Looking for help with interpreting my OLS models

Question

I have been busy building an explainatory regression model for a companies' social behavior. In the table below you find the variables, ordered by theme. The English to French variables are dummies, indicating the legal system a company has to comply with.

From these models, conclusions about what influences a companies' social behavior will be drawn. Since I'm a law student (with no statistics course in the curriculum) I've been looking at other scientific papers in which regression results are presented. I have some questions:

1. I present the coefficients and the significance levels. Many authors present the coefficients and the t-values, and indicate significance level with * (for 1%) and ** (for 5%). What does the t-value indicate / add to the information this table presents?
2. Papers regularly test 6 to 8 models. Why? I guess this is to test the robustness of the coefficients but am unsure. Also, is there a rule of thumb to see which models need testing. In other words: do the six models presented here cover model testing or do the results call for more models to be tested? And if so, which models?
3. About the conclusions: take, for instance, (under Culture), uncertainty avoidance. It's effect on company behavior is significant in models (A) to (D), but not in (E) and (F). What should I report? That uncertainty avoidance does of does not have an effect on social behavior?

Many questions, most of which basic probably. But I'm trying my best to get this right and any help is much appreciated :-) Also other comments regarding these models that are not covered in my questions, are welcome.

Answer 1

While agreeing with @gung 's comment above, it might be possible to point you to some general ideas, please bear in mind that these aren't complete answers. A good book will help.

1. The t-values are another effect size measure (like the coefficient) but they are on a standard scale, so that, according to some people you can compare them across variables, saying which is most important.

2. Model testing and selection is a huge area. Perhaps, in your field, it is typical to present 6 to 8 models, but it is by no means always done. My view is that model selection should be driven by substantive concerns and by the MAGIC criteria (see the link for what those are).

3. Don't confuse significance with importance and don't confuse either with what should be reported. My view is that you should report results that are interesting.

However, all three questions will elicit somewhat different views from different people.