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* Staley Smth Steves 1946 O the theory of scales of measuremet 4 Wkpeda, Excel help 4 Frequecy Dstrbuto Wdows (McroSoft) OpeOffce.org 4.1 4
(cm) 3 10 7 BMI ( ) (m) 2 BMI 18.5 18.5 25 25 30 30 100 BMI BMI 1: 4.2 100 5 1 5 : 1 12 2 26 3 15 4 7 5 5 2 (Hstogram) 5
2 (tally mark) x skewess L L L L kurtoss, excess ; leptokurtc ; platykurtc Hstogram 2 4 10 100 2 6
Q 1, Q 2, Q 3 Q 1, Q 3 360 1. (max) (m) rage 2. (class) 10 20 Starjes k = 1 + log 2 = 1 + 3.3 log 1 0 3. (class wdth) R/k 4. 7
3 (Boxchart) A B C D E F G 1 ( ) ( ) 2 a 0 a 1 x 1 f 1 F 1 = f 1 p 1 = f 1/ P 1 = p 1 3 a 1 a 2 x 2 f 2 F 2 = f 1 + f 2 p 2 = f 2/ P 2 = p 1 + p 2 4 a 2 a 3 x 3 f 3 F 3 = f 1 + f 2 + f 3 p 3 = f 3/ P 3 = p 1 + p 2 + p 3 5 6 a k 1 a k x k f k F k = p k = f k / P k = 1 7 1 x = (a 1 + a )/2,( = 1, 2,, k) F k = f 1 + f 2 + + f k =, P k = p 1 + p 2 + + p k = 1 =max( ) =m( ) D2 D6 =frequecy, ( A2 A6) CTRL+SHIFT+ENTER E2 =D2 E3 =D2+D3 E3 E4 E6 F2 =D2/D$7 frequecy 1. 2 2. 1 3. 4. 8
4 5 5 (average,mea) (SD,stadard devato),meda ( (varace) (kurtoss, excess)(bulge ) (skewess) (rage) (m) (max) (sum) (sze) 1. Excel -VBA 2.OK 3. OK 9
{X, = 1,, }, sort (Order Statstcs) {X (), = 1,, } X 1, X 2,, X X (1) X (2) X () X 1 + X 2 + + X = X (1) + X (2) + + X () X k x 1, x 2,, x k (k ) ( ) x 1 x 2 x k f 1 f 2 f k p 1 p 2 p k 1 2 f = 1, = 1, 2,, X = X 1 + X 2 + + X = x 1 f 1 + x 2 f 2 + + x k f k = j x f j, f = f 1 + f 2 + + f k = X2 = X2 1 + X 2 2 + + X 2 = x 2 1 f 1 + x 2 2 f 2 + + x 2 k f k = j x2 j f j, 1 1 X = 1 (X 1 + X 2 + + X ) = x 1 p 1 + x 2 p 2 + + x k p k = j x j p j, X2 = 1 (X2 1 + X 2 2 + + X 2 ) = x 2 1 p 1 + x 2 2 p 2 + + x 2 k p k = j x j p 2 j, X = 1 =1 X = 1 k j=1 x jf j = k j=1 x jp j AVERAGE SE SE = s = (X X) 2 = X2 X2 j = x2 j f j X 2 j = x2 j p j X 2 ( 1) ( 1) ( 1) 1 Me Me = X ((/2)+1) ( ) = X ((+1)/2) ( ) = meda( ) 2 = quartle(, 2) Mo ( ) MODE 2 #N/A (Not Avalable) max f MODE # N/A (Not Avalable) SD SD = s = (X X) 2 STDEV VAR ( 1) 10
s 2 s 2 = 1 1 VAR (X X) 2 = ( 1 ) (X X j ) 2 = 1 2 <j =1 VARP ( 1) v 2 = 1 (X X) 2 = 1 =1 k x 2 jf j X 2 = j=1 k x 2 jp j X 2 j=1 k x 2 jp j X 2 KW KURT 1 ( ) 4 X X 3 s 3 SK SKEW 1 ( ) 3 X X s L L L R L R = max( ) m( ) () MAX x 1, x 2,, x max x MIN x 1, x 2,, x m x SUM x 1, x 2,, x x, N COUNTA 95.0% 95% 1/2 95% TM(trmmed mea) TRIMMEAN TRIMMEAN(, ) (1) (2) 20 0.2 20 0.2 = 4 2 2 4 MD (Mea Devato) = 1 X X j=1 11
Z () Z = X X s x ( 0 1 50 10( 100) 10Z + 50 X 100 15 Q 1, Q 2, Q 3 25% 4 25% Q 1 2 50% 3 75% 3 =QUARTILE(, ) (, QUARTILE ) = (0, ), (1, 1 (25%)) (2, 2 = (50%)) (3, 3 (75%)) (4, ) Q 3 Q 1 (dectle) (percetle) ( 4 CV(Coeffcet of Varato)= s x X ( ) 10% 10% 0.9 1.1 68.3% 0.31100 68.3 0.31 ± 0.031 X N(µ, σ 2 ) µ 0.6826 68.3% ±2 σ 0.9544 X 6 1 2 (sample covarace): =COVAR( A, B) Cov(x, y) = 1 1 = COV AR(x, y ) (X X)(Y Y ) 1 2 X, Y 0 12
1 N 1 +1 2 COVAR N=2 2 COVAR VARP 2 ( ) ( ) (0 ) (sample correlato coeffcet): =CORREL( A, B) = correl(x, y ) x s x, y s y ρ = Cov(x, y) s x s y ( x = Cov, y ) s x s y X X, Y Y, = 1, 2,, s x s y N CORREL PEARSON 2 N 3 CORREL ( PEARSON) 2 2 2 1 +1 2 ( ) ( ) (0 ) 13
6 1 0.7 0.7 0.4 0.4 0.2 0.2 0 0 0.2 0.2 0.4 0.4 0.7 0.7 1 (Speama s rak correlato coeffcet) r s = 1 6 (x y ) 2 ( 2 = 1 1) (x y ) 2 / ( ) 1 3 x, y 1, 2,, =[COUNT( ) + 1 - RANK(,, 0) - RANK(,, 1)]/2 RANK(,, ) 0...3 2 1 0 1 2 3... 2 2 2 0 2 14
7: 9 8 7 Corrado G 0 1 10 15
0 1 Wkpeda (G coeffcet) 100 G Idex http://www.sustaablemddleclass.com/g-coeffcet.html Japa 24.9 Uted Kgdom 36.0 Swede 25.0 Ira 43.0 Germay 28.3 Uted States 46.6 Frace 32.7 Argeta 52.2 Paksta 33.0 Mexco 54.6 Caada 33.1 South Afrca 57.8 Swtzerlad 33.1 Namba 70.7 ( 0.24 0.36 0.4 0.56 0.66 Bob Sutclffe (2007), Postscrpt to the artcle World equalty ad globalzato (Oxford Revew of Ecoomc Polcy, Sprg 2004), http://steresources.worldbak.org/intdecineq/resources/psbsutclffe.pdf. Retreved o 2007-12-13 G = 1 2 1 0 L(x)dx = 1/2 1 0 L(x)dx 1/2 or = 1 2 L(x )(.e.l(x) ) L(x) y G L (1, 1) y = x 45 1 0 L(x)dx (0.8, 0.6) y = L(x) (0.4, 0.2) 0 1 x (0, 0) F (1) = 1, 2,, 16
x x 1 x 2 x p = f(x ) p 1 p 2 p F F 1 = p 1 F 2 = p 2 + F 1 F = p + F 1 = 1 L = j=1 x jf(x j ) / L = L = j=1 x jf(x j ) L +1 + L (F +1 F ) 2 ( = 1, 2,, ) L 0 = 0 L 1 L 2 L 1 L = 1 0 1 (2) < x < x f(x) F (x) = x f(t)dt L(x) = x / tf(t)dt L (0 x 1) L = tf(t)dt () L(0) = 0 L(x) L(y) L(1) = 1, 0 < x < y < 1 () 0 < L(x) x, 0 < x < 1 x = (x, = 1, 2,, ) F = (/, = 1, 2,, ) s xy G CV(x) R XF G = CV (x) R XF X = {x 1, x 2,, x } x = 1 x ( ) x x j,, j = 1, 2,, ()D D = 1 2 x x j = 2 2 x x j,j,j 2 {(, j);, j = 1, 2,, } <j ( 1)/2 { < j;, j = 1, 2,, } G G = D 2x {x 1, x 2,, x } (order statstcs) <j x (1) x (2) x () ( ) <j x x j = x 1 x 2 + x 1 x 3 + + x 1 x + x 2 x 3 + + x 2 x + + + x 1 x = ( ) x (2) x (1) + ( ) x (3) x (1) + + ( ) x () x (1) + ( ) x (3) x (2) + + ( ) x () x (2) + + + ( ) x () x ( 1) 17
<j x x j = ( 1)x () + (( 2) 1) x ( 1) + + (1 ( 2)) x (2) + (0 ( 1)) x (1) = x () ( + 1)x () = 2 x () ( + 1)x = 2 ( x () x ) x = x () = x, = ( + 1)/2 x = (x (1), x (2),, x () ) F = (F ) = F = 1 s 2 F = s F F = ( 1 2) (F F j ) 2 <j 2 s XF = = = = + 1 2 1 1 (x () x)(f F ) ( 1 1 (x () x) + 1 ) ( ) 2 1 1 (x () x) X F ρ ρ = s XF s X s F = 1 1 D = 4 2 ( x () x ), (x () x) D 4 = ( 1, 2,, ) = 1 1 (F F ) 2 = + 1 12 ( ) ( / ) + 1 s X 12 ( ) (x () x) = S xy G = D 2X D = ( 1 ) 4 x () x (j) = ( x () x ) ( 1) 2 <j D 2x = 2 ( ) (x () x) = 2 ( 1)x x s XF = 2 x ρs Xs F = 2 + 1 + 1 x ρs X 12 = ρcv (X) 3 + 1 3 0.577 G G =,j x x j / 2 2x = 1 2 x x x j 0.577ρCV <j 18
8 R-2 1 / LINEST X Y (1 Y a X + b Y = a X b Y = a e X Y = a logx R2 OK 9 R2 0.5 0.8 0.8 R2 2 [ ] Mcrosoft Offce Excel ( : Offce ) Mcrosoft Offce Excel Excel (Mcrosoft Offce ) [Excel ] [ ] [ ] [Excel ] 1. 2. 3. R-2 R Y 2 (X 1, X 2,, X ) b Y a 1 X 1 + a 2 X 2 + + a X + b A (Y ) B (X 1 ) C (X 2 ) b Y a 1 X 1 + a 2 X 2 + b a 1, a 2, b 19
11 10 A B C 1 Y X1 X2 2 10 18 10 3 12 17 11 4 3 3 2 5 14 26 15 6 4 7 5 7 10 18 9 8 6 10 6 9 11 15 13 10 8 15 7 11 11 14 14 R 0.98 R2 0.96 R2 0.95 0.78 10.00 F 2.00 110.61 55.31 90.29 0.00 7.00 4.29 0.61 9.00 114.90 t P - 95% 95% 95.0% 95.0% 0.82 0.65 1.26 0.25 0.72 2.36 0.72 2.36 X 1 0.25 0.07 3.53 0.01 0.08 0.42 0.08 0.42 X 2 0.49 0.11 4.47 0.00 0.23 0.74 0.23 0.74 20
12 Y = 0.25 X 1 + 0.49 X 2 + 0.82 2 Y 2 X P P 0.05 X 0 t p 0 0 0 Y X (1) P (T t) < (2) t < t t tv t = tv 5%(0.05) 1%(0.01) k 1 k tv 2 5% 0.1 2 t P NG 21
3 0.7 R2 0.5 R2 R2 R2 R2 AIC 9 http://www.stat.go.jp/data/dex.htm http://www.pref.chba.jp/outle/statstcs/dex-j.html 22