statstcs statstcum (EBM) 2 () : ( )GDP () : () : POS STEP 1: STEP 2: STEP 3: STEP 4: 3 2

Size: px

Start display at page:

Download "statstcs statstcum (EBM) 2 () : ( )GDP () : () : POS STEP 1: STEP 2: STEP 3: STEP 4: 3 2"

はるまさいちぬの
5 years ago
Views:

1 (descrptve statstcs) pvot table

2 statstcs statstcum (EBM) 2 () : ( )GDP () : () : POS STEP 1: STEP 2: STEP 3: STEP 4: 3 2

3 ( ) () ( ) 3.2 3

4 IQ Stanley Smth Stevens 1946 On the theory of scales of measurement 4 Wkpeda, Excel help 4 Frequency Dstrbuton Hstogram QC Wndows MacOS LnuX (McroSoft) OpenOffce.org () 4

5 4.1 sun open-offce calc

6 5 5.1 [] Mcrosoft Offce Excel ( : Offce ) Mcrosoft Offce Excel Excel (Mcrosoft Offce ) [Excel ] [ ] [] [Excel ] CALC No. (cm) (kg) (cm) #N/A

(cm) 3 10 7 BMI ( ) (m) 2 BMI (body mass ndex) 18.5 18.

7 (cm) BMI ( ) (m) 2 BMI (body mass ndex) BMI BMI 3: 5.1 #N/A (Non Avalable) 6 -pvot table A1:A10 7

8 A (1) (4) (1) 200? (2) ? (3) ? (4) ?? (1) A1:A10 (2) []-[] (3) [Excel ] [] [ ] (4) [] $A$1:$A$10 [] [ ] (5) [ ] [] (6) [] (7) [], [OK] (8) [] D1 (9) [] (10) D2 -[] (11) [ ] 200, [ ] 500 [] 100 (12) [OK], : 8

9 4 (tally mark) (Hstogram) x skewness L L L L kurtoss, excess ; leptokurtc ; platykurtc Hstogram 9

10 : Q 1, Q 2, Q 3 Q 1, Q

11 (1) (max) (mn) range (2) (class) Starjes k = 1 + log 2 n = log 1 0n (3) (class wdth) R/k (4) 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/n P 1 = p 1 3 a 1 a 2 x 2 f 2 F 2 = f 1 + f 2 p 2 = f 2/n 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/n P 3 = p 1 + p 2 + p a k 1 a k x k f k F k = n p k = f k /n P k = 1 7 n 1 x = (a 1 + a )/2,( = 1, 2,, k) F k = f 1 + f f k = n, P k = p 1 + p p k = 1 =max() =mn() D2 D6 =frequency, ( A2 A6) CTRL+SHIFT+ENTER E2 =D2 E3 =D2+D3E3 E4 E6 F2 =D2/D$7 frequency (1) 2 (2) 1 (3) (4) 11

12 5 (Boxchart)

13 8 (average,mean) (SD,standard devaton),medan ( (varance) (kurtoss, excess)(bulge ) (skewness) (range) (mn) (max) (sum) (sze) (1) Excel -VBA (2)OK (3) OK n {X, = 1,, n}, sort (Order Statstcs) {X (), = 1,, n} X 1, X 2,, X n X (1) X (2) X (n) X 1 + X X n = X (1) + X (2) + + X (n) X k x 1, x 2,, x k (k ) () x 1 x 2 x k f 1 f 2 f k n p 1 p 2 p k 1 2 f = 1, = 1, 2,, n X = X 1 + X X n = x 1 f 1 + x 2 f x k f k = j x f j, f = f 1 + f f k = n X2 = X2 1 + X X 2 n = x 2 1 f 1 + x 2 2 f x 2 k f k = j x2 j f j, 1 n 1 n X = 1 n (X 1 + X X n ) = x 1 p 1 + x 2 p x k p k = j x j p j, X2 = 1 n (X2 1 + X X 2 n) = x 2 1 p 1 + x 2 2 p x 2 k p k = j x j p 2 j, X = 1 n n =1 X = 1 n k j=1 x jf j = k j=1 x jp j AVERAGE 13

14 SE SE = s = (X X) 2 = X2 nx2 j = x2 j f j nx 2 j = x2 j p j X 2 n n(n 1) n(n 1) n(n 1) n 1 Me Me = X ((n/2)+1) () = X ((n+1)/2) () = medan() 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 (n 1) s 2 s 2 = 1 n 1 VAR n (X X) 2 = ( 1 n ) (X X j ) 2 = n n 1 2 <j =1 VARP (n 1) n v 2 = 1 n n (X X) 2 = 1 n =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 n s 3 SK SKEW 1 ( ) 3 X X n s L L L R L R = max() mn() () MAX x 1, x 2,, x n max x MIN x 1, x 2,, x n mn x SUM x 1, x 2,, x n x n, N COUNTA 95.0% 95% 1/2 95% j=1 14

15 TM(trmmed mean) TRIMMEAN TRIMMEAN(, ) (1) (2) = MD (Mean Devaton) = 1 n X X Z () Z = X X s x ( ( 100) 10Z + 50 X Q 1, Q 2, Q 3 25% 4 25% Q % 3 75% 3 =QUARTILE(, ) (, QUARTILE ) = (0, ), (1, 1 (25%)) (2, 2 = (50%)) (3, 3 (75%)) (4, ) Q 3 Q 1 (dectle) (percentle) ( 4 CV(Coeffcent of Varaton)= s x X ( ) 10% 10% % ± X N(µ, σ 2 ) µ X % ±2 σ

16 (sample covarance): =COVAR( A, B) Cov(x, y) = 1 n 1 = COV AR(x, y ) (X X)(Y Y ) n n 1 2 X, Y 0 1 N COVAR N=2 2 COVAR VARP 2 () () (0 ) (sample correlaton coeffcent): =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,, n s x s y N CORREL PEARSON 2 N 3 16

17 8 CORREL ( PEARSON) ( ) ( ) (0 ) (Speaman s rank correlaton coeffcent) r s = 1 6 (x y ) 2 n(n 2 = 1 1) (x y ) 2 / ( ) n 1 3 x, y 1, 2,, n =[COUNT() RANK(,, 0) - RANK(,, 1)]/2 RANK(,, )

18 2 0 : 2 9: Corrado Gn

12 1 Wkpeda (Gn coeffcent) 100 Gn Index http://www.sustanablemddleclass.com/gn-coeffcent.html Japan 24.9 Unted Kngdom 36.0 Sweden 25.0 Iran 43.0 Germany 28.3 Unted States 46.6 France 32.7 Argentna 52.

19 12 1 Wkpeda (Gn coeffcent) 100 Gn Index Japan 24.9 Unted Kngdom 36.0 Sweden 25.0 Iran 43.0 Germany 28.3 Unted States 46.6 France 32.7 Argentna 52.2 Pakstan 33.0 Mexco 54.6 Canada 33.1 South Afrca 57.8 Swtzerland 33.1 Namba 70.7 ( Bob Sutclffe (2007), Postscrpt to the artcle World nequalty and globalzaton (Oxford Revew of Economc Polcy, Sprng 2004), Retreved on G = L(x)dx = 1/2 1 0 L(x)dx 1/2 or = 1 2 L(x )(.e.l(x) ) L(x) 19

20 y G L (1, 1) y = x L(x)dx (0.8, 0.6) y = L(x) (0.4, 0.2) 0 1 x (0, 0) F (1) = 1, 2,, n x x 1 x 2 x n p = f(x ) p 1 p 2 p n F F 1 = p 1 F 2 = p 2 + F 1 F n = p n + F n 1 = 1 L = j=1 x jf(x j ) / L = L = n j=1 x jf(x j ) L +1 + L (F +1 F ) 2 ( = 1, 2,, n) L 0 = 0 L 1 L 2 L n 1 L n = (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,, n) F = (/n, = 1, 2,, n) s xy G CV(x) R XF G = CV (x) R XF n X = {x 1, x 2,, x n } x = 1 n x ( ) x x j,, j = 1, 2,, n ()D D = 1 n 2 x x j = 2 n 2 x x j,j <j 20

21 ,j n2 {(, j);, j = 1, 2,, n} <j n(n 1)/2 { < j;, j = 1, 2,, n} G G = D 2x {x 1, x 2,, x n } (order statstcs) x (1) x (2) x (n) n ( ) <j x x j = x 1 x 2 + x 1 x x 1 x n + x 2 x x 2 x n x n 1 x n = ( ) x (2) x (1) + ( ) x (3) x (1) + + ( ) x (n) x (1) + ( ) x (3) x (2) + + ( ) x (n) x (2) ( ) x (n) x (n 1) <j x x j = (n 1)x (n) + ((n 2) 1) x (n 1) + + (1 (n 2)) x (2) + (0 (n 1)) x (1) = x () (n + 1)x () = 2 x () n(n + 1)x = 2 ( x () x ) x = x () = nx, = n(n + 1)/2 x = (x (1), x (2),, x (n) ) F = (F ) = F = 1 n s 2 F = s F F = ( 1 n 2) (F F j ) 2 <j 2 s XF = = = n = n + 1 2n 1 n 1 (x () x)(f F ) ( 1 n 1 (x () x) n n + 1 ) ( ) 2n 1 n 1 (x () x) n X F ρ ρ = s XF s X s F = 1 n 1 D = 4 n 2 ( x () x ), (x () x) nd 4 = 21 ( 1 n, 2 n,, n ) n = 1 n 1 (F F ) 2 = n n ( ) ( / ) n + 1 s X n 12n ( ) (x () x) = S xy n

22 G = D 2X D 2x = 2 (n 1)x n D = ( 1 n ) 4 x () x (j) = ( x () x ) n(n 1) 2 <j ( ) (x () x) = 2 n x s XF = 2 x ρs Xs F = 2 n + 1 n + 1 x ρs X 12n = ρcv (X) 3n G = n + 1 3n,j x x j /n 2 2x G = 1 n 2 x x x j 0.577ρCV <j 11 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 R R2 2 (1) (2) (3) R-2 R Y 2 (X 1, X 2,, X n ) b 22

13 Y a 1 X 1 + a 2 X 2 + + a n X n + b A (Y ) B (X 1 ) C (X 2 ) b Y a 1 X 1 +

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.

23 13 Y a 1 X 1 + a 2 X a n X n + 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 10 A B C 1 Y X1 X R 0.98 R R F

24 t P - 95% 95% 95.0% 95.0% X X Y = 0.25 X X Y 2 X P P 0.05 X 0 t p Y X (1) P (T t) < (2) t < t t tnv t = tnv 5%(0.05) 1%(0.01) n k 1 n k tnv 2 5% t P NG 3 24

25 R2 0.5 R2 R2 R2 R2 AIC

26 13 / = 2+3 A2:B10 A2;B10 A2 B10 = (,,, ) 26

27 1 (true) false 1 2 =rand(): 1 27

28 =f =and( 2) =or( 2) =sum( 2) =sumf( ) =count( ) =countf( ), 1 2 {=f(and( 2),, )} {=f(or( 2) )} 2 Ctrl, Shft, Home actve( shft+ ctrl+ arrow key ), nonactve () [] [ ] [ ] /VBA VBA Vsual Basc 3 28

29 , abs() round() nt() sum( 1 2) average( 1 2 ) count( 1 2) counta( 1 2 ) max( 1 2) mn( 1 2) mode( 1 2) medan( 1 2 ) rank() quartle var( ) varp( ) stdev( ) stdevp( ) normdst( ) normnv( ) frequency(, ) = (), % 2 ( ) 25% 50%75% /(n-1) /n populaton varance var standard devaton varp standard devaton of populaton,true true false x nverse (0) 4 29

2 () : ( )GDP () : () : POS STEP 1: STEP 2: STEP 3: STEP 4: 3 2

2 () : ( )GDP () : () : POS STEP 1: STEP 2: STEP 3: STEP 4: 3 2 / //descrptvea1-a.tex 1 1 2 2 3 2 3.1............................................. 3 3.2............................................. 3 4 4 5 9 6 12 7 15 8 19 9 22 1 statstcs statstcum (EBM) 1 2 () : (