建立地圖簡化數學模型的主要目的，在於描述地圖簡化的規律，提供地圖簡化地物數量選取指標，進而指導地圖製圖作業。本研究探用之數理統計法就是利用數學或邏輯的方法，經由統計觀測、統計歸納及統計分析等步驟，揭示地物的客觀規律。本文擬以地圖地名為研究對象，以台灣北中南東四區，各選一個縣為樣本，分別為；桃園縣、台中縣、台南縣及花蓮縣。按內政部出版之經建版地形圖，計測不同比例尺地形圖（2/25萬～1/50萬）中地名數量，並應用Excel軟體之迴歸統計功能，進行曲線擬合之測試，以決定適當的迥歸模型。研究結果顯示地名保留率(Y)與地圖上比例尺分母(X)之間存在冪次函數之迴歸關係(Y=aX(上標 b))，且地圖上比例尺對地名保留率具高解釋力，這對於地圖編製之地名選取工作具實務參考價值。
The main goals to establish mathematical models for map generalization lie to describe rules which maps are generalized, to provide selection index for quantity of land feature, and then to supervise processes for mapping workflow. This research adopts the mathematical statistic method to indicate objective regular patterns of land features by means of statistical observations, induction and analysis. This article takes the map geographic name as the research object, (north, south, central, east) four parts of Taiwan as study areas, and respectively chooses a county as the resources of sample data. They are: Taoyuan county, Taichung county, Tainan county and Hualien County. According to the economic construction version of topographic maps published by Ministry of Interior, we measured on the different scale topographic maps (scaled from 1/25,000~1/50,000) to Associate Professor, Department of Information Management, Ching Yun University. calculate the quantity of geographic names. We also used the Excel software and carried on tests to the curve fitting processes in order to decide the suitable regression model. The findings show that geographic name retention rate (Y) and map scale factor (X) have regressive relationship functioned as (Y=aX(superscript b)) and that map scale to geographic name retention rate has high explanation strength. The results offer practical reference values to the selection of geographic names regarding mapping technique.
