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Al &al&ular el de%er(inan%e de la (a%riz de &orrela&ión pode(os sa-er sies posi-le o no .a-lar de (ul%i&olinealidad 'a /ue es%a es%* presen%e&uando el de%er(inan%e es o %iende a &ero 1n es%e &aso se puedeo-servar /ue el de%er(inan%e es 0,03 lo /ue ade(*s se ve a+e&%adopor -a4os &oe+i&ien%es en la (a%riz ' un %a(ao de (ues%ra grande 6or lo an%erior pode(os de&ir /ue puede /ue no e7is%a (ul%i&olinealidaden%re los da%os

Al analizar el gra+i&o de &orrela&ión pode(os ver /ue ninguno de los&oe+i&ien%es es (a'or a 0,5 lo /ue se puede a%ri-uir al %a(ao de(ues%ra

Con respe&%o al gr*+i&o de dispersión de puede de&ir /ue no se vening8n %ipo de pa%rón lineal en%re las varia-les independien%es, seo-serva (u&.a varia-ilidad

-$ 9a varia-le /ue (enos in+luen&ia y es a/uella /ue al a4us%ar el (odelo&o(ple%o presen%a un (enor valor de %, ' la /ue (*s in+luen&ia a la

respues%a es a/uella &on uno (a'or 6ode(os en%on&es de&ir /uea/uella /ue (enos in+luen&ia es x5 , lo &ual se ve sopor%ado por la

(a%riz de &orrela&ión

9a varia-le /ue (*s in+luen&ia es x7 , lo &ual se puede ver no solo en

la (a%riz de &orrela&ión sino %a(-ién al .a&er las prue-as para el(odelo de y dependiendo de &ada una de las varia-les por separado,donde un (a'or : represen%a una &on (a'or in+luen&ia so-re larespues%a

&$Modelo de Regresión 9ineal M8l%iple a4us%ado

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̂y=0,2745+1,1497 x1+1,6941 x

2+1,9266 x

3+1,8753 x

4+1,0739 x

5+1,6173 x

6+1,8379 x

7

d$

;igni+i&an&ia glo-al H

0:Todos los β j=0

H 1: Almenos un β j ≠0

F 7,192=250,valor p

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1n -ase al valor p pode(os op%ar por re&.azar H 0 , por lo /ue

pode(os &on&luir /ue el (odelo &o(ple%o es -ueno en %ér(inos de /ue

al (enos un β j es di+eren%e de &ero

;igni+i&an&ia Marginal

H 0: β

1=0

H 1: β

1≠0

t 0,25;192=10,677 ,valor p

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H 0: β

5=0

H 1: β

5≠0

t 0,25;192=8,947 ,valor p=3,1 x10−16

1n -ase al valor p pode(os op%ar por re&.azar H 0 , por lo /ue

pode(os &on&luir /ue el &oe+i&ien%e β5 es signi+i&a%iva(en%e di+eren%e

de &ero ' por %an%o es i(por%an%e para el (odelo

H 0: β

6=0

H 1: β

6≠0

t 0,25;192=15,123 ,valor p

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9os resul%ados presen%ados por es%as prue-as son &onsis%en%es &onnues%ras o-serva&iones ini&iales, es de&ir no se presen%a(ul%i&olinealidad grave en el (odelo 'a /ue se ve /ue el

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g$ A.ora realiza(os backwards elimination para &o(pro-ar lo di&.o

an%erior(en%e por (edio del (é%odo de %odas las regresiones posi-les Al ver los da%os arro4ados por el progra(a pode(os &on&luir /ue es%ose+e&%iva(en%e apo'an %odas las de&isiones %o(adas an%erior(en%e, esde&ir no .a' dis&repan&ia 'a /ue el (é%odo nos arro4a un (odelo&o(ple%o &o(o .a-ía(os es%a-le&ido /ue de-ería ser, &on los (is(os Bpara &ada varia-le en&on%rados al .a&er el (odelo de regresión lineal(8l%iple &o(ple%o

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.$

Al o-servar la gr*+i&a an%erior pode(os o-servar /ue .a' ! valoresa%ipi&os 6ara sa-er si son in+luen&iales se &al&ulan las (edidas de

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in+luen&ia para &ada uno &on lo /ue &on&lui(os /ue ninguno de es%os esreal(en%e in+luen&ial

)r*+i&as para los supues%os so-re residuales

or(alidad H

0: el error seajustaa una distribui!n normal

H 1: elerror no seajusta a una distribui!nnormal

1s%o lo pode(os &on&luir en -ase al gra+i&o D, al ver /ue es%epresen%a una +or(a lineal posi%iva op%a(os por no re&.azar Ho 'a /uees%o indi&a nor(alidad 9o /ue &o(pro-a(os al .a&er la prue-a de;.apiroDEilF ' el valor p /ue es%a nos arro4a

=ndependen&ia H

0: los errores sonindependientes

H 1: los errores son dependientes

Respe&%o a la independen&ia pode(os o-servar /ue en el gr*+i&o AC:solo uno de los valores so-repasa los lí(i%es, sin e(-argo es%o no lo.a&e por (u&.o ' al ver el gra+i&o 6AC: &o(pro-a(os /ue se puedede&ir /ue es%o es po&o signi+i&a%ivo ' así op%ar por no re&.azar Ho,&on&lu'endo /ue los residuos son independien%es

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1l segundo es el in%ervalo de predi&&ión para dados valores de x &on el de &on+ianza

4,787127 $ E[ y∨ x ]$8,542351

Ejercicio 2

a$

̂y=1,9483(1−e−e−(−1,2699+14,3631 x)

)

" =0,1025

-$

&$

̂y=1,9483(1−e−e−(−1,2699+14,3631 x )

)

̂y=1,9483 (1−e−e−(−1,2699+14,3631 (0) )

)=1,9483 (1−e−e1,2699

)=1,89292014

1s%o indi&a /ue &uando el grosor del &a-le %iende a &ero, su sensi-ilidad%iende a ",2

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d$ =n%ervalo de &on+ianza del 5 para β1 ' β2

0,927727 $ β1

$2,968873

−2,7409$ β2$0,2011

=n%ervalo de &on+ianza del 0 para I

%̂1=0,927727 (1−e−e

2 ,7409

)=0,927726828

%̂2=0,927727 (1−e−e

−0,2011

)=0,5182393009

%̂3=2,968873 (1−e−e

2,7409

)=2,96887245

^%4=2,968873 (1−e−e−0,2011

)=1,658447655

0,5182393009$ %̂$2,96887245

Ejercicio 3

a%os

J7i%oG e(-rión nor(al

5 e7peri(en%os

6ri(ero@ dosisG 2,5> %a(ao de (ues%raG !> é7i%osG0,5?!$G"

;egundo@ dosisG 5> nG!> é7i%osG0,5?!$G!3

Ter&ero@ dosisG "0, nG!!> é7i%osG0,?!!$G2

Cuar%o@ dosisG 25> nG5> é7i%osG"?5$ G5

uin%o@ dosisG50> nG2> é7i%osG"?2$G2

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lo&it (%̂ )=−0,3386+0,3120 x

%̂= 1

1+e(0,3386−0,3120 x)

Cuando la dosis es igual a pg la pro-a-ilidad de o-%ener un e(-rión nor(al,es de&ir &on 2 o4os, es de@

%̂= 1

1+e(0,3386−0,3120(8))=0,8963

Anexos, códigos en R

#Codigo %aller &o(pu%a&ional 2a, e4er&i&io ", R9M

sour&e?L.%%ps@dldrop-o7user&on%en%&o(u0"0genera%eda%aRL$da%os?20005!!"$

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r(?da%os$

d ND read%a-le?LOsersAR1Ao&u(en%sda%os20005!!"%7%L, .eader GTRO1$

.ead?d$

#(a%riz de &orrela&ion

&or?d$

de%?&or?d$$

## es%o per(i%e (e4orar el gra+i&o de &orrela&ion

panel&or ND +un&%ion?7, ', digi%s G 2, pre+i7 G LL, &e7&or, $

P

usr ND par?LusrL$> one7i%?par?usr$$

par?usr G &?0, ", 0, "$$

r ND a-s?&or?7, '$$

%7% ND +or(a%?&?r, 0"2!35$, digi%s G digi%s$Q"

%7% ND pas%e0?pre+i7, %7%$

i+?(issing?&e7&or$$ &e7&or ND "5

%e7%?05, 05, %7%, &e7 G "5$

S

##)ra+i&o de Correla&ion

pairs?d, loerpanel G panels(oo%., upperpanel G panel&or, las G "$

##)ra+i&o de disperion

pairs?d$

##Modelo de R9M

( ND l(?' U 7" V 72 V 7! V 73 V 75 V 7 V 7, da%a G d$

su((ar'?($

##(odelo de regresion (arginal

#7"

(" ND l(?' U 7", da%a G d$

su((ar'?("$ # es%o nos per(i%e ver los -e%as

#72

(2 ND l(?' U 72, da%a G d$

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su((ar'?(2$

#7!

(! ND l(?' U 7!, da%a G d$

su((ar'?(!$#73

(3 ND l(?' U 73, da%a G d$

su((ar'?(3$

#75

(5 ND l(?' U 75, da%a G d$

su((ar'?(5$

#7

( ND l(?' U 7, da%a G d$

su((ar'?($

#7

( ND l(?' U 7, da%a G d$

su((ar'?($

#%odos los %ér(inos sin in%era&&iones( ND l(?' U 7" V 72 V 7! V73 V 75 V 7 V 7, da%a G d$

su((ar'?($

anova?($

##pa/ue%e W&arW

i+?re/uire?&ar$$ ins%allpa&Fages?L&arL$

li-rar'?&ar$

##

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re/uire?leaps$

##(e%odo de %odas las regresiones posi-les

%odas ND regsu-se%s?' U , da%a G d, n-es% G "2, reall'-igG TRO1$

resul%ado ND su((ar'?%odas$ou% ND i%.?resul%ado, &-ind?.i&., rs/, rss, ad4r2, &p, -i&$$Q,D"

p ND ro;u(s?ou%Q,"@5$

ou% ND da%a+ra(e?(odelo G "@RZE?ou%$, p, ou%$

ou%

#-a&Fards eli(ina%ion

(-a&F ND s%ep?(, dire&%ion G W-a&FardW$

su((ar'?(-a&F$

##analisis residual

#gra+i&a(en%e

par?(+ro G &?2, 2$$

plo%?($

##residuales &rudos vs &ada varia-le

# residualesr ND residuals?($

# vs 7"

par?(+ro G &?", !$$

plo%?d[7", r, las G ", 'la- G WResidualW, (ain G L\n\n7"L$

a-line?. G 0, &ol G 2, l%' G 2$

# vs 72

plo%?d[72, r, las G ", 'la- G WResidualW, (ain G L\n\n72L$

a-line?. G 0, &ol G 2, l%' G 2$

# vs 7!

plo%?d[7!, r, las G ", 'la- G WResidualW, (ain G L\n\n7!L$

a-line?. G 0, &ol G 2, l%' G 2$

# vs 73


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a-line?. G 0, &ol G 2, l%' G 2$

# vs 75


a-line?. G 0, &ol G 2, l%' G 2$# vs 7


a-line?. G 0, &ol G 2, l%' G 2$

# vs 7


a-line?. G 0, &ol G 2, l%' G 2$

##residuales es%uden%izados vs &ada varia-le

# vs 7"

par?(+ro G &?", !$$

r ND rs%uden%?($

plo%?d[7", r, las G ", 'la- G WResidualW, 7la- G LL, (ain G L\n\n7"L$

a-line?. G 0, &ol G 2, l%' G 2$

# vs 72plo%?d[72, r, las G ", 'la- G WResidualW, 7la- G LL, (ain G L\n\n72L$

a-line?. G 0, &ol G 2, l%' G 2$

# vs 7!

plo%?d[7!, r, las G ", 'la- G WResidualW, 7la- G LL, (ain G L\n\n7!L$

a-line?. G 0, &ol G 2, l%' G 2$

# vs 73

plo%?d[73, r, las G ", 'la- G WResidualW, 7la- G LL, (ain G L\n\n73L$

a-line?. G 0, &ol G 2, l%' G 2$

# vs 75


a-line?. G 0, &ol G 2, l%' G 2$

# vs 7


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a-line?. G 0, &ol G 2, l%' G 2$

# vs 7


a-line?. G 0, &ol G 2, l%' G 2$##dis%an&ia de CooF

# gra+i&o

par?(+ro G &?", "$$

plo%?(, .i&. G 3, las G "$

# valores

&ooFsdis%an&e?($

## (edidas de in+luen&ia

in+luen&e?($

##valida&ion de supues%os

# nor(alidad

s.apiro%es%?r$

# a&+ ' pa&+

par?(+ro G &?", 2$$a&+?r, las G ", (ain G LL$

pa&+?r, las G ", (ain G LL$

# (edia

(ean?r$

##in%ervalo &on+ianza

predi&%?(,da%a+ra(e?7"G0"5 , 72 G 05 , 7!G0 , 73G0 , 75G "23! , 7G

0 , 7G0$, in%ervalG L&on+iden&eL, &on+levelG0$

##in%ervalo de predi&&ion

## &ual es el valor esperado de Y &uando 7"G0"5, 72 G 05, 7!G0, 73G0,75G "23!, 7G 0, 7G0]

predi&%?(, da%a+ra(e?7"G0"5 , 72 G 05 , 7!G0 , 73G0 , 75G "23! , 7G0 , 7G0$, in%ervalGLpredi&%ionL, &on+levelG0$

#Codigo Taller &o(pu%a&ional 2a, e4er&i&io 2, R9#=ngresar da%os

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7NDse/?005,020,-'G00"$

s.o?7$

'ND&?"5","3,"3,"3!,"!5,"",0,05,05,03,05,05,052,05!,03,050$

dNDda%a+ra(e?7,'$

#1s%i(ar

ANDnls?'U-e%a"^?"De7p?D?e7p?D?-e%a2V-e%a!^7$$$$$, s%ar%Glis%?-e%a"G",-e%a2GD"2,-e%a!G"3!$,da%aGd$

su((ar'?A$

#)ra+i&o

i%.?d, plo%?7,', lasG"$$

poin%s?d[7,predi&%?A$, %'peGWlW,&olG"3$

#Codigo Taller &o(pu%a&ional 2a, e4er&i&io !, R9

#=ngresar los da%os

da%osNDda%a+ra(e?7,'$

'ND&?",",",",",",",",",",",",",",",",",",",0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,",",",",",",",",",",",",",",",",",",",",",",",",",",",",",",",",",",0,0,",",",",",",",",",",",",",",",",",",",",",",",",",",",",",0,0,0,0,",",",",",","$

7ND&?25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,"0,25,25,25,25,25,50,50$

## nu(ero de "0

i%.?da%os, %a-le?'$$

## propor&iones

prop%a-le?i%.?da%os, %a-le?'$$$

##(odelo

(NDgl(?'U7, da%aGda%os,+a(il'G-ino(ial$

su((ar'?($

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