Statistics is important as it allows for different analyses to occur within the field of GIS as it explores, summarizes and illustrates relationships that may exist within datasets. One of the forms of regressions that was touched upon was Ordinary Least Squares. Ordinary Least Squares (OLS) is a simple regression model which assumes a linear relationship between the dependent variable(s) and the independent variable(s). OLS estimates what impact unknown parameters have an attempts to minimize the differences between observed and predicted results. Ordinary Least squares regression applies the same formula to an entire study space. If the relationship between the degree of influence the independent variables influence the dependant variable, then the regression equation will not accurately estimate the relationship in all areas.
However, this gap in research tools is what required the creation of GWR analysis. The general idea behind GWR is that relationships between variables are subject to spatial non-stationarity, meaning that the relationship is not constant over space. A model exploring these relationships must alter over space to reflect the spatial variation in the structure of the data. A regression equation is formed for each point at those surrounding it, creating a subset of data for each point that weights the importance of those closest to the centre. Understanding spatial variations in relationships between dependent and independent variables within a space is critical to many different types of studies, making it a very useful and adaptable model. Many scholars utilize both OLS and GWR to compare utility of both models. When performing regression analyses in the future, I will always consider using both to investigate the spatial stationarity of the relationships I’m examining- geography always has an impact!