidence interval of coefficient `j` of `mdl`. The name of coefficient `j` of `mdl` is in `mdl``.CoefNames`.

## Examples

expand all

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 $p$-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`.