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Unformatted text preview: Spatial statistics and Generalized Least Squares Regression ESM 206C May 20, 2008 pH and NO3 in Norwegian lakes 50 100 150 200 250 300 350 4.5 5.0 5.5 6.0 6.5 NO3.1981 pH.1981 Call: lm(formula = pH.1981 ~ NO3.1981, data = lake) Residuals: Min 1Q Median 3Q Max 0.888624 0.410622 0.007402 0.386811 1.237405 Coefficients: Estimate Std. Error t value Pr(>t) (Intercept) 5.7130797 0.1218255 46.896 < 2e16 *** NO3.1981 0.0032446 0.0009186 3.532 0.00106 **  Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.5103 on 40 degrees of freedom Multiple RSquared: 0.2377, Adjusted Rsquared: 0.2187 Fstatistic: 12.47 on 1 and 40 DF, pvalue: 0.001056 pH of Norwegian Lakes 6 8 10 12 58 59 60 61 62 Longitude (degrees E) Latititude (degrees N) Questions about Norwegian lake data • Is there spatial autocorrelation in pH values? • How can we interpolate and smooth those values? • Is there a relationship between pH and NO 3 , taking into account spatial autocorrelations in both variables? Semivariogram • Semivariance is half the average squared difference between pairs of lakes a certain distance apart • Measures variance among sites as a function of distance • Also called empirical variogram 1 2 3 4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 distance semivariance Theoretical variogram 1 2 3 4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 distance semivariance 8 Theoretical variogram 1 2 3 4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 distance semivariance Nugget Sill Range Theoretical variogram Summary of the parameter estimation Estimation method: WLS (weighted least squares) Parameters of the spatial component: correlation function: gaussian (estimated) variance parameter sigmasq (partial sill) = 0.3175 (estimated) cor. fct. parameter phi (range parameter) = 0.7817 Parameter of the error component: (estimated) nugget = 0.0773 Minimised weighted sum of squares: 4.2704 Call: variofit(vario = pH.vg, ini.cov.pars = c(0.4, 1), cov.model = "gaussian") 1...
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This note was uploaded on 08/06/2008 for the course ESM 206 taught by Professor Kendall,berkley during the Spring '08 term at UCSB.
 Spring '08
 KENDALL,BERKLEY
 Environmental Science

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