GIS5935 - Lab 11 - Multivariate Regression, Diagnostics and Regression in ArcGIS

In this week's lab we continued our lesson on regression analysis.  In Part A we performed multivariate regression analyses using the Data Analysis Correlation and Regression Tools in Excel.  In our multivariate regression we had a singular dependent variable and multiple independent variables.

We used the analysis results to predict a selling price for a house with 4 bedrooms and a lot size of 5100.  Next we added data for an outlier feature and reran the analyses and re-predicted a selling price.

In Part B we continued using Excel to create a correlation coefficient matrix to help determine which variables to use in a multivariate regression analysis of cirrhosis data.  Comparing Adjusted R Squared values of different variable combinations helped determine the best fit model.

In Part C we again used Excel to perform a multivariate regression using the provided variable combination to analyze 911 call data from Portland, Oregon.  Using a provided shapefile created from the same 911 call data we used the Spatial Statistics Tool, Ordinary Least Squares (OLS) in ArcGIS to analyze both a one independent variable (bivariate) model and a three independent variable (multivariate) model.  Using the output results from these tools enabled us to perform the six checks to determine if we had a properly specified and a statistically sound model.

In Part D we used the Exploratory Regression tool to find the OLS model that best explains/predicts the dependent variable.  The exploratory regression report summarizes the statistical data of the different independent/explanatory variables as well as combinations of these variables.   The diagnostic data and checks that the exploratory regression report provides can be used to select combinations of explanatory variables that would best model/predict the dependent variable.  Comparing Adjusted R Squared values and AIC values of each model combination as well as their coefficients/slopes, p-values, and VIF values can aid in selecting or creating models that are the best fit for predicting/explaining the dependent variable.

Below I have provided three snapshots of the spatial correlation of the residual data of three different models for the 911 call data analysis.  "Residuals are the unexplained portion of the dependent variable."

This first snapshot is of the residuals from a bivariate model using Population values only to predict the number of 911 calls.  You can see there is clustering of data which is an indication that more variables are needed.

OLS Residual Output Results - Bivariate Model with "Pop" as the only independent/explanatory variable

The 2nd snapshot is of the residuals from a multivariate model of the same data but using three independent variables in the regression analysis (Pop, LowEduc, and Dst2UrbCen).  The multivariate regression analysis explained more of the variability in the dependent variable but there was still some clustering,

OLS Residual Output Results - Multivariate Model with "Pop", "LowEduc", and "Dst2UrbCtr" as the three independent/explanatory variables used in the model

The 3rd snapshot is of the residuals from the multivariate model selected from the Exploratory Regression tool results which used four independent variables (Pop, Jobs, LowEduc, and Dst2UrbCen).  This model was the best fit for the 911 Call Data and would more accurately predict the number of 911 calls from a particular census tract.

OLS Residual Output Results - Multivariate Model with "Pop", "Jobs", "LowEduc", and "Dst2UrbCtr" as the four independent/explanatory variables used in the model based on Exploratory Regression results

GIS5935 - Lab 10 - Introductory Statistics, Correlation and Bivariate Regression

This weeks lab had us focus on reviewing fundamental statistics and how to perform linear regression analysis.  The lab was divided into three parts where we performed various statistical analysis tasks on provided data sets.  In part C of the assignment we determined the relationship between the annual precipitation amounts collected at two different stations over a series of years (1931-2004).  Initially, we are provided with precipitation amounts for both stations from 1950-2004.  Using this data we are able to perform linear regression analysis to determine the slope and intercept.  For years 1931-1949 we only are provided with precipitation amounts for Station B.  Using the information gathered from the linear regression analysis we are able to predict the precipitation amounts for Station A for the years 1931-2004.

Bivariate Linear Regression To Predict Annual Rainfall Amounts At Station A From Values Obtained At Station B

Using bivariate linear regression analysis to predict the value of one variable from the value of another, assumes that all data is continuous and normally distributed.  "The relationship is assumed to be linear and for now only uses two variables and does not consider any spatial effects."

GIS5935 - Lab 9 - Accuracy of DEMs

In this lab we learned how to perform accuracy assessments of Digital Elevation Models (DEMs).  In our assignment we used elevation field data gathered via survey methods as reference points to compare to elevation values from a LIDAR raster at the same location.   Calculating the error or difference between the two elevation values enabled us to perform statistical calculations to determine the overall accuracy of the LIDAR DEM.  Our field data also included different landcover attributes.  We could refine our DEM accuracy assessment by landcover type.  In our assignment I found Bare Earth, Low Grass to be the most accurate landcover type in the LIDAR DEM.  It had the lowest RMSE while Fully Forested was the most inaccurate landcover type.  Using the mean error value (-.00558) I was able to conclude that the LIDAR data showed little bias.  

Accuracy              Bare Earth,     High Grass         Brush Land  Fully             Urban  Combined

Metric                  Low Grass     Weeds, Crops     Low Trees    Forested                                     

Sample Size         48                  55                       45                 98                 41        287          

Accuracy 68th      .010               .023                    .048              .049              .036     .029

Accuracy 95th      .027               .193                    .233              .215              .147     .185

RMSE                  .105               .181                    .246              .394              .200     .276

Field data elevation points via high-accuracy survey methods displayed on high resolution bare earth DEM obtained through LIDAR in North Carolina counties (Wake, Nash, Edgecombe, Halifax, Franklin)

GIS5935 - Lab 8 - Surface Interpolation

Hello,

In the 2nd part of this lab we used different surface interpolation methods to estimate water quality in Tampa Bay.  We were provided data from 41 observation points where water quality samples were taken.  It is important to understand your data; where is it sparse or dense, where are there irregularities, and redundancies and use this knowledge to explain trends.  You may need to remove outliers and normalize data prior to applying an interpolation method.

To estimate the water quality of Tampa Bay we compared four different techniques, Thiessen, IDW (Inverse Distance Weighted), Spline Regularized and Spline Tension.

The Thiessen interpolation method provided more information about the data you are working with.  Any location within in a Thiessen polygon is “closer to its associated point than to any other point input feature.”  Using Thiessen interpolation I think is similar to creating a Voronoi Map in Geostatistical Analyst.  The disadvantage to using this technique is that when you assign each location within the polygon the same value as the nearest point, you could over generalize your data and not account for differences despite them being closely located together.   

The IDW method estimates cell values by averaging the values of the sample data in the neighborhood of each cell.  The closer a point is to the center of the cell being estimated the more influence or weight it has in the averaging calculation.

There are two Spline methods: Regularized and Tension.  The regularized method creates a smooth, gradually changing surface but may have values that lie outside the range of the sample/input data.  The tension method controls the stiffness of the surface based on the input data but creates a less smooth surface with values constrained by the range of the sample/input data.

I've chosen to display my Spline with Tension Interpolation of the water quality in Tampa Bay as I felt it was the best method to estimate water quality based on the data we were provided via the 41 sample locations.

Spline with Tension Interpolation Method

GIS 5395 - Lab 7 - TINs and DEMs

This week's lab had us learn about the differences between TINs (Triangular Irregular Networks) and DEMs (Digital Elevation Models).  A TIN is a "vector version of a 3D surface).  DEMs are rasters that describe elevation.  We used both ArcMap and ArcScene to view and modify TINs and DEMs in the various lab exercises.  We learned how to modify vertical exaggeration, use lighting or illumination to display the image more clearly.  In ArcMap and ArcScene you can alter the symbology of a TIN to display the slope, aspect, nodes, and elevation of the TIN.  A DEM raster would require us to use tools to create a slope and aspect rasters.  We also compared the contour lines of DEMs versus TINs for a particular study area.  Depending on your application a TIN may be more useful than a DEM if your study area is narrower and more detail is needed.  Below is a screen capture of a TIN with nodes, edges, and contour lines.

TIN Symbology

I enjoyed learning how to create, edit, and change the symbology of a TIN.  I have a better understanding of how TINs and DEMs are different.

GIS 5935 - Lab 6 - Location-Allocation Modeling

This weeks lab was our final assignment under the Networks topic.  I really have enjoyed this topic's assignments and have a much better appreciation for these analyses and their broad uses.  As with previous assignments we familiarized ourselves with the topic by completing Exercise 9 of the Network Analyst Tutorial in Part A of the assignment.  Part B had us apply this newly acquired knowledge to use a location-allocation analysis to optimize the reassignment of market areas to distribution centers.  First we used the Network Analyst location-allocation model to determine which distribution center best served each customer.

Location-Allocation Network Analysis - Which Distribution Center Best Serves Each Customer?

Inspecting the above map we could see that a number of customers would be better served by distribution centers that did not fall in their market area grouping.  In order to further analyze which market centers would be better served by a different distribution center we performed a series of table manipulations by using spatial and table joins and using the Summary Statistics tool as well as the Summarize menu option in the opened Attribute Table.  These statistical calculations enabled us to determine which distribution center was responsible for the majority of customers in each market area.  Using this criteria we reassigned 13 market areas to different distribution centers.  There were some weaknesses in this analysis.  Some market areas could be served by two distribution centers because they both served an equal number of customers.  Another issue was at least one market area was bifurcated and the reassignment didn't make sense for the entire market area but rather a portion of it.  Ideally, this market should have been separated into two distinct market areas.

Location-Allocation Analysis of Market Area Assignments to Distribution Centers

This was probably my most favorite lab assignment of this class thus far.  While the table manipulations were cumbersome and confusing at first, the overall capabilities of this network analysis method were impressive.