Confidence Intervals

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The NLIN Procedure

Confidence Intervals

Parameter Confidence Intervals

The parameter confidence intervals are computed using the Wald based formula:

$\hat{\beta_i} +- stderr_i * t( N - P, 0.05/2)$

where stderr_i is the standard error of the i^th parameter $\hat{\beta_i}$ and t(N - P, 0.05/2) is a t statistic with N - P degrees of freedom, N is the number of observations, and P is the number of parameters. The confidence intervals are only asymptotically valid.

Model Confidence Intervals

Model confidence intervals are output when an OUT= data set is specified and one or more of the options L95M=, L95=, U95M=, or U95= is specified. The values of these terms are

$H &=& w_i x_i(X^'{WX})^{-1} x_i^' \L95M &=& f( {\beta}, z_i) - \sqrt{MSE * H} * ... ....95/2) \U95 &=& f( {\beta}, z_i ) + \sqrt{MSE (H + 1/w_i)} * t( N - P, 0.95/2) \$

where $X=\partial{f} / \partial {\beta}$ and x_i is the ith row of X. These results are derived for linear systems. The intervals are approximate for nonlinear models.

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