# Validation of a model w/ new observations where the IVs are computed variables

I need to validate a linear regression model which was developed as follows -

1. There were 90 observations at the time of development
2. Each observation has variables $z_1$ and $z_2$ associated with where $z_1$, $z_2$ are non-negative integers such that $z_1 < z_2$
3. The dependent variable y is defined as: $y = \ln((z_1+0.5) / (z_2+0.5))$ where $\ln$ is the natural logarithm (the 0.5 is added mainly to deal with cases where $z_1 = 0$)
4. There are two independent variables $x_1$ and $x_2$; however, they were not entered directly into the regression when estimating the parameters - what was done was to regress $y$ against $x_1$ to obtain a linear equation and the output of this equation goes as input into the model (same for $x_2$)
5. If we denote the linear equations above by $l_1$ and $l_2$, then the parameter estimates obtained by regressing $y$ against $l_1(x_1$) and $l_2(x_2)$ - both of them were significant at the 99.99% level

Now I have additional 16 observations with observed values of $z_1$, $z_2$, $x_1$ and $x_2$. I need to test whether the model still works.

One easy test I can think of is to "score" the new observations based on the regression equation obtained in item 5 above, and then check the observed values of $y$ (can be defined as we have $z_1$ and $z_2$) against the predicted value of $y$.

My question is - are there any additional tests I can do to prove or disprove that the model works?

-