For my capstone I intend to look at the mathematics behind regression analysis using panel data, or panel data modeling. A panel of data consists of two components: a cross-section and a time-series. For instance, the data I am using consists of individual observations for each of the 58 counties of California over a span of 8 years (2000-2007). This means that each variable in the regression has 464 (58 \cdot 8) observations. An advantage of this approach is the ability to account for variability over time as well as across the cross-section. Also, it allows for analysis of data with a limited number of observations over time (provided there are substantial cross-sectional observations) or a limited number of observations over the cross-section (provided there are sufficient time-series observations).

The general form of a panel data model is y_{it} = \alpha_i + \beta'x_{it} + \epsilon_{it}. In the model, i represents the cross-sectional units, t represents the time-series units, y represents the dependent variable, x represents the independent variables, \alpha represents the individual effects coefficients, \beta' represents the set of coefficients for the independent variables, and \epsilon represents the error terms. This is just the general form of the panel data model. The specific variations of the model that I will be looking at will be discussed in a later blog post.