Linear regression is used as follows:

```
lm(Continuous1 ~ Factor_3Level * Factor_2Level, data = Data1)

```

What are the problems following this up with this:

```
glm(Factor_2Level ~ Continuous1 + Factor_3Level, data = Data1, family = "binomial")

```

The variable names describe the data types. `Factor_3Level` and `Factor_2Level` are independent. The results from `lm()` are that both factors are significant, the interaction term is not significant ($p=.23$), and the R-squared is $0.34$.

`Continous1` was measured under test conditions, where each combination of the levels of the two factors (six possibilities) was tested 25 times. (These two factors were physically altered for the test.) The assumptions of linear regression are satisfied. `Continous1` does not "exist" without the two factors having values. It is assumed there are multiple unknown environmental factors which also affect `Continuous1` (which are difficult to identify and/or measure).

I think independence is violated by using logistic regression this way. As `Factor_2Level` is tied to the conditions of the original test. The regression will probably be significant, but I don't think the r-squared will be accurate. Is that correct? Is there a different reason a test like this should not be done in reverse? What is the name of the related principal? In reverse, the independent variables can't be causing the dependent variable, rather the model predicts what state the dependent variable is in.

Insofar as a concrete example is required, consider the following. The behavior of animal K1 in a wildlife park is being measured, such as pacing/hour (times around the perimeter). The manipulated variables are the presence of a neighboring animal, V2, in a certain extended area, which can be selected for with a gate (and waiting briefly), and the selection can be done on a rainy day, sunny day, or cloudy day. If the park officials don't know whether V2 is present in the neighboring area, can the pacing rate of K1, given that it's sunny (the most significant factors from the earlier multiple regression test study) give them a good idea?

**This question is about the validity of manipulating or selecting for an environmental variable, and then turning around and trying to predict that variable. This question is not about the example.**