Rによる計量分析：データ解析と可視化 - 第3回 Rの基礎とデータ操作・管理
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1 R 3 R [email protected] October 23, 2017 (Toyama/NIHU) R ( 3 ) October 23, / 34
2 Agenda R 5 RStudio (Toyama/NIHU) R ( 3 ) October 23, / 34
3 10/30 (Mon.) 12/11 (Mon.) New! 1/9 (Tue.) New! (Toyama/NIHU) R ( 3 ) October 23, / 34
4 (regression analysis) (OLS) (GLM) (inferential statistics) = ( ) ( ) ( ) (Toyama/NIHU) R ( 3 ) October 23, / 34
5 50% 30% Google ( R ( ) (Toyama/NIHU) R ( 3 ) October 23, / 34
6 (Toyama/NIHU) R ( 3 ) October 23, / 34
7 ( ) ( ) ( ) (Toyama/NIHU) R ( 3 ) October 23, / 34
8 datum ( ) (1) (2) ( ( ) ) ( ( ) ( ) ( ) GDP (Toyama/NIHU) R ( 3 ) October 23, / 34
9 (unit of observation) (unit of analysis) (variable) GDP, 2 GDP (constant) ( ) (Toyama/NIHU) R ( 3 ) October 23, / 34
10 4 1 (nominal scale): 2 ( ) 2 (ordinal scale): ( ) 1 2 ( ) 3 (interval scale): ( ) (2 ) (0 ) 4 (ratio scale): (0) (0 ) 50kg 100kg 50kg 2 ( ) > > > (Toyama/NIHU) R ( 3 ) October 23, / 34
11 (statistic) ( ) ( ) ( ) ( ) ( ) (Toyama/NIHU) R ( 3 ) October 23, / 34
12 (mean, average) n ( ) x = (x 1, x 2,..., x n ) x x = n i=1 n = (x 1 + x x n ) n (1) (median) n x m m df(x) 1 2 and m df(x) 1 2 (2) m n 2 (Toyama/NIHU) R ( 3 ) October 23, / 34
13 (mode) ( ) x = (1, 1, 1, 1, 1, 2, 3, 4, 5, 6) 1 3 (outlier) (e.g., ) (e.g., ) (Toyama/NIHU) R ( 3 ) October 23, / 34
14 500, 100, n = 10, 000 ( x = 500, m = 500) Median Mean Frequency ( x = 594, m = 501) Frequency /10, 000 = 1/100 ( robust) (Toyama/NIHU) R ( 3 ) October 23, / 34
15 (IQR) (unbiased variance) n x = (x 1, x 2,..., x n ) x σ 2 x n σx 2 i=1 = (x i x) 2 n 1 (3) σ 2 x σ x (standard deviation, sd) ( ) (3) ( ) n 1 n ( ) ( ) x x (Toyama/NIHU) R ( 3 ) October 23, / 34
16 (IQR) (inter-quartile range, IQR) ( ) (1 ) n x = (x 1, x 2,..., x n ) x x 4 IQR 3 Q 3/4 (upper quartile) 1 Q 1/4 (lower quartile) Q 3/4 Q 1/4 m = Q 2/4 = Q 1/2 Q 0/4 Q 4/4 ( ) IQR 50% [Q 1/4 1.5IQR, Q 3/ IQR] (outlier) (box-and-whisker plot) ( ) q/10 q (Toyama/NIHU) R ( 3 ) October 23, / 34
17 (population) ( ) ( ) 2 (data generating process) (sample) (sampling) ( ) (statistical inference) ( ) (error) ( ) ( ) (Toyama/NIHU) R ( 3 ) October 23, / 34
18 (sample size): ( ) N (number of samples): ( ) ,500 2, ,500 ( ) 2,000 ( ) (Toyama/NIHU) R ( 3 ) October 23, / 34
19 ( ) (parameter) (parameter) (e.g., ) % ( ( ) ( standard error) 1 ( ) 2 (Toyama/NIHU) R ( 3 ) October 23, / 34
20 (Central Limit Theorem, CLT) ( ) n X 1, X 2,..., X n X n, σ 2 X X E[X] n Z n (X n E[X] ) 0, 1 ( ) N (0, 1) ( ) Z n = n(xn E[X]) n(xn E[X]) = (4) σ 2 X σ X X n E[X] N (0, σx 2 /n) ( ) n X n E[X] µ, σ ( σ 2 ) N (µ, σ 2 ) (Toyama/NIHU) R ( 3 ) October 23, / 34
21 ( ) ( ) n X 1, X 2,..., X n X n, σx 2 X E[X] ( ) n 95% X n 1.96 σx 2 /n E[X] X n /n (5) X n N (E[X], σx 2 /n) 95% ( ) = σ 2 X (Toyama/NIHU) R ( 3 ) October 23, / 34
22 (5) E[X] 95% (confidence interval, CI) (standard error, SE): σx 2 /n = σ X/ n ( ) σx n ( n ) 95% CI [X n 1.96SE, X n SE] 95% (X n E[X]) n ( ) t t 1.96 (Toyama/NIHU) R ( 3 ) October 23, / 34
23 ( ) α% α (confidence coefficient) 95%, 90%, 99% ( 94%, 96%, etc. ) 5% 10% 1% p < 0.05, p < 0.1, p < 0.01 ( (Type I/α error) ( ) 5%, 10%, 1%) (Type I/α error) H 0 (e.g., ) H 0 (interval estimation) 100 ( ) 95% 95 95% 1 (point estimation) (Toyama/NIHU) R ( 3 ) October 23, / 34
24 SD = σ X, SE = σ X / n SD > SE n (n 2) n n ( ) n SE = σx/ n SE 95% [Xn 1.96SE, X n SE] (Toyama/NIHU) R ( 3 ) October 23, / 34
25 α% 1 1 α% α% ( ) 100 ( ) 95% 95 95% % % % 0 1 (Toyama/NIHU) R ( 3 ) October 23, / 34
26 (file) path: URL PC URL education_2017/r_2017/ sample ( ) path /Users/Gaku/Desktop/sample sample.csv path /Users/Gaku/Desktop/sample.csv path OS (Win 10 ) Google!. sample.csv.csv, sample.xls.xls OS (Win 10 ) Google! (Toyama/NIHU) R ( 3 ) October 23, / 34
27 R (R path, encoding ) R /. R ( ) (1) (2) ( ) Mac Macintosh HD ( / ) Windows C (Toyama/NIHU) R ( 3 ) October 23, / 34
28 R R a ( ) ( ) a A R (Toyama/NIHU) R ( 3 ) October 23, / 34
29 R R A A A A A A R Google Error: object x not found (1) (2) (Toyama/NIHU) R ( 3 ) October 23, / 34
30 R (object) R R x 1 > x < <- ( = ) R ( ) ( ) vector, matrix, data.frame (tibble), list (e.g., ) 1 > x2 <- x/2 2 > x2 3 [1] 1 (Toyama/NIHU) R ( 3 ) October 23, / 34
31 R R double ( ), integer ( ), logical ( ), character ( ), factor ( ) 1 > x_num < > x_num 3 [1] 2 4 > x_chr <- "2" 5 > x_chr 6 [1] "2" 7 > class(x_num) 8 [1] "numeric" 9 > class(x_chr) 10 [1] "character" (Toyama/NIHU) R ( 3 ) October 23, / 34
32 R ( ) (5 8 ) x_chr 2 2 (9 10 ) 1 > num_vec <- c(1, 2, 3, 4, 5, 6) 2 > mean(num_vec) 3 [1] > chr_vec <- c("1", "2", "3", "4", "5", "6") 5 > mean(chr_vec) 6 [1] NA 7 Warning message: 8 In mean.default(chr_vec) : argument is not numeric or logical: returning NA 9 > mean(as.numeric(chr_vec)) 10 [1] 3.5 (Toyama/NIHU) R ( 3 ) October 23, / 34
33 R 1 (URL: /r_2017/rcode_fall2017/) 2 R 2. R R R (Toyama/NIHU) R ( 3 ) October 23, / 34
34 ( ) (1 ) R R 1 3, 6 ( ) Gelman & Hill. Data analysis. Chap. 1 2 ( ) Stata 5 ( ) 1 2 ( ) R R (Toyama/NIHU) R ( 3 ) October 23, / 34
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Rによる計量分析：データ解析と可視化 - 第2回 セットアップ
R 2 2017 Email: [email protected] October 16, 2017 Outline 1 ( ) 2 R RStudio 3 4 R (Toyama/NIHU) R October 16, 2017 1 / 34 R RStudio, R PC ( ) ( ) (Toyama/NIHU) R October 16, 2017 2 / 34 R ( ) R
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第11回：線形回帰モデルのOLS推定
11 OLS 2018 7 13 1 / 45 1. 2. 3. 2 / 45 n 2 ((y 1, x 1 ), (y 2, x 2 ),, (y n, x n )) linear regression model y i = β 0 + β 1 x i + u i, E(u i x i ) = 0, E(u i u j x i ) = 0 (i j), V(u i x i ) = σ 2, i
Stata11 whitepapers mwp-037 regress - regress regress. regress mpg weight foreign Source SS df MS Number of obs = 74 F(
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2 2012 4 ( ) 2 2012 4 1 / 42 X Y Y = f (X ; Z) linear regression model X Y slope X 1 Y (X, Y ) 1 (X, Y ) ( ) 2 2012 4 2 / 42 1 β = β = β (4.2) = β 0 + β (4.3) ( ) 2 2012 4 3 / 42 = β 0 + β + (4.4) ( )
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kubostat2017c p.1 2017 (c), a generalized linear model (GLM) : [email protected] http://goo.gl/76c4i 2017 11 14 : 2017 11 07 15:43 kubostat2017c (http://goo.gl/76c4i) 2017 (c) 2017 11 14 1 / 47 agenda
第13回：交差項を含む回帰・弾力性の推定
13 2018 7 27 1 / 31 1. 2. 2 / 31 y i = β 0 + β X x i + β Z z i + β XZ x i z i + u i, E(u i x i, z i ) = 0, E(u i u j x i, z i ) = 0 (i j), V(u i x i, z i ) = σ 2, i = 1, 2,, n x i z i 1 3 / 31 y i = β
講義のーと : データ解析のための統計モデリング. 第２回
Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20
: (EQS) /EQUATIONS V1 = 30*V F1 + E1; V2 = 25*V *F1 + E2; V3 = 16*V *F1 + E3; V4 = 10*V F2 + E4; V5 = 19*V99
218 6 219 6.11: (EQS) /EQUATIONS V1 = 30*V999 + 1F1 + E1; V2 = 25*V999 +.54*F1 + E2; V3 = 16*V999 + 1.46*F1 + E3; V4 = 10*V999 + 1F2 + E4; V5 = 19*V999 + 1.29*F2 + E5; V6 = 17*V999 + 2.22*F2 + E6; CALIS.
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1 2 . sum Variable Obs Mean Std. Dev. Min Max ---------+----------------------------------------------------- var1 13.4923077.3545926.05 1.1 3 3 3 0.71 3 x 3 C 3 = 0.3579 2 1 0.71 2 x 0.29 x 3 C 2 = 0.4386
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講義のーと : データ解析のための統計モデリング. 第３回
Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20
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講義のーと : データ解析のための統計モデリング. 第５回
Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20
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spurious correlation spurious regression xt=xt-1+n(0,σ^2) yt=yt-1+n(0,σ^2) n=20 type1error(5%)=0.4703 no trend 0 1000 2000 3000 4000 p for r xt=xt-1+n(0,σ^2) random walk random walk variable -5 0 5 variable