Variograms.ppt.ppt

Variograms Brian Klinkenberg Geography To get there, we’ll consider Correlation Tobler’s first law of geography Spatial autocorrelation Three dimensions of scale Units of observation Regionalized variables Variograms Correlation What is correlation? What does it measure? [n] a statistical relation between two or more variables such that systematic changes in the value of one variable are accompanied by systematic changes in the other [n] a statistic representing how closely two variables co-vary; it can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation); what is the correlation between those two variables? [n] a reciprocal relation between two or more things [Source: /dictionary/correlation] Correlation Suppose we have two variables X and Y, with means XBAR and YBAR respectively and standard deviations SX and SY respectively. The correlation is computed as: The correlation coefficient, r, quantifies the direction and magnitude of correlation. Correlation Correlation What is variance? (Contrast with correlation) The correlation coefficient is the covariance divided by the standard deviations of the two variables (normalized): Tobler’s first law of geography Spatial autocorrelation Extending the concept of correlation by incorporating space. Note, however, that the concept of spatial autocorrelation is actually more related to that of variance than of correlation since we are examining the nature of the variability of a variable with itself through space. Spatial autocorrelation “Usually autocorrelation means correlation among the data from different time periods. Spatial autocorrelation means correlation among the data from locations. There could be many dimensions of spatial autocorrelation, unlike autocorrelation between periods.” [/od/economicsglossary/g/spatial.htm] Spatial autocorrelation “Is a term referring to the degree of relationship that exists between two or more spatial variables, such