Can I use calculated data for regression analysis.
case 1: first run OLS $y = \alpha+\beta x$, and get $\hat\beta$, then calculate $z = h^\hat\beta$, at last run $m = \gamma + \mu z$.
case 2: follow the same settings as case 1, run $z = \zeta + \rho p$.
case 3: use matlab solve equation $k_i = \sum_j d_{ij} k_j$ for $k_i$, then run $w = \theta + \pi k$.
where $\alpha$,$\beta$,$\gamma$,$\mu$,$\zeta$,$\rho$,$\theta$,and $\pi$are coefficients, the other letters denote the variables.I have the variables y,x,h,m,p,$d_{ij}$,w. All the relationships between variables are from the models.
They are independent cases that I ran into.
I am going to estimate the coefficients $\mu$,$\rho$,and $\pi$.