# More comlex regression models: Terminology and Software

#### mmercker

##### Member
Hi,
I would like to couple two regression models and solve them simultaneously. That means: I have one regression equation:

$$\hat Y_i = \hat \alpha_0 + \hat \alpha_1 X_i$$ with
$$Y_i \sim N(\hat Y_i, \sigma_1^2)$$

and $$\hat Y_i$$ is again the predictor in a second regression model:

$$\hat Z_i = \hat \beta_0 + \hat \beta_1 \hat Y_i$$ with
$$Z_i \sim N(\hat Z_i, \sigma_2^2)$$

The idea is that I want to propagate the uncertainties connected with $$\hat Y_i$$ to the final confidence intervals for $$\hat Z_i$$.

Does somebody know how such "coupled models" are named? And are there packages in R to solve them, or do you know other statistical software for that?

Many thanks in advance for any help!