linear model:

`$$\begin{aligned}
Y_i
&amp;= f(x_{0i}, x_{1i}, ..., x_{Ni}) \\
&amp;= \beta_0 x_{0i} + \beta_1 x_{1i} + \beta_2 x_{2i} + ... + \varepsilon_i
\end{aligned}$$`

All 3 goals are trying to model the DGP, but with different emphases and interpretations.

&lt;br&gt;

**Three key differences** among the goals:
1. Focus: outcome vs. coefficients.
2. Whether selection bias matters.
3. Interpretation.


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# Diff 1. Focus: outcome vs. coefficients.

`$$\color{#6A5ACD}{Y_i} = f(x_{0i}, x_{1i}, ..., x