MATLAB Examples

Compute Coefficient Confidence Intervals

This example shows how to compute coefficient confidence intervals.

Load the sample data and fit a linear regression model.

load hald
mdl = fitlm(ingredients,heat);

Display the 95% coefficient confidence intervals.

coefCI(mdl)
ans =

  -99.1786  223.9893
   -0.1663    3.2685
   -1.1589    2.1792
   -1.6385    1.8423
   -1.7791    1.4910

The values in each row are the lower and upper confidence limits, respectively, for the default 95% confidence intervals for the coefficients. For example, the first row shows the lower and upper limits, -99.1786 and 223.9893, for the intercept, $\beta_0$ . Likewise, the second row shows the limits for $\beta_1$ and so on.

Display the 90% confidence intervals for the coefficients ($\alpha$ = 0.1).

coefCI(mdl,0.1)
ans =

  -67.8949  192.7057
    0.1662    2.9360
   -0.8358    1.8561
   -1.3015    1.5053
   -1.4626    1.1745

The confidence interval limits become narrower as the confidence level decreases.