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# coefCI

Clase: CompactLinearModel

Confidence intervals of coefficient estimates of linear model

## Sintaxis

```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 using the confidence level 1 – alpha.

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Linear model object, specified as a full `LinearModel` object constructed using `fitlm` or `stepwiselm`, or a compacted `CompactLinearModel` object constructed using `compact`.

Confidence interval, specified as a numeric value in the range [0,1]. `alpha` is the probability that the confidence interval does not contain the true value.

## Output Arguments

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Confidence intervals, returned as a k-by-2 numeric matrix. The jth row of `ci` is the confidence interval of coefficient j of `mdl`. The name of coefficient j is stored in the `mdl` property `CoefficientNames`.

## Ejemplos

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Fit a linear regression model for auto mileage based on the `carbig` data. Then obtain the default 95% confidence intervals for the resulting model coefficients.

Load the data and create a table.

```load carbig Origin = nominal(Origin); tbl = table(Horsepower,Weight,MPG,Origin);```

Fit a linear regression model. Use horsepower, weight, and origin as predictor variables, and miles per gallon as the response variable.

```modelspec = 'MPG ~ 1 + Horsepower + Weight + Origin'; mdl = fitlm(tbl,modelspec);```

View the names of the coefficients.

`mdl.CoefficientNames`
```ans = 1x9 cell array Columns 1 through 4 {'(Intercept)'} {'Horsepower'} {'Weight'} {'Origin_France'} Columns 5 through 7 {'Origin_Germany'} {'Origin_Italy'} {'Origin_Japan'} Columns 8 through 9 {'Origin_Sweden'} {'Origin_USA'} ```

Find confidence intervals for the coefficients of the model.

`ci = coefCI(mdl)`
```ci = 9×2 43.3611 59.9390 -0.0748 -0.0315 -0.0059 -0.0037 -17.3623 -0.3477 -15.7503 0.7434 -17.2091 0.0613 -14.5106 1.8738 -18.5820 -1.5036 -17.3114 -0.9642 ```

Fit a linear regression model for auto mileage based on the `carbig` data. Then obtain confidence intervals for the resulting model coefficients at the 99% level.

Load the data and create a table.

```load carbig Origin = nominal(Origin); tbl = table(Horsepower,Weight,MPG,Origin);```

Fit a linear regression model using horsepower, weight, and origin as the predictor variables, and miles per gallon as the response variable.

```modelspec = 'MPG ~ 1 + Horsepower + Weight + Origin'; mdl = fitlm(tbl,modelspec);```

Find 99% confidence intervals for the coefficients.

`ci = coefCI(mdl,.01)`
```ci = 9×2 40.7365 62.5635 -0.0816 -0.0246 -0.0062 -0.0034 -20.0560 2.3459 -18.3615 3.3546 -19.9433 2.7955 -17.1045 4.4676 -21.2858 1.2002 -19.8995 1.6238 ```

The confidence intervals are wider than the default 5% confidence intervals.

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## Alternatives

You can create the intervals from the model coefficients in `mdl``.Coefficients.Estimate` and an appropriate multiplier of the standard errors `sqrt(diag(mdl.CoefficientCovariance))`. The multiplier is `tinv(1-alpha/2,dof)`, where `level` is the confidence level, and `dof` is the degrees of freedom (number of data points minus the number of coefficients).