AN APPLICATION OF TREND-SURFACE MAPPING TO THE DISTRIBUTION OF RESIDUALS FROM A REGRESSION¹

Abstract

One hundred fifty-four towns with at least one commercial service and twenty inhabitants each are dispersed irregularly through Gippsland, Australia. A general relationship of their services S to population P is log S = 0.699 log P -0.367. The spatial pattern of residuals from this relationship is apparently made up of purely local elements. The fitting of low-order, partial trend-surfaces to the residuals establishes the presence of a weak but significant regional trend in their distribution. There are only minor differences between the map of residuals from regression and that of the deviations from the regional trend of those residuals. The explanation of the spatial character of the residuals, therefore, can remain in this case primarily in terms of local factors. The regional trend nevertheless needs explanation in terms of regionally operative factors that have not yet been established but which would not be suggested by more conventional methods of mapping residuals. residual from regression represents the A portion of an observed value of a dependent variable unexplained by the one or more independent variables included in the analysis. The mapping of residuals depicts the areal distribution of departures from a generalized statistical relationship,2 with the critically read earlier drafts and made valuable suggestions concerning both style and content.2The mapping of residuals from regression, as a useful tool in manv eeoerauhical moblems. was dis-1966), pp. 78-79, recently emphasized the value of the technique in economic geography. , Visual Com-278-80, 298-99, described some uses of residual parison of Isopleth Maps as a Means of Determining maps in hypothesis testing in human geography, and Correlation Between Spatially Distributed Phenom-

Livestock development planning in Uganda: Identification of areas of opportunity and challenge

“…This method of exploratory spatial data analysis has a relatively long history within quantitative geography, being first described in detail by E.N. Thomas in the early 1960s (Thomas 1960) with refinements to the method developed in the following years (Robinson, Lindberg, and Brinkman 1961;Robinson and Fairbairn 1969). Early adopters of this approach generally mapped residuals from simple OLS regressions.…”