Lab 11: Regression using a GIS

In this lab I used the lessons in regression we learned last week and used them in ArcMap. This allowed me to familiarize myself with how ArcMap processes and reports regressions. The performance of a model can be evaluated using the six Ordinary Least Squares (OLS) checks. They are as follows:

1. Are the explanatory variables helping your model? This can be checked by examining the p-value of the variables and confirming that they are statistically significant.
2. Are the relationship what you expected? This is checked by looking at the signs of the coefficients and making sure they make sense. If a variable has a negative coefficient when you expect it to be positive something is wrong with your model.
3.  Are any of the explanatory variables redundant? This is easily checked by examining the Variance Inflation Factors (VIF). If the VIF shows that any of the variables are redundant you may have to remove one.
4. Is the model biased? The Jarque-Bera test looks for bias or skewed residuals. If it is significant you may have an issue with your model.
5. Do you have all key explanatory variables? If you run the Spatial Correlation (Global Moran's I) tool it will provide you with information about whether or not your residuals are clustered, dispersed, or random. If your distribution isn't random you may need more key variables in your model
6.  How well are you explaining your dependent variable? This is easily evaluated by looking at the adjusted r-squared value. The higher the number the bigger the percent of variation is explained by your model. If you are trying to compare this model to others you can also look at the Akaike's Information Criterion (AIC). The AIC means nothing by itself but it is useful to compare it to other models. The model with the lowest AIC is usually the better one.