As a social scientist, one of my most widely applicable analysis tools is statistical regression. Statistical regression compares the values of several variables across data points in order to estimate a relationship between those variables (for an example of my work using statistical regression, see my economics thesis). On a deeper level, regression analysis is a tool which deconstructs a dependent variable as a function of multiple independent variables. Regression analysis can therefore be seen as a means to understand a broad process through the functioning of constituent processes.
Statistical regression, in the traditional sense, is an eminently quantitative process. I, however, will attempt to extend the functionality of regression to analyze trends which are not so easily quantifiable. In doing so, I will attempt to define the shape of my example cities through the functioning of constituent processes which form them. In the absence of a mathematical framework to guide this analysis, I will instead adopt a spatial and temporal framework, where I will attempt to plot trends in the forces which have shaped these cities through the physical layout of the cities over time.
In statistical regression, it is essential to account for as many variables as possible that could be relevant to the relationship being analyzed, as omitting important variables has the potential to bias the significance of other results. Nevertheless, there is usually one variable of interest whose relationship with the dependent variable motivates the analysis. As I plot these relationships, I will focus on the spatial and temporal distribution of urban tree canopy as the variable whose reciprocal relationship with city shape I am most interested in investigating. By using the urban forest as a lens with which to view urban development, I will generate a unique perspective on the shape of cities throughout space and time.
Much as the goal of statistical regression is to estimate the relationship between variables through comparing multiple data points, I will hopefully be able to use the cities which I study to compare the reciprocal influence of tree canopy on city development in general. This has important policy implications—if I can establish a generalized relationship between the urban forest and urban development, it can inform city policy surrounding urban trees going forward.