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# predint

Prediction intervals for cfit or sfit object

## Syntax

ci = predint(fitresult,x)
ci = predint(fitresult,x,level)
ci = predint(fitresult,x,level,intopt,simopt)
[ci,y] = predint(...)

## Description

ci = predint(fitresult,x) returns upper and lower 95% prediction bounds for response values associated with the cfit object fitresult at the new predictor values specified by the vector x. fitresult must be an output from the fit function to contain the necessary information for ci. ci is an n-by-2 array where n = length(x). The left column of ci contains the lower bound for each coefficient; the right column contains the upper bound.

ci = predint(fitresult,x,level) returns prediction bounds with a confidence level specified by level. level must be between 0 and 1. The default value of level is 0.95.

ci = predint(fitresult,x,level,intopt,simopt) specifies the type of bounds to compute.

intopt is one of

• 'observation' — Bounds for a new observation (default)

• 'functional' — Bounds for the fitted curve

simopt is one of

• 'off' — Non-simultaneous bounds (default)

• 'on' — Simultaneous bounds

Observation bounds are wider than functional bounds because they measure the uncertainty of predicting the fitted curve plus the random variation in the new observation. Non-simultaneous bounds are for individual elements of x; simultaneous bounds are for all elements of x.

[ci,y] = predint(...) returns the response values y predicted by fitresult at the predictors in x.

 Note:   predint cannot compute prediction intervals for non-parametric regression methods such as Interpolant, Lowess, and Spline.

## Examples

Generate data with an exponential trend:

```x = (0:0.2:5)';
y = 2*exp(-0.2*x) + 0.5*randn(size(x));```

Fit the data using a single-term exponential:

`fitresult = fit(x,y,'exp1');`

Compute prediction intervals:

```p11 = predint(fitresult,x,0.95,'observation','off');
p12 = predint(fitresult,x,0.95,'observation','on');
p21 = predint(fitresult,x,0.95,'functional','off');
p22 = predint(fitresult,x,0.95,'functional','on');```

Plot the data, fit, and prediction intervals:

```subplot(2,2,1)
plot(fitresult,x,y),hold on,plot(x,p11,'m--'),xlim([0 5])
title('Nonsimultaneous observation bounds','Color','m')
subplot(2,2,2)
plot(fitresult,x,y),hold on,plot(x,p12,'m--'),xlim([0 5])
title('Simultaneous observation bounds','Color','m')
subplot(2,2,3)
plot(fitresult,x,y),hold on,plot(x,p21,'m--'),xlim([0 5])
title('Nonsimultaneous functional bounds','Color','m')
subplot(2,2,4)
plot(fitresult,x,y),hold on,plot(x,p22,'m--'),xlim([0 5])
title('Simultaneous functional bounds','Color','m')```