l Multiple Linear Regression Principal Component Regression l Slides: 26 Download presentation 本日の内容 l 重回帰分析(Multiple Linear Regression )と 主成分回帰(Principal Component Regression)の復習 l 部分的最小二乗法(Partial Least Squares)とは 5 / 26 MLRを使ってみる 6 / 26 l 例題:温度と反応率の関係を求める l 正解: 実験 x. A T 1 T 2 1 2 3 4 5 T 1, T 1 real T 2, T 2 real 102. 0 100. 0 111. 7 120. 0 120. 5 130. 0 129. 6 140. 0 140. 3 MLR 100. 2 100. 0 111. 1 120. 0 119. 4 130. 0 128. 7 140. 0 140. 8 ˆx. A 0. 00 0. 1 0. 2 0. 3 0. 4 0. 002 0. 098 0. 200 0. 299 0. 401 推定 MLRとPCRの比較 15 / 26 l MLR xˆA = 0. 0218 T 1 - 0. 0107 T 2 - 1. 1461 = 0. 0218(T 1, real + v 1 ) - 0. 0107(T 2, real + v 2 ) - 1. 1461 = 0. 00111 Treal + 0. 0218 v 1 - 0. 0107 v 2 - 1. 1461 l PCR(主成分1個) ノイズに対する係数が小さい! MLRとPCRの比較 MLR 16 / 26 PCR PCRとPLSの比較 24 / 26 l 外気圧 P のデータも利用して反応率を推定する (外気圧は反応率とは無関係) P 実験 x. A T 1 T 2 1 2 3 4 5 T 1 T 2 P 102. 0 111. 7 120. 5 129. 6 140. 3 100. 2 111. 1 119. 4 128. 7 140. 8 1013 1020 998 1022 1015 x. A 0. 0 0. 1 0. 2 0. 3 0. 4 Simple linear regression and multiple regressionMultiple regressionSurvival analysis vs logistic regressionLogistic regression vs linear regressionLogistic regression interaction interpretationLinear regression with multiple featuresMultiple linear regression varianceMultiple linear regression varianceRegression equation in excelIn multiple linear regression model, the hat matrix (h) isMse econometricsLinear regression assumptions spssMultiple linear regression interpretationMultiple regression equationLinear regression with multiple variables machine learningParallel analysis spss"mitu"Jmp pcaGeneralized principal component analysisPrincipal component analysisGeneralized principal component analysisRadial component of linear accelerationConfidence interval multiple regressionExtra sum of squares multiple regressionMultiple regression analysis with qualitative informationDefinition of multiple regressionMultiple regression analysis adalah