There are three primary reasons you might want to use regression analysis: If you find that involvement is the key factor, you may need to increase equipment and the number of officers dispatched. If you find that response time is the key factor, you might need to build more fire stations. Modeling property loss from fire as a function of variables such as degree of fire department involvement, response time, or property values.Modeling traffic accidents as a function of speed, road conditions, weather, and so forth, to inform policy aimed at decreasing accidents.Modeling high school retention rates to better understand the factors that help keep kids in school.Regression analysis can be used for a large variety of applications: Regression analyses, on the other hand, make a stronger claim: they attempt to demonstrate the degree to which one or more variables potentially promote positive or negative change in another variable. The graphic below depicts both positive and negative relationships, as well as the case where there is no relationship between two variables: Scatterplots: a positive relationship, a negative relationship, and a case where two variables are unrelatedĬorrelation analyses, and their associated graphics depicted above test the strength of the relationship between two variables. You can also express this negative relationship by stating that the number of crimes increases as the number of patrolling officers decreases. Conversely, if you find that the number of crimes goes down as the number of police officers patrolling an area goes up, the relationship is said to be negative. Another way to express this positive relationship is to say that search and rescue events decrease as daytime temperatures decrease. If you find that the number of search and rescue events increases when daytime temperatures rise, the relationship is said to be positive there is a positive correlation. Linear relationships are either positive or negative. When used properly, these methods provide powerful and reliable statistics for examining and estimating linear relationships. GWR provides a local model of the variable or process you are trying to understand/predict by fitting a regression equation to every feature in the dataset. Geographically weighted regression (GWR) is one of several spatial regression techniques, increasingly used in geography and other disciplines.
It provides a global model of the variable or process you are trying to understand or predict (early death/rainfall) it creates a single regression equation to represent that process. It is also the proper starting point for all spatial regression analyses. OLS is the best known of all regression techniques. You might also use regression to predict rainfall or air quality in cases where interpolation is insufficient due to a scarcity of monitoring stations (for example, rain gauges are often lacking along mountain ridges and in valleys). Modeling the factors that contribute to college graduation rates, for example, enables you to make predictions about upcoming workforce skills and resources. By modeling spatial relationships, however, regression analysis can also be used for prediction. You may want to understand why people are persistently dying young in certain regions of the country or what factors contribute to higher than expected rates of diabetes. Regression analysis allows you to model, examine, and explore spatial relationships and can help explain the factors behind observed spatial patterns. These tools include Ordinary Least Squares (OLS) regression and Geographically Weighted Regression. Tools in the Modeling Spatial Relationships toolset help you answer this second set of why questions. What are the factors contributing to higher than expected traffic accidents? Are there policy implications or mitigating actions that might reduce traffic accidents across the city and/or in particular high accident areas?.Can we model the characteristics of places that experience a lot of crime, 911 calls, or fire events to help reduce these incidents?.Why are there places in the United States where people persistently die young? What might be causing this?.Where do we find a higher than expected proportion of traffic accidents in a city?Īnalysis of 911 emergency call data showing call hot spots (red), call cold spots (blue), and locations of the fire/police units responsible for responding (green crosses)Įach of the questions above asks "where?" The next logical question for the types of analyses above involves "why?".Where are the hot spots for crime, 911 emergency calls (see graphic below), or fires?.Are there places in the United States where people are persistently dying young?.Using the Hot Spot Analysis tool, for example, you can ask questions like these: The Spatial Statistics toolbox provides effective tools for quantifying spatial patterns.