Confidence Interval for Parameter of Nonlinear Regression

Definition

Suppose a Nonlinear Regression Model $Y_i=f({\mathbf{X}}_i,\mathbf{\theta })+{ϵ}_i,i=1,2,\dots ,n$ The $100(1-\alpha )\%$ confidence interval for ${\theta }_j$ is obtained as ${\hat{\theta }}_j\pm t_{\alpha /2}(n-p)SE({\hat{\theta }}_j)$ where $SE({\hat{\theta }}_j)$ is the Standard Error for Parameter of Nonlinear Regression ${\theta }_j$, and $p-1$ is the number of explanatory variables.