久留米.ppt
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1 Excel n i a i a 2S S = P (x i Äa) 2 a S 2 3 S = 8a 2 Ä 96a = 8(aÄ6) = n(aäx) 2 + S; se = p V =n 4 S V se se S+V S+FV F = F(1; nä 1; 0:05) =t(nä 1;0:05) aa, b nx nx S = (y iäby i) 2 = (y iä (a+ bx i)) 2 i=1 i=1 5 6
2 7 8 S a, b 9, 10 ExcelLINEST a,b LINEST b b
3 b q q V se(by) = e 60 = 14:643=6 60 = 0:201 LINEST b a =4 b b a S S q q Ve se(by) = = 14:643=6 = 0: LINEST b Se+ Ve= = Se+F Ve= *2.441 =29.25 a,b S S 17 18
4 y=8 x 8 y=8 x 8 =(8-a)/b=(8-3.96)/1.36=2.974 y = a + bx (1) y = 8 + b(xä x8) (2) x 8 Excel x 8 x 8 Se= y=8 y-hat x8 S+V y =a +bx (1) y = 8 + b(xä x8) = 8 + bxä bx8(2) a, b 1 bx 8 24
5 x y y = ab x ; log(y) = log(a) + log(b)x = ax b ; log(y) = log(a) +alog(x) ab x ax b log(y) log(x) log(y) a,b 27 +c ab x b<1 y = y 1 + (y 0 Ä y 1 )b x = y1 + (y0ä y1)exp(bx) 28 y
6 Box-Cox p y* y* p p= y É = yp Ä 1 p 31 ( T y = A exp Ä Å ÄE RT 32 x0 y0 bl br x0 1000/ =277K 33 S ( ( 34 y maxäy min y = y min exp(ä(a + bx)) max y min y = = y max 1 + exp(ä(a + bx)) y max 1 + exp(äb(xäx 50 )) x= 50 =2 y=y max /2 a (1) (2) 35 Emax y = EmaxÅxç x ç +EC ç 50 y = = E max 1 + ECç 50 x ç E max 1 +exp(ç(ln(ec 50)Äln(x))) 36
7 Emax Michaelis-Menten x Michaelis-Menten b=1 y max y = 1 + exp(äb(ln(x)äln(x 50))) x ln(x) log(x) y-hat=ymax/(1+exp(-b*(ln(x)-ln(x50)))) B A Bx A y A = f (x) = g(ln(x)) y B = f (cçx) = g(ln(c) + ln(x)) x x Emax c=2 A 0.192, 0.48, 1.2, 3 4 y B A A , 0.98, 2.4, 6 4 ymin ymax bd50 c 41 42
8 y maxäy min by A = y min exp(äb(ln(x)ä ln(x 50 )) by B = y maxäy min y min exp(äb(ln(cx)äln(x 50 )) 43 AB A,B5, =12 44 A=4 B=2 (18+20)/2=19 22 A=6, B=3 (19+22)/2= , A,B A B d x A B dx A B 46 0, 1, 2, 3, 4,
9 Excel y =y inf Ä (y inf Äy 0 ) exp(bx) x=0 y 0 y 0 y = y inf B R2= y inf B 4 52 t=0 x x 0 dy dx = (y0ä y1)bebx ) (y 0Ä y 1)B (x = 0) c B c B = y 0 Äy 1 53 B y 0 y inf Se y :00175=3 F = 0:01872=(24Ä9) ô 0:6 54
10 <p<2) p Gauss-Newton 59 60
11 n=10 f= = =0.2 f= = n=10 p=f/n 65 p-hat=1/(1+exp(-(a+b*ln(x)))) -2ln(L)=-2*LN(BINOMDIST(f, n,p-hat,false)) p-hat=1/(1+exp(-b*(ln(x)-ln(x50)))) 66
12 2 p-hat 1 bp = 1 + exp(ä(a + bln(x))) 1 bp = 1 + exp(äb(ln(x)äln(x 50)) 2-2ln(L)) 2 Excel =BINOMDIST(f, n,, FALSE) p-hat -2ln(L) L L p=f/n z=ln(p/(1-p)) a+bx 2 z=b(x-x 50 ) % ~ % 0 Excel VBA R, S Excel 72
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1234567 0.1234567 = 2 3 =2+3 =2-3 =2*3 =2/3 =2^3 1:^, 2:*/, 3:+- () =2+3*4 =(2+3)*4 =3*2^2 =(3*2)^2 =(3+6)^0.5 A12 =A12+B12 ( ) ( )0.4 ( 100)0.9 % 1 2 Excel =sum( ) =average( ) B15:D20 : $E$26 E26 $ =A26*$E$26
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漸化式のすべてのパターンを解説しましたー高校数学の達人・河見賢司のサイト
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