ejercicio resuelto de regersion

7/26/2019 Ejercicio Resuelto de Regersion

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EJEMPLO

X Y X Y XY

1 152.00 50.00 23104.0 2500.0 7600.0 7.40

2 155.00 61.50 24025.0 3782.3 9532.5

3 152.00 54.50 23104.0 2970.3 8284.0

4 155.00 57.50 24025.0 3306.3 8912.5

5 157.00 63.50 24649.0 4032.3 9969.5

12

Total 771.00 287.0 118907.0 16591.0 44298.5

promedio 154.20 57.4

Coeficiente de Correlacin

0.92

Coeficiente de Regresin

2.293

_ _

n = 12 X= 154.20 Y= 57.4

_

SC(X =

SC(X = 118907.0 ! 285331.68 = -166424! _ _

S"(XY =

S"(XY = 44298.5 ! 106212.96 = -61"14#

LO $%E &O'PERM()E )E&ER LO' COE*(C(E&)E' +E a ,

L%E.O/

#= !61914.5 = 0!2!166424.7

X2 ! n (X2 =

XY n(X (Y =

=/n))y(-y/n)()x(-x(

y/nx-xy=r2222

yx

=/n)x(-X

y/nx-xy=b 22yx


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a= 57.4 ! 0.372 $ 154.20 =

(&)ERPRE)&+O

E&)O&CE' L EC%C(O& +E L RE.RE'(O& E')(M+ E'/

Y = !75.446 % 0.8676 X

Y = 0.03 % 0.372 X

Coe&i'iente de 'orrela'in ) 0.92

0.372

*l +alor de # = 0.868 indi'a el in'remento del pe,o en -iloramo,/ en promedio/

*l +alor de a/ no tiene interpreta'in pr'ti'a en el eemplo/ ,e interpretara 'omo

na a talla de 180 ,e o#tiene n pe,o de 80.7 -.

Cnto ,e e,pera e pe,e (en promedio na per,ona e mide 1.60 m

Se o#tene)

Y= 0.03 % 0.372 $ 13000 =

a e'a'in de ere,in ineal e,timada para la, +aria#le, e,tatra pe,o me,tran/

)rataiento 2

$5incena P

X Y X Y XY

1 2 14.0 4.0 196.0 28.0 43

2 3 20.0 9.0 400.0 60.0 76

3 5 32.0 25.0 1024.0 160.0 109

Coe&i'iente de determna'in 2)

por 'ada 'entmetro de amento en la e,tatra de lo, ;om#re, adlto,.

el +alor o#tenido/ en promedio/ para el pe,o Y/ 'ando la e,tatra e, 0.

S,titendo el +alor de inter>, en la e'a'in)


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4 7 42.0 49.0 1764.0 294.0 142

5 8 44.0 64.0 1936.0 352.0 ?*:@

25 152.0 151.0 5320.0 894.0

5


0.99


5.57

25 = 5

"rom. X 5

152.0 = 30.4

"rom. Y 5

5.2

30.2 25 5.2

1064 924.16 139.84

178.8 152 26.8

X ! 5 = 0.192 ( ! 3 X= 0.192 ! 0.76

Y ! 30.4 5.15 (A ! 5 Y= 5.15A % 4.65

= (5.15 A 6 % 4.65 = 35.55 B

2x

2x = ! =

2y ! =

2xy ! =

=/n))y(-y/n)()x(-x(

y/nx-xy=r

2222yx

=/n)x(-X

y/nx-xy=b 22yx


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)rataiento

)rtaiento 2

$5incena P

X Y X Y XY

1 60 3.1 3600.0 9.6 186.0

2 61 3.6 3721.0 13.0 219.6

3 62 3.8 3844.0 14.4 235.6

4 63 4.0 3969.0 16.0 252.0

5 65 4.1 4225.0 16.8 266.5

311 18.6 19359.0 69.8 1159.7

5


0.91


0.19

"ara en'ontrar la e'a'in de rere,in/ lo primero e ,e en'entra pen

,arla para &ormar la e'a'in de rere,in.

"a,o 1)Cente el nmero de +alore,D = 5

"a,o 2)E,'ar XY/ X2

Con,lte la ta#la ,iiente

$5incena P

X Y

60 3.1

61 3.6

62 3.8

63 4.0

65 4.1

311 18.6

5

"a,o 3)E,'ar FX/ FY/ FXY/ FX2.FX = 311

=/n))y(-y/n)()x(-x(

y/nx-xy=r

2222yx

=/n)x(-X

y/nx-xy=b 22yx

=/n))y(-y/n)()x(-x(

y/nx-xy=r

2222yx

=/n)x(-X

y/nx-xy=b 22yx


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FXY = 1159.7

FX2 = 19359

"a,o 4)Splente en la &rmla de la pendiente por en'ima de deter

Slope(# = (DFXY ! (FX(FY G (DFX2 ! (FX2

= (5798.5 ! 5784.6G(96795 ! 96721

= 13.9G74

= 0.19

"a,o 5)H;ora/ de ne+o ,plente en la &rmla anterior inter'eptar

Inter'eptar(a = (FY ! #(FX G D

"a,o 6)H 'ontina'in/ ,,titir e,to, +alore, en la e'a'in de re

,,titir el +alor en la e'a'in anterior.

a e'a'in de rere,in( = a % #A

311 = 62.2

"rom. X 5

18.6 = 3.72

"rom. Y 5

2.96

3871.8 3868.84 2.96

13.964 13.8384 0.1256

FY = 18.6

= ((5$(1159.7!(311$(18.6G((5$(19359!(3112

= (18.6 ! 0.19(311G5

= (18.6 ! 59.09G5

= !40.49G5

= !8.098

a e'a'in de rere,in( = a % #A

Spono e ,i eremo, ,a#er el +alor aproAimada de la +aria#l

= !8.098 % 0.19(64.

= !8.098 % 12.16

= 4.06

2x

2x = ! =

2y ! =


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231.9 231.384 0.556

X ! 5 = 0.192 ( ! 3 X= 0.192 ! 0.76

Y ! 30.4 5.15 (A ! 5 Y= 5.15A % 4.65

= (5.15 A 6 % 4.65 = 35.55 B

)rataiento #

$5incena P

X Y X Y XY1 ?*:@ 1.0 ?*:@ ?*:@ 43

2 4.0 ?JH


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5 25.0 ?JH


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00

67.00 -.

de a'erdo a la pre#a :/ rela'in.

=.S.C

.S.P-b=r

(y)

(xy)yx2


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=.S.C

.S.P-b=r

(y)

(xy)yx2


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diente/ inter,e''in

=.S.C

.S.P-b=r

(y)

(xy)yx2


12/21

inado

ado.

re,in &rmla

e A = 64. *nton'e, podemo,


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Na';o,

L0 L1 L2

T4 T5 T6

0.00 ?*:@ ?*:@

0.00 ?*:@ ?*:@

0.00M ?*:@ ?*:@


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ejercicio resuelto de regersion

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