Einige Anmerkungen zur Regressionsanalyse raumbezogener Daten - Erläutert am Beispiel einer Niederschlags-Abfluß-Regression

Abstract

Regression analysis belongs to the most frequently applied statistical methods in geography. A basic but mostly ignored assumption of this model is the independence among the regression residuals. Concerning spatial variates this means the spatial autocorrelations to be zero. Otherwise all important, statistics of the regression equation may be misestimated, which leads to incorrect inferences and nonoptimal applications. Based on the geographically important concept of spatial autocorrelation, an appropriate procedure to detect spatial dependencies in regression residuals is summarized (CLIFF/ORD, 1973). A hydrologie example of regression analysis between A = runoff and N = rainfall (mm/a) - defined on a 6 x 6 lattice in the upper Fulda region (FRG) - points out the methodological importance as well as the geographical implications of significant spatial auto correlations among the residuals and the regression variables themselves. Hydrologie reflections and various computations recommend acceptance of a linear trend surface model combined with the predictor N. Another solution, including spatially lagged variables i.e. an autoregressive component, is discussed and shown to be effective too.