More complex than simple and multiple regressions? I am currently in an Econometrics class that requires us to write a research paper that showcases our skills in regression/ modeling.  What is slightly more complex than simple and multiple regressions that I may be able to learn and utilize in my research project?  I realize that the model depends on the research question, but I'd like to learn different types of modeling anyhow.

Thanks.
Welcome to the wonderful world of econometrics! Most introductory econometrics courses will extend Ordinary Least Squares (OLS) by considering binary outcomes models such as the logit and probit.

Whilst OLS is typically restricted to modelling continuous outcomes bound between $-\infty$ and $\infty$, in research one will often come across data where this is not the case. The most elementary extension is the binary (yes/no) outcome data.

This data takes the form of a yes/no (coded 1/0). Clearly, OLS runs into several problems. First and foremost (for your purposes) is the fact that you can predict outcomes outside of the range $[0,1]$. The simplest solution: logistic regression.

Logistic regression estimates the probability that $y=1$ conditional on your explanatory variables. It does this creating a mapping of your regression equation $\beta_0 + \beta_1 x$ on to the space $[0,1]$ by considering:
$$ \ln \left( \frac{P(y=1)}{1-P(y=1)} \right) = \beta_0 + \beta_1x $$
Depending on what data you can find (and what software you have available - for example EViews, R, Stata and SPSS all have built in routines for logistic regression) this might be an interesting way to proceed.