Expo Bio Gompertz

7/23/2019 Expo Bio Gompertz

1/25

DETERMINACION POR DCCR

Numero de factores (n) 2

1.414213!

san"ua#a

$%

&a'or a'fa ()

- 2 0- 0 " 2

- 0 " 1

0 " 0

0 " 1

0 " 2

0 " 3

0 " !

0 " 5

0 " 6

0 " 7


2/25

M o d e l : Y A = a * e x p ( - e x p ( b - c * T A ) )

y = ( , 6 1 0 8 5 7 ) * e x p ( - e x p ( ( 2 , 7 2 3 3 3 ) - ( , 0 3 0 3 9 5

: 1

: 2

: 3

: !

: 5

: 6

: 7

: 8

- 2 0 0 2 0 ! 0 6 0 8 0 1 0 0 1 2 0 1 ! 0

T A

- 0 " 2

- 0 " 1

0 " 0

0 " 1

0 " 2

0 " 3

0 " !

0 " 5

0 " 6

0 " 7


3/25

( b - c * T A ) )

3 ) - ( , 0 3 0 3 9 5 ) * x ) )

: 8

: 9

: 1 0

: 1 1

: 1 2

1 2 0 1 ! 0 1 6 0 1 8 0 2 0 0 2 2 0


4/25

Tiempo (h) N1 Log (N/No) N2 Log (N/No)

3 . 3 .

3! 2 *.14!1 3 *.!!+

4, 3 *.!!+ 3 *.!!+

! 4 .1+1 4 .,

-2 .14+ .14++! ! .2341 - .31

1, - .331 , .3+

12 + .433- 1 .4--1

144 1 .4--1 12 .31

1!, 14 .!21 12 .2,

1+2 12 .2, 12 .2,

24 14 .!21 13 .!++

21! 13 .!++

22,

24

Ensayos pH Umax TG

1 -.2+ 2.44 .1+ 3-.33234

2 -.2+ 4.! .23 3.!--,3

3 ,.-1 2.44 .2 2,.23-3,

4 ,.-1 4.! .2 2,.2,+-,

- 3. 0.022 31.5734

! + 3. 0.020 34.!2143

- , 2 .2, 24.,+2+

, , .2 2-.+11!

+ , 3. 0.037 1!."411!

1 , 3. .2 13.2141

11 , 3. .43 1!.112-1

12 , 3. 0.04! 14.41!45

#a$ame%$o&e'oia e $eimien%o (Umax)

*oe+ien%e # *oe+ien%e #

Intercepci 125!"801 0"00! -1"689!! .1,

(1) pH (L) -286"390 0"00! 0"!0177 .1,

pH (Q) 16"630 0"005 -0"02!76 .1,

(2) CS (L) -18"837 0"339 0"07091 .1!4

CS (Q) -0"550 0"619 -0"00859 .34

1L by 2L 3"061 0"202 -0"00135 .---

,-E L-G

Std.Err. Pure Err t(3) p

M $% & 125! 801 15! !7!1 8 1231 0 003900

*onen%$aionsangaa ()

,ase 'ag ()

RegressnCoeff.


5/25

(1)p () -286"390 36"3297 -7"8831 0"00!25!

p (*) 16"630 2"231! 7"!530 0"005001

(2)+ () -18"837 16"5891 -1"1355 0"338683

+ (*) -0"550 0"9936 -0"5531 0"618768

1 by 2 3"061 1"8789 1"6291 0"201782

A,= 124.,1*2,!.3+$%/1!.!3$%$%*1,.,3-C*.

&EL*- E *E*6ENT (Umax)

Std.Err. Pure Err t(3) p

Mea#$%#&e'c" -1"689!! 0"359!!7 -!"70012 0"018220

(1)p () 0"!0177 0"08!536 !"75262 0"017679

p (*) -0"02!76 0"005192 -!"76858 0"017518

(2)+ () 0"07091 0"038601 1"83695 0"16353!

+ (*) -0"00859 0"002312 -3"71501 0"03392!

1 by 2 -0"00135 0"00!372 -0"309!6 0"777222

RegressnCoeff.


6/25

N3 Log (N/No) N4 Log (N/No)

3 . 3 .

3 *.!!+ 2 *.14!1

! .2!,, 4 .,

- .31 ! .2341

- .31 , .3+1 .4--1 , .3,4

1 .4--1 11 .4+-3

11 .1!! 12 .2,

14 .!21 1! .!!1

1! .!!1 1 .!32

13 .!++ 1 .!4!3

1 .4--1 1 .!4!3

1 .!4!3

1, .-112

a

!.- 0"61 2"72 0"03

-.,+ 0"57 3"29 0"0!

3.-3 0"57 2"33 0"0!

41.13 0"66 2"53 0"0!

"4.04 0.556 3.529 0.039

55.!5 0.644 2.727 0.031

4.-4 0"53 3"16 0"05

43.3- 0"58 2"87 0"0!

37.14 0.644 3.145 0.058

43.,2 0"62 !"69 0"08

42.- 0"63 3"89 0"07

41.21 0.62 4.20 0.08

Tiempo e gene$aion (TG) *$eimien%o maximo (a)

*oe+ien%e # *oe+ien%e #

131,.- .2 .2,+2 .!+

*3.+3- .2 .11-++ .41

1,.24 .2 *.113, .1!+

*3.!42 .3 *.13!124 .11-

.-, .+ *.2,+4 .

2.22, .24+ .43+12 .,

TE6# E GENE-*N (TG)

-95! Cnf."#$t %95! Cnf."#$t

763 195 17!6 !06 M $% &


7/25

-!02"007 -170"772 (1)p ()

9"529 23"732 p (*)

-71"631 33"957 (2)+ ()

-3"712 2"613 + (*)

-2"919 9"0!0 1 by 2

C/3.!1$%C

#8L-*N 6-96- (a)

-95! Cnf."#$t %95! Cnf."#$t

-2"83336 -0"5!552! Mea#$%#&e'c"

0"1327! 0"670798 (1)p ()

-0"0!128 -0"008235 p (*)

-0"0519! 0"193755 (2)+ ()

-0"01595 -0"001231 + (*)

-0"01527 0"012561 1 by 2


8/25

N5 Log (N/No) N" Log (N/No) N7 Log (N/No)

3 . 3 . 3 .

2 *.14!1 3 *.!!+ 3 *.!!+

4 .1+1

3 . 4 ., .1+!3

4 .1+1 4 .1+1 - .331! .2341 - .31 1 .4+

, .3+ + .433- + .433-

, .3,4 + .412 1 .4--1

12 .2, 11 .1!! 13 .!++

11 .4+-3 12 .31 12 .31

1 .!4!3

1 .!4!3

1 .!4!3

1 .!32

Umax TG a

0"973 56"70 0"019 3-.33 .!1

0"991 57"89 0"023 3.!, .-

0"950 30"88 0"025 2-.+, .!

0"97! !1"13 0"025 2,.2+ .!!

0.969 66"55 0"02! 2+.4 .

0.991 62"16 0"023 2+.+3 .!3

0"985 !0"7! 0"028 24.,! .3

0"97! !3"37 0"025 2-.+1 .,

0.986 39"11 0"0!3 1!.24 .!2

0"983 !3"82 0"052 13.21 .!2

0"980 !2"07 0"0!3 1!.11 .!3

0.!2 !0"!1 0"0!! 1.+ .!4

Std.Err. Pure Err t(3) p -95! Cnf."#$t %95! Cnf."#$t

1318 570 128 !876 10 2622! 0 001973 909 665 1727 !75

RegressnCoeff.


9/25

-300"937 30"2181 -9"95881 0"00215! -397"10! -20!"769

18"2!5 1"8560 9"83028 0"002238 12"338 2!"151

-53"6!2 13"798! -3"88753 0"030171 -97"55! -9"729

5"078 0"8265 6"1!!92 0"008669 2"!!8 7"709

2"228 1"5628 1"!2558 0"2!9227 -2"7!6 7"201

Std.Err. Pure Err t(3) p -95! Cnf."#$t %95! Cnf."#$t

0"250892 0"580772 0"!3200 0"69!910 -1"59738 2"099169

0"117959 0"136588 0"86362 0"!51320 -0"31672 0"5526!3

-0"015138 0"008389 -1"80!50 0"168917 -0"0!18! 0"011560

-0"13612! 0"062370 -2"18253 0"117071 -0"33!61 0"06236!

-0"02859! 0"003736 -7"65!56 0"00!631 -0"0!0!8 -0"016706

0"0!3912 0"00706! 6"21627 0"008391 0"021!3 0"066393

RegressnCoeff.


10/25

N! Log (N/No) N Log (N/No) N10 Log (N/No)

3 . 3 . 3 .

3 *.!!+ 3 . 3 *.!!+

4 ., 4 .1+1 4 .,

.14+ , .3,4 , .3+

- .31 1 .4+ 1 .4--1+ .412 11 .1!! 11 .4+-3

1 .4--1 13 .!++ 13 .,!3

12 .2, 14 .!1-3 14 .!21

11 .4+-3 14 .!1-3 14 .!21

11 .1!! 1! .!!1 1! .!-34

1 .4--1 1, .-112 1- .!,!4

12 .2, 1! .!-34 1! .!!1

1! .!-34 1 .!32

1 .!32

1 .!32

e.'e//# oe"

Mea#$%#&e'c" 125!"801

(1) () -286"390

(*) 16"630

(2) () -18"837

(*) -0"550

1 by 2 3"061

++

(1) () 369"!78

(*) !!! 279


11/25

(2) () 29"266

(*) 2"!!6

1 by 2 21"227

ac o 4& 167"927

'e ''o' 23"995


12/25

N11 Log (N/No) N12 Log (N/No)

3 . 3 .

3 *.!!+ 3 *.!!+

4 ., 4 .1+1

, .3+ , .3,4

+ .433- 1 .4+11 .4+-3 11 .1!!

13 .!++ 13 .,!3

14 .!1-3 14 .!1-3

14 .!21 14 .!1-3

1! .!!1 13 .,!3

1- .!++ 1, .-112

1- .!,!4 1! .!!1

13 .,!3

+&d"''" 'e '' &(3) p -95" #"4& 95" #"4&

15!"!7!1 8"12305 0"003900 763"195 17!6"!06

36"3297 -7"88307 0"00!25! -!02"007 -170"772

2"231! 7"!5301 0"005001 9"529 23"732

16"5891 -1"135!8 0"338683 -71"631 33"957

0"9936 -0"55306 0"618768 -3"712 2"613

1"8789 1"62909 0"201782 -2"919 9"0!0

d M+ p

1 369"!782 !6"19523 0"006512

1 !!! 2787 55 5!7!1 0 005001


13/25

1 29"2663 3"65911 0"151696

1 2"!!6! 0"30587 0"618768

1 21"2267 2"65393 0"201782

3 55"9757 6"99855 0"072166

3 7"9982


14/25

-N&- ,ase Lag

SS df &S '

(1)p (") 369"!78 1 369"!782 52"387!2

p () !39"288 1 !39"2876 62"28552

(2)CS (") 29"266 1 29"2663 !"1!959

CS () 2"831 1 2"8312 0"!01!2

1" *+ 2" 21"227 1 21"2267 3"00968", of '#t 167"921 3 55"9738 7"93638

Pure Error 21"158 3 7"0528

/ot, SS 1083"835 11

SS df &S '

6oe'o 1!2.- , 132.,3 1!.!3

esios 21"2 3 -. 6-

To%a' 1083"8 11

a .+,4-,2 !.0

E$$o$ .1+21, 2.0

-N&- TG

SS df &S '

(1)p (") 369"!78 1 369"!782 52"387!2

p () !!!"279 1 !39"2876 62"28552

(2)CS (") 29"266 1 29"2663 !"1!959

CS () 2"831 1 2"8312 0"!01!2

1" *+ 2" 21"227 1 21"2267 3"00968

", of '#t 167"921 3 55"9738 7"93638

Pure Error 21"158 3 7"0528

/ot, SS 1083"835 11

SS df &S '

6oe'o 1!2.- , 132.,3 1!.!3

esios 21"2 3 -. 6-

To%a' 1083"8 11

a .+,4-,2 !.0

E$$o$ .1+21, 2.0


15/25

-N&- Umax

p SS df &S

0"005!!0 (1)p (") 0"0000 1"0000 0"0000

0"00!2!0 p () 0"0010 1"0000 0"0010

0"13!!27 (2)CS (") 0"0000 1"0000 0"0000

0"571360 CS () 0"0006 1"0000 0"0006

0"181178 1" *+ 2" 0"0000 1"0000 0"00000"061371 ", of '#t 0"0000 3"0000 0"0000

Pure Error 0"0001 3"0000 0"0000

/ot, SS 0"0015 11"0000

' t,*, SS df &S

!.!5 6oe'o .14 ,. .2

esios 0"0001 3. .

To%a' 0"0015 11.

a .+234!,,2 2.3

E$$o$ .-!311, 7.7

p

0"005!!0

0"00!2!0

0"13!!27

0"571360

0"181178

0"061371

' t,*,

!.!5


16/25

' p

0"0818 0"7935

26"120! 0"01!5

0"000! 0"9861

15"9387 0"0281

0"1079 0"76!10"2178 0"8787

' ' t,*,

4.5250 !.!452

6-:


17/25

4 & & e d + ' a c e ; a ' 4 a b l e : a

2 a c & o ' / , 1 < l o c / , 1 2 # / M + e / 4 d a l =

; : a

> b / e ' ? e d ? / " ' e d 4 c & e d ; a l e /

2 a c & o ' / , 1 < l o c / , 1 2 # / M + e / 4 d a l = 3 1 , 9 8 6 9 !

; : a / e A

2 5 3 0 3 5 ! 0 ! 5 5 0 5 5 6 0

> b / e ' ? e d ; a l e /

3 0

3 5

! 0

! 5

5 0

5 5

6 0

6 5

7 0

7 5

1'ed4c&ed;

al5e/


18/25

a ' 4 a b l e : a

+ e / 4 d a l = , 0 0 0 ! ! 3 7

0 , 6 5

0 , 6

0 , 5 5

0 , 5

0 , ! 5

0 , !

3 1 , 9 8 6 9 !

5 5 6 0 6 5 7 0

2 a c & o ' / , 1

0 , 5 0 0 , 5 2 0 , 5 !

0 , 5 2

0 , 5 !

0 , 5 6

0 , 5 8

0 , 6 0

0 , 6 2

0 , 6 !

0 , 6 6

0 , 6 8

1'ed4c&ed;

al5e/


19/25

4 & & e d + ' a c e ; a ' 4 a b l e : a

2 a c & o ' / , 1 < l o c / , 1 2 # / M + e / 4 d a l = , 0 0 0 ! ! 3 7

; : a

6 , 8 7 , 0 7 , 2 7 , ! 7 , 6 7 , 8 8 , 0 8 , 2 8 , ! 8 , 6 8 , 8 9 , 0 9 , 2

p

1 , 5

2 , 0

2 , 5

3 , 0

3 , 5

! , 0

! , 5

5 , 0

5 , 5

+

> b / e ' ? e d ? / " ' e d 4 c & e d ; a l e /

2 a c & o ' / , 1 < l o c / , 1 2 # / M + e / 4 d a l = , 0 0 0 ! ! 3 7

; : a

0 , 5 2 0 , 5 ! 0 , 5 6 0 , 5 8 0 , 6 0 0 , 6 2 0 , 6 ! 0 , 6 6 0 , 6 8> b / e ' ? e d ; a l e /


20/25

0 , 6 5

0 , 6

0 , 5 5

0 , 5

0 , ! 5

0 , !8 , 8 9 , 0 9 , 2

y = ( ,

: 1

: 2

: 3

- 2 0 0 2 0 ! 0

- 0 , 2

- 0 , 1

0 , 0

0 , 1

0 , 2

0 , 3

0 , !

0 , 5

0 , 6

0 , 7

0 , 8


21/25

M o d e l : Y A = a * e x p ( - e x p ( b - c * T A ) )

y = ( , 6 5 9 7 2 9 ) * e x p ( - e x p ( ( 2 , 5 2 7 5 9 ) - ( , 0 3 7 1 3 9 ) * x ) )

: 2

: 3

: !

: 5 : 6

: 7

: 8

: 9 : 1 0 : 1 1 : 1 2 : 1 3

: 1 !

2 0 ! 0 6 0 8 0 1 0 0 1 2 0 1 ! 0 1 6 0 1 8 0 2 0 0 2 2 0 2 ! 0

T A


22/25

3

: 1 !

2 0 2 ! 0


23/25

$0c Cc $0 c

-1"00000 -1"00000 -.2+2,+322 2.44

-1"00000 1"00000 -.2+2,+322 4.!

1"00000 -1"00000 ,.--1!-, 2.44

1"00000 1"00000 ,.--1!-, 4.!

-1"!1!21 0"00000 - 3.1"!1!21 0"00000 + 3.

0"00000 -1"!1!21 , 2

0"00000 1"!1!21 ,

0"00000 0"00000 , 3.

0"00000 0"00000 , 3.

0"00000 0"00000 , 3.

0"00000 0"00000 , 3.


24/25

++ d M+

(1) () 369"!78 1 369"!782 !6"19523

(*) !!!"279 1 !!!"2787 55"5!7!1

(2) () 29"266 1 29"2663 3"65911

(*) 2"!!6 1 2"!!6! 0"30587

1 by 2 21"227 1 21"2267 2"65393ac o 4& 167"927 3 55"9757 6"99855

'e ''o' 23"995 3 7"9982

To&al ++ 1090"523 11

++ d M+

MODEO 1!4.,2 - 12.11-1! 22.++!3,-

REIDO 2!.441 4 !.!1243,

TOTA 1+.23 11

R2 .+--3,!

error tota5 .2424!14 6


25/25

p

0"006512

0"005001

0"151696

0"618768

0"2017820"072166

p &abla

.4444+, !.+421+3

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Expo Bio Gompertz