一组空气污染数据的主成分分析

精品文档---下载后可任意编辑【说明】下面的多元统计分析练习题摘自 R.A. Johnson 等编写的《应用多元统计分析（第五版）》，原书为：Richard A. Johnson and Dean W. Wichern. Applied Multivariate Statistical Analysis (5th Ed). Pearson Education, Inc. 2024。我看的是中国统计出版社（China Statistics Press）2024 年发行的影印本。第一题为原书第 1.6 题，即第 1 章的第 6 题，第二题为原书第 8.12 题，即第 8 章的第 12 题。第二题用的是第一题的数据。1 习题1.6. The data in Table 1.5 are 42 measurements on air-pollution variables recorded at 12:00 noon in the Los Angeles area on different days.(a) Plot the marginal dot diagrams for all the variables.(b) Construct the , Sn, and R arrays, and interpret the entries in R. AIR-POLLUTION DATAWind (x1)Solar radiation (x2)CO (x3)NO (x4)NO2(x5)O3 (x6)HC (x7)898721282710743953710343563108852815469142810389052121249847412155572642114478251111138645213946715410336914212737727418103107042117310724181039774191038764177387153164496742132396933953106253144498842763880421311453033523683511023488432763678421111387921710366243983103731723871411073752411284548658436754110243103541692885419102586316122586721318277974925377952862668621114384043652Source: Data courtesy of Professor G.C. Tiao.8.12. Consider the air-pollution data listed in Table 1.5. Your job is to summarize these data in fewer than p=7 dimensions if possible. Conduct a principal component analysis of the data using both the covariance matrix S and the correlation matrix R. What have you learned? Does it make any difference which matrix is chosen for analysis? Can the data be summarized in three or fewer dimensions? Can you interpret the principal components?2 部分解答2.1 部分统计参数利用 Excel 计算的平均值（）和标准差WindSolar radiationCONONO2O3HCAverageStdevExcel 给出的协方差矩阵 SWindSolar radiationCONONO2O3HCWindSolar ...