1/17 ` <kumazawa@biwako.shiga-u.ac.jp> http://www.biwako.shiga-u.ac.jp/sensei/kumazawa/ 6............................................ 5 1............................... 1 1.1 I II III 1 1.2 2 1.3 2 2...................................... 2 3........................................ 3 3.1 4 3.2 4 4............................................ 4 5............................................ 4 7............................................ 7 8................................................ 9 9.....................................10 9.1 10... 10... 12 9.2 12 9.3 13 9.4 13 9.5 13 9.6 13 9.7 13 10............................................. 13 11....................................... 16 1 OR R OR I II III 1.1 I II III I II I 1/17
2/17 II III 1.2 R III 1.3 R 2 descriptive statistics inferential statistics ( ) X 1,X 2,,X n : n estimation testing prediction significance interval A B 2/17
3/17 ( )/ 10 + 50 = n i=1 x i n = x, = n i=1 (x i x) 2 n n x i 5 Statistical Quality Control 7? 1959 1997 Mauna Loa is the largest volcano on Earth with an estimated volume of 9,600 cubic miles (40,000 cubic kilometers). It makes half of the area of the Island of Hawaii. Mauna Loa began to form nearly a million years ago. There is a caldera, Mokuaweoweo, at the summit and rift zones extend to the northeast and southwest. Mauna Loa is in the shieldbuilding stage and is one of the most active volcanoes on Earth, erupting 15 times since 1900. The last eruption was in 1984 and sent lavas within 4 miles (6.5 km) of Hilo. (http://volcano.oregonstate.edu/ ) FreeWare R plot(co2) R MacOS Windows Unix Linux OS Australia New Zealand http://cran.r-project.org/ 3 data sample 3/17
4/17 3.1 qualitative data nominal scale ordinal scale CD 3.2 quantitative data continuous data discrete data 1 interval scale ratio scale 4 1. simple random sampling 2. systematic sampling 3. stratified sampling 4. two stage sampling 1 2 5. 2 stratified tow stage sampling 2 5 1. parameter 4/17
5/17 2. 3. T.Bayes 1710-1761 6 1 2 x y r = s xy sxx s yy (x 1,y 1 ),(x 2,y 2 ),,(x n,y n ) 2 n s xy = n i=1 (x i x)(y i y) n 1 s yy = n i=1 (y i y) 2 n 1, s xx = n i=1 (x i x) 2, n 1 n, x = 1 i, y = n i=1x 1 n s xy,s xx,s yy,x,y x y r xy Pearson x y -1 +1 +1-1 0 20 50m R n y i i=1 50m running income age 7.7 342 23 8.2 923 43 8.5 985 50 7.8 581 35 8.0 627 33 7.8 388 25 7.7 290 20 8.2 860 44 8.5 787 48 8.1 654 37 8.4 788 39 7.7 334 22 7.9 412 29 8.3 915 46 8.2 648 43 7.9 761 33 7.8 589 30 8.4 946 47 7.8 477 28 7.7 412 25 5/17
6/17 50m 0.86 50m 0.93 0.94 3 R cor(d) d 50m 3 r xy r zx r zy (1 rzx)(1 2 rzy) 2 3-0.05382888 50m Mammal species 0 5 10 15 20 25 f f d d f d e c d d c c c e e d d d e e b b c e a a b b e c c e a a a a a b a b b b c f f f f f 0 5 10 15 20 25 30 Productivity 6 a f 0.7056966 6/17
7/17 0 5 10 15 20 25 30 d e f 25 20 15 10 Mammal species 25 20 a b c 5 0 15 10 5 0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Productivity 9 7 t X Y t X Y 1 100 10 2 200 20 3 100 10 4 200 20 5 100 10 6 200 20 7 100 10 8 200 20 9 100 10 10 200 20 Numbers 0 50 150 250 2 4 6 8 10 Index X 100 200 10 20 Y 7/17
8/17 t X Y 1 100 10 2 200 20 3 100 10 4 200 20 5 100 10 6 200 20 7 100 10 8 200 20 9 100 10 10 200 20 Numbers 1 2 3 4 5 6 2 4 6 8 10 Index X Y, 120 X Y X Y 0.241 0.387 0.615 0.723 1 1 1.88 1.52 11.9 5.20 29.5 9.55 84.0 19.2 165 30.1 248 39.5 0 50 150 250 Y 0 10 20 30 40 X X Y (x i,y i ) n i=1 { yi (β 0 + β 1 x i ) } 2 X Y 8/17
9/17 X Y -1.422958-0.94933-0.486133-0.32434 0.0000000 0.000000 0.6312718 0.418710 2.4765384 1.648658 3.3843903 2.256541 4.4308168 2.954910 5.1059455 3.404525 5.5134287 3.676300 1 1 2 3 4 5 logy 1 0 1 2 3 logx mercury 0.241 0.387 venus 0.615 0.723 earth 1 1 mars 1.88 1.52 jupiter 11.9 5.20 saturn 29.5 9.55 Uranus 84.0 19.2 Neptune 165 30.1 Pluto 248 39.5 1 = 1.50 1011m 2 3 1619 1 : 2 : 3 : 2 3 8 4 9/17
10/17 EXPLORATORY DATA ANALYSIS Histogram of x Density of x Boxplot of x Q Q Plot of x Sturges 7 Gaussian Shapiro-Wilk SQC Statistical Quality Control 7 9 7 QC7 (i) Graph, Control Chart (ii) Pareto Diagram (iii) Histogram (iv) Cause and Effect Diagram (v) Scatter Diagram (vi) Stratification (vii) CheckSheet 7 5 R qcc 9.1 9.1.1 (i) 10/17
11/17 (ii) (iii) 100% (iv) median 25% 1 first quartile 25% 3 third quartile 1 3 1 3 1.5 1 3 boxplot (v) qqnorm qqline 1 3 11/17
12/17 9.1.2 Shewhart control chart CL Center Line UCL Upper Control Limit LCL Lower Control Limit (i) x x (ii) R R (iii) x x (iv) p p (v) pn pn (vi) c (vii) u 3 9.2 Pareto Pareto chart 12/17
13/17 9.3 9.4 Fishbone Diagram Cause and Effect diagram Communication SKills ambiguity lack of knowledge Knowledge Literacy Incorrect Deliver Procedures Manual automated Transport carriers Information 9.5 2 9.6 9.7 10 R airquality 1973 5 9 153 Ozone Solar.R Wind Temp Month Day R help airqualtiy 13/17
14/17 6 0 100 250 60 80 0 10 20 30 Ozone 0 50 150 0 150 300 Solar.R Wind 5 15 60 80 Temp Month 5 6 7 8 9 0 10 25 Day 0 50 100 5 10 15 20 5 6 7 8 9 30 15 2 2 airq airq 0 50 150 250 60 70 80 90 Ozone 0.35 0.60 0.70 0 50 100 0 100 200 300 Solar.R 0.057 0.28 Wind 0.46 5 10 15 20 60 70 80 90 Temp 0 50 100 150 5 10 15 20 14/17
15/17 Temp < 82.5 Wind < 7.15 Wind < 10.6 Temp < 88.5 Solar.R < 205 Solar.R < 79.5 48.71 61.00 Temp < 77.5 74.54 83.43 102.40 12.22 20.97 34.56 Temp<82.5 28.1 Wind>=7.15 Call: lm(formula = Ozone Temp * Wind * Solar.R + I(Solar.Rˆ2) + I(Tempˆ2) + I(Windˆ2)) Residuals: Min 1Q Median 3Q Max -38.879-11.231-2.706 8.824 70.546 Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) 5.670e+02 2.077e+02 2.730 0.00748 ** Temp -1.073e+01 4.308e+00-2.491 0.01439 * Wind -3.232e+01 1.176e+01-2.749 0.00709 ** Solar.R -3.140e-01 5.593e-01-0.561 0.57581 I(Solar.Rˆ2) -3.610e-04 2.576e-04-1.401 0.16421 I(Tempˆ2) 5.815e-02 2.399e-02 2.424 0.01715 * I(Windˆ2) 6.095e-01 1.473e-01 4.138 7.32e-05 *** Temp:Wind 2.373e-01 1.370e-01 1.733 0.08624. Temp:Solar.R 8.433e-03 7.523e-03 1.121 0.26499 Wind:Solar.R 2.063e-02 4.899e-02 0.421 0.67450 Temp:Wind:Solar.R -4.340e-04 6.605e-04-0.657 0.51264 --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Residual standard error: 17.84 on 100 degrees of freedom 15/17
16/17 (42 observations deleted due to missingness) Multiple R-squared: 0.7387, Adjusted R-squared: 0.7126 F-statistic: 28.27 on 10 and 100 DF, p-value: < 2.2e-16 3 Call: lm(formula = log(ozone) Temp + Wind + Solar.R + I(Windˆ2), subset = (1:length(Ozone)!= 17)) Residuals: Min 1Q Median 3Q Max -2.01817-0.27787-0.01111 0.31407 1.29569 Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) 0.6741274 0.6466060 1.043 0.299545 Temp 0.0474201 0.0060421 7.848 3.76e-12 *** Wind -0.2232387 0.0598210-3.732 0.000309 *** Solar.R 0.0024195 0.0005477 4.418 2.43e-05 *** I(Windˆ2) 0.0073580 0.0026307 2.797 0.006137 ** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Residual standard error: 0.4928 on 105 degrees of freedom (42 observations deleted due to missingness) Multiple R-squared: 0.6907, Adjusted R-squared: 0.679 F-statistic: 58.63 on 4 and 105 DF, p-value: < 2.2e-16 11 (i) Web Wikipedia : http://ja.wikipedia.org/wiki/ (ii) google goo yahoo http://www.google.co.jp/ http://www.goo.ne.jp/ http://www.yahoo.co.jp/ AND 1 AND 2 AND AND OR 2 ( OR ) AND 16/17
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