GIS5935 Lab 12: Spatial Regression in ArcGIS

Spatial regression using tools in ArcGIS was the topic for this week. The two tools used were Ordinary Least Squares and Geographically weighted regression. The second part of the lab consisted of carrying out a regression analysis using both tools and comparing the results. Two shapefiles were used as the data for this, one consisting of the locations of all crimes reported for a specific county in one year, and the other consisting census tracts for the county with different demographic variables. From there, one crime was selected on which to perform the analysis, then 3 variables were also selected. Then the crime rate for each census tract was determined to be used at the dependent variable

First, the OLS tool was ran on the selected variables. Then the GWR tool was ran on the same variables. For the GWR, I tried using both adaptive and fixed kernel types, then ran the Global Moran's I tool on both results to see which one resulted in a better performing model. Using the adaptive kernel type seemed to work better. From there I read through the statistics of all of the results to compare and see how the model improved.

The GWR improved on the OLS a good bit. The adjusted R-squared improved from about 35% with the OLS to about 40% with the GWR. The AIC was also lowered from 1916 to 1909.

GIS 5935 Lab 11: Regression in ArcGIS

This week's assignment consisted of using tools in ArcGIS to perform a regression analysis. Previously, similar assessments to these had been carried out in Excel, but ArcGIS takes it a couple steps further. While in Excel you can determine all of the necessary elements for a regression analysis such as correlation, adjusted R-squared, P-value and everything else for all of your variables, ArcGIS helps to determine the performance of the analysis and which variables should be included or excluded.

The performance of the model is determined using the Ordinary Least Squares tool, which generates a regression analysis using dependent and independent variables from a feature class. The results of this tool can be viewed to help to determine which variables work better, and which ones could be biased or redundant and should possibly be excluded. One way this tool works very well is how it analyzes the residuals and determines spatial autocorrelation and whether explanatory variables are missing. If there is an issue, it advises to use the Spatial Autocorrelation tool on the residuals, which tells whether the residuals are randomly distributed or clustered. This is an especially useful tool for improving models because it's a simple, straightforward method to determine the distribution of each variable and can help pinpoint issues and potential problems with the regression analysis.

GIS 5935 Lab 10: Bivariate Regression

For this assignment, I used a regression analysis to determine the missing rainfall data for Station A between 1931 and 1949. In order to accomplish this, I first had to determine the slope and the intercept coefficient for the relationship between the two sets of available data for the variables. Then I multiplied the the slope with the value of Station B for each year, and added the intercept coefficient to determine the rainfall that was missing for each year for Station A. While something like rainfall is impossible to precisely predict, the statistics used here could be very useful in similar scenarios. It's not very different from recent previous assignments, like surface interpolation. It may not be precise, but it gives you a good idea of what the reality probably is or was.

The results can be seen below:

Year	Station B	Station A
1931	1005.84	1013.45
1932	1148.08	1133.81	Slope:	0.846171
1933	691.39	747.37	Intercept:	162.3421
1934	1328.25	1286.27
1935	1042.42	1044.40
1936	1502.41	1433.64
1937	1027.18	1031.51
1938	995.93	1005.07
1939	1323.59	1282.33
1940	946.19	962.98
1941	989.58	999.70
1942	1124.60	1113.94
1943	955.04	970.47
1944	1215.64	1190.98
1945	1418.22	1362.40
1946	1323.34	1282.11
1947	1391.75	1340.00
1948	1338.97	1295.34
1949	1204.47	1181.53

GIS5935 Lab 8: Surface Interpolation

In the first part of this lab, I compared the results of using Spline and IDW interpolation methods to create a Digital Elevation Model. This was done by using elevation data points as the input for each technique, then running each tool with the same parameters and comparing the results.

Overall, the difference in the results of the two interpolation methods wasn't extremely substantial, but there were some notable differences. Throughout a majority of the data, the difference in elevation between the two datasets is anywhere from 2 to 12 feet. But there are also several places where the difference is 30 to 40 feet. The areas with these larger differences, however, are mostly the areas without elevation data points, which shows how each interpolation process will give slightly different results. 

Below is map layout that shows the areas of difference in the two methods:

GIS5935: DEM Accuracy

The purpose of this lab was to determine the accuracy of a Digital Elevation Model. In order to do this, first, "true" test points had to be acquired. For this project, this consisted of field data collected using high-accuracy survey methods. The test points were essentially combined with the DEM using the Extract Values to Points tool in ArcGIS. Then, the elevation of the DEM at each point was compared to the true elevation. Using an Excel spreadsheet, the DEM's elevation was subtracted from the field data to find the difference, and this was used to find statistics for the Room Mean Square Error, the 95th percentile, and the 68th percentile. The results can be observed and compared to each Land Cover classification to find trends and consistencies within each type and help to determine any bias. Below are the results for this particular analysis:

Land Cover:                         A                             B                             C

Sample Size:                       48                           55                           45          

Accuracy 68^th:                    0.001                     0.023                     0.049                               

Accuracy 95^th:                    0.027                     0.194                     0.233

RMSE:                                   0.105                     0.181                     0.246    

                                              

Land Cover:                        D                             E                              Combined

Sample Size:                       98                           41                           287

Accuracy 68^th:                    0.051                     0.035                     0.029

Accuracy 95^th:                    0.214                     0.147                     0.185

RMSE:                                   0.394                     0.199                     0.276