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Lab 3: Geographically-Weighted Regression
Regression analysis uses the tools in the Modeling Spatial Relationships toolsets to help us understand why certain spatial pattern occurred. Ordinary Least Squares (OLS) and Geographically Weighted Regressions (GWR) are two of the tools. By modeling, examining and exploring the spatial relationship of one phenomenon, these two tools can help evaluate relationships between two or more featured attributes to find and explain the factors behind this observed spatial patterns.
Ordinary Least Squares (OLS) is the proper starting point of all spatial regression analysis. It provides a global model of the variables or process you are trying to understand or predict. Global model means that a single regression equation is created to generate predictions by modeling the relationship between a dependent variable and a set of explanatory variables (independent variables). The regression equation generated by using this tool applies to the whole geographical region. OLS works the best when the spatial pattern is homogenous, meaning that all data satisfies the assumptions inherently required by this analysis.
GWR provides a local model of the variables or process for the phenomenon that you are trying to understand/ predict by fitting a regression equation to every feature in the dataset. In other words, no like OLS analysis that applies a single regression equation to all spatial locations, GWR constructs separate equations for each spatial location.
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The map shows whether gender places a role in affecting children’s social ability. Again, the social variation of fitness model is observed in this map. Low association between gender and social ability is marked as red, and high association is marked as green. Downtown Vancouver, Grandview Woodland, Arbutus Ridge, UBC, and Victoria Fairview districts have lower association, suggesting that gender does not play a role in determining children’s social skills. Whereas in Sunset, Riley Park Little Mountain, Southern Dunbar, and Shaughnessy district, we found that gender is a variable that explains social ability. Female students are more likely than male students to achieve higher social ability scores in these districts. R2 value shows that our prediction of Kingsway, Downtown and Sunset is accurate, but gender as an explanatory variable does not fit the model well, which implies that other variable might have a stronger contribution to the pattern of social skills across Vancouver.