How to compare results from two regressions? We have performed two linear regressions (OLS), one with data from 2009 and one with data from 2014. All the variables are the same, both the dependent and the six independent variables. The sample sizes are however different!
We want to be able to compare the results from these two regressions. For instance, we want to test whether some of the independent variables have more significance in one year compared to the other. And also, just a general comparison of the two models: is the dependent variable more explained in one of them?
How can we do this? Are there any statistical tests? 
 A: It depends on what you understand for having more significance. Have you considered using all data and adding a factor (levels "2009" and "2014")? You could draw some conclusions based on the interaction coefficients significance.
A: To start with, and given that this is a school project, one simple approach would be to look at the $R^2$ of the two regressions. They tell you how much of the variation in the dependent variable is explained by your explanatory variables. If it differs a lot, you may be able to say that your explanatory variables explain more of the variation in one year than the other. Though note that the explanatory power of such a comparison is limited. 
As a second exercise, you can use a t-test to see if the coefficients are different from each other. You can either test for equality, or if you have reason to believe that the association between these variables strengthened or weakened, then you can use a one sided t-test. For the t-test, you can use  
$t = \frac{\beta^1_i-\beta_i^2 }{\sqrt{\sigma_i^2(\beta^1_i) + \sigma_i^2(\beta^2_i)} } $
where $\beta_i^j$ is the $i$-th coefficient in regression $j \in {1,2}$, and $\sigma_i^2(\beta_i^j)$ is the estimated variance of said coefficient.
The approach suggested by Victor is preferable, though. So, if you manage to execute the regression again, set it up with a dummy for one of the year, interacted with all variables.
