A Geometrical Interpretation of Collinearity: A Natural Way to Justify Ridge Regression and Its Anomalies

Justifying ridge regression from a geometrical perspective is one of the main contributions of this paper. To the best of our knowledge, this question has not been treated previously. This paper shows that ridge regression is a particular case of raising procedures that provide greater flexibility by transforming the matrix X associated with the model. Thus, raising procedures, based on a geometrical idea of the vectorial space associated with the columns of matrix X , lead naturally to ridge regression and justify the presence of the well-known constant k on the main diagonal of matrix X ^′ X . This paper also analyses and compares different alternatives to raising with respect to collinearity mitigation. The results are illustrated with an empirical application.     

主成分回归在区域现金净投放分析中的应用

选取安徽省马鞍山市六项主要经济指标,利用主成分回归方法建立区域现金净投放预测模型。模型分析结果表明,第三产业增加值对现金净投放量变化影响最大,其次是贷款余额、GDP、存款余额和固定资产投资,而物价因素对其影响最小。     

利用DOM及DEM数据进行输电工程勘测设计研究

依据山东省地理信息中心已有1／10000比例尺的DOM（数字正射影像图,Digital Orthophoto Map）和DEM（数字高程模型,Digital Elevation Model）数据,通过核线共线方程恢复生成大场景三维立体模型,然后进行架空输电线路路径优选、测量平断面图,再进行外业采集交叉跨越和重要断面数据,并用外业实际测量数据对原数据进行拟合修正,最后生成三维漫游。研究将标准测量4D数据应用到架空输电工程勘测设计全过程,通过工程实际应用,提出了应用方法及注意事项等。