Issue link: http://read.dmtmag.com/i/33025
that’s closest to the line of best fit, and it varies from 0 ≤ r2 ≤ 1. It’s most often used as a measure of how certain one can be in making predictions from the linear relationship (regression equation) among variables. It’s in the Relationships With that quickie stat review, now consider the left side of Figure 1 that calculates the correlation between elevation and slope maps discussed last month. The gridded maps provide an ideal format for identifying pairs of values for the analysis. In this case, the 625 Xelev and Yslope values form one large table that’s evalu- ated using the correlation equation shown. The spatially aggregated result is r = +0.432, suggesting a somewhat weak overall positive linear correlation between the two map surfaces. This translates to r2 = 0.187, which means that only 19 percent of the total variation in y can be explained by the linear relationship between Xelev and Yslope . The other 81 percent of the total variation in y remains unexplained, which suggests that the overall linear relationship is poor and doesn’t support useful regression predictions. The right side of Figure 1 uses a spatially disag- gregated approach that assesses spatially localized correlation. The technique uses a roving window that identifies the 81 value pairs of Xelev and Yslope within a five-cell reach, then evaluates the equation and assigns the computed r value to the window’s center position. The process is repeated for each of the 625 grid locations. For example, the spatially localized result at column 17, row 10 is r = +0.562, suggesting a fairly strong positive linear correlation between the two maps in this portion of the project area. This translates to r2 third of the total variation in y can be explained by the linear relationship between x and y. Spatial Specificity? Figure 2 depicts the geographic distributions of the spatially aggregated correlation (top) and the spatially localized correlation (bottom). The overall correlation statistic assumes that the r = +0.432 is uniformly distributed, thereby forming a flat plane. Spatially localized correlation, however, forms a continuous, quantitative map surface. The correlation surrounding column 17, row 10 is r = +0.562, but the northwest portion has significantly higher positive correlations (red, with a maximum of +0.971), and the central portion has strong negative correlations (green, with a minimum of -0.568). The overall correlation primarily occurs in the southeast- ern portion (brown)—not everywhere. The “bottom line” of spatial statistics is that = 0.316, which means that nearly a it provides spatial specificity for many traditional statistics as well as insight into spatial relationships and patterns that are lost in spatially aggregated nonspatial statistics. In this case, it suggests that the red and green areas have strong footholds for regression analysis, but the mapped data need to be segmented, and separate regression equations should be developed. Ideally, the segmentation can be based on existing geographic conditions identified through additional grid-based map analysis. This “numerical mindset of maps” is catapulting GIS beyond conventional mapping and traditional statistics, ahead of long-established spatially aggre- gated metrics—with the joint analysis of geographic and numeric distributions inherent in digital maps providing the springboard. Author’s Note: For more information, see the online book Beyond Mapping III at www.innovativegis.com, Topic 16, Characterizing Patterns and Relationships, and Topic 28, Spatial Data Mining in Geo-Business. M AY 2O11 / WWW . GEOPLA CE .C O M 11 Figure 2. Spatially aggregated correlation provides no spatial information (top), while spatially localized correlation “maps” the direction and strength of the mutual relationship between two map variables (bottom).