# Documentation

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# confint

Confidence intervals for fit coefficients of `cfit` or `sfit` object

## Syntax

```ci = confint(fitresult) ci = confint(fitresult,level) ```

## Description

`ci = confint(fitresult)` returns 95% confidence bounds `ci` on the coefficients associated with the `cfit` or `sfit` object `fitresult`. `fitresult` must be an output from the `fit` function to contain the necessary information for `ci`. `ci` is a 2-by-`n` array where `n = numcoeffs(fitresult)`. The top row of `ci` contains the lower bound for each coefficient; the bottom row contains the upper bound.

`ci = confint(fitresult,level)` returns confidence bounds at the confidence level specified by `level`. `level` must be between `0` and `1`. The default value of `level` is `0.95`.

## Examples

```load census fitresult = fit(cdate,pop,'poly2') fitresult = Linear model Poly2: fitresult(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) ci = confint(fitresult,0.95) ci = 0.0061242 -25.086 19641 0.0069581 -21.934 22618```

Note that `fit` and `confint` display the confidence bounds in slightly different formats.

## Tips

To calculate confidence bounds, `confint` uses R-1 (the inverse R factor from QR decomposition of the Jacobian), the degrees of freedom for error, and the root mean squared error. This information is automatically returned by the `fit` function and contained within `fitresult`.

If coefficients are bounded and one or more of the estimates are at their bounds, those estimates are regarded as fixed and do not have confidence bounds.

Note that you cannot calculate confidence bounds if `category(fitresult)` is `'spline'` or `'interpolant'`.