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NAME: Grid and Theme Regression 3.1e Aka: grid_regression.avx Last modified: August 29, 2006 TOPICS: Regression, R-Square, Slope, Scatterplot, ANOVA, SLR, Grid, P-value, Statistics, Distributions, t, F, logistic, normal, skewness, kurtosis, binomial, probability, critical, Poisson, chi-square, Model, Sequential Sums of Squares, Parameter AUTHOR: Jeff Jenness Wildlife Biologist, GIS Analyst Jenness Enterprises 3020 N. Schevene Blvd. Flagstaff, AZ 86004 USA jeffj@jennessent.com DESCRIPTION: This extension allows you to conduct Simple and Multiple Linear Regression analyses for both tabular and grid data. Regression can be conducted with fields in a table or between two grids. This extension also gives you the ability to calculate a wider range of summary statistical data than the basic set provided by ESRI, and the power to generate probability values and critical values from a wide range of statistical distributions. ** Simple and Multiple Linear Regression on Themes and Tables: This function uses Least Squares methods to calculate the linear relationship between an one or more independent Predictor variables and a dependent Response variable. Predictor and response values are drawn from fields in an ArcView table or a point/line/polygon theme feature attribute table. ** Simple and Multiple Linear Regression on Grids: This function calculates the linear relationship between one or more predictor grids and a response grid, again using Least Squares methods. ** Summary Statistics: From any numeric field in a table, this function will calculate the Mean, Standard Error of the Mean, Confidence Intervals, Minimum, 1st Quartile, Median, 3rd Quartile, Maximum, Variance, Standard Deviation, Average Absolute Deviation, Skewness (normal and Fisher’s G1), Kurtosis (normal and Fisher’s G2), Number of Records, Number of Null Values, and Total Sum. ** Probability Calculators: This function will allow you to calculate the probability, cumulative probability and inverse probability (i.e. given a cumulative probability, calculate the corresponding critical value) of a wide range of statistical distributions, including the Beta, Binomial, Cauchy, Chi-Square, Exponential, F, Logistic, LogNormal, Normal, Poisson, Student’s T and Weibull distributions. This function is available as a general calculator that remains open until you are finished with it, or as a Table tool that performs the calculations on all selected records in a table. NOTE: This extension was developed for the Inland Water Resources and Aquaculture Service (FIRI) of the United Nations Food and Agriculture Organization (FAO), for use in a training program to teach managers how to utilize GIS technology when managing fisheries. See Geographic Information Systems in fisheries management and planning. Technical manual, by G. de Graaf, F.J.B. Marttin, J. Aguilar-Manjarrez & J. Jenness. FAO Fisheries Technical Paper No. 449. Rome. 162p. Certain tools (esp. the Field Statistics and the histogram) were originally developed by the author for the University of Arizona’s Saguaro project (see http://saguaro.geo.arizona.edu/) and are included here with their permission. The Theme and Table Regression tools were originally developed for the FAO-FIRI African Water Resource Database project, and portions of this manual are adapted from the documentation for that project. The author gratefully acknowledges the assistance of Joe Dooley of Spatial Data Services & Mapping (Namibia), and José Aguilar-Manjarrez and Claudia Riva of FAO for their assistance in writing and editing that manual. The Statistical Probability tools are almost identical to those in the author’s Statistics and Probability Tools extension (see http://www.jennessent.com/arcview/stats_dist.htm) and are included because they enhance and complement the regression functions. The manual for that extension has also been adapted into this manual. REQUIRES: Spatial Analyst This extension also requires that the file "avdlog.dll" be present in the ArcView/BIN32 directory (or $AVBIN/avdlog.dll) and that the Dialog Designer extension be located in your ArcView/ext32 directory, which they usually are if you're running AV 3.1 or better. The Dialog Designer doesn't have to be loaded; it just has to be available. If you are running AV 3.0a, you can download the appropriate files for free from ESRI at: http://www.esri.com/software/arcview/extensions/dialog/index.html REVISIONS: Version 2.0 (January 22, 2004) adds tools for Theme and Table regression, plus incorporates the probability tools. Version 2.1 (May 16, 2004) repairs a bug that, in some circumstances, incorrectly calculated P-values and R-Squared values when there were null values in the dataset. Version 3.0 (August 13, 2005) adds functions to build custom models and conduct multiple regression analyses. Version 3.1 (September 8, 2005) • Corrects a bug that produced an error message stating that “Assertion ‘Positive buffer size’ failed. • Corrects a bug triggered by applying an inverse transformation to a predictor grid. • Modifies the Field Statistics tools so that you can generate statistics on multiple subsets of your data, based on one or more category fields. • Makes several minor formatting changes to the regression report. • Adds tools to the regression and scatterplot GUI allowing you to describe your model and to predict new observations using that model. • Adds tools to the scatterplot GUI allowing you to modify and enhance the graphic attributes of the plot. Version 3.1a (September 22, 2005) • Again corrects a bug that produced an error message stating that “Assertion ‘Positive buffer size’ failed. This error appears to only affect ArcView 3.2a and earlier installations. Version 3.1b (October 12, 2005) • Corrects a bug which may say either “Variable theLinkText has not been initialized” or “Variable theConfBandTheme has not been initialized”, and which was related to generating a scatterplot without generating confidence bands. • Corrects an issue related to Grid-based regression scatterplots, in which the scatterplot point X-coordinates were close, but not exactly equal to, the predictor values in the point attribute table. • Corrects another issue related to Grid-based regression scatterplots in which the analysis was constrained within a polygon, in which the X- and Y-scales were incorrect. Version 3.1c (February 18, 2006) • Corrects a bug which appears to occur only on Asian or Chinese installations of ArcView. The problem was that I used some unusual characters in the Avenue code, which caused ArcView to crash when the extension was loaded on a Chinese computer. Version 3.1e (August 29, 2006) •Corrects a bug which appears when you conduct grid regression and do not choose to calculate confidence bands or intervals, producing a message stating that ArcView cannot convert a string to a number. •Added functions to check the extension scripts. These functions are added as menu items in the View, Table and Project “Help” menus. Recommended Citation Format: For those who wish to cite this extension, the author recommends something similar to: Jenness, Jeff. 2006. Grid and Theme Regression 3.1e (grid_regression.avx) extension for ArcView 3.x. Jenness Enterprises. Available at: http://www.jennessent.com/arcview/regression.htm. Please let me know if you cite this extension in a publication (jeffj@jennessent.com). I will update the citation list to include any publications that I am told about. ----------------------------------------------------------------------------- General Instructions: 1) Begin by placing the "grid_regression.avx" file into the ArcView extensions directory (../../Av_gis30/Arcview/ext32/). 2) After starting ArcView, load the extension by clicking on File --> Extensions… , scrolling down through the list of available extensions, and then cli