Ejemplos de Ecuacion de Regresion

y x1 x2160 1.5 4112 2.2 3

69 1 1.690 2 1.2

123 0.8 3.4186 1.6 4.8

Resumen

Estadsticas de la regresinCoeficiente de correlacin mltiple 0.9590096181Coeficiente de determinacin R^2 0.9196994477R^2 ajustado 0.8661657461Error tpico 15.9155154231Observaciones 6

ANLISIS DE VARIANZAGrados de libertad Suma de cuadrados

Regresin 2 8703.4224397803Residuos 3 759.9108935531Total 5 9463.3333333333

Coeficientes Error tpicoIntercepcin 14.5617692633 26.9048784474x1 12.1608677278 13.0870794326x2 30.1091937832 5.1529653971

Anlisis de los residuales

Observacin Pronstico y Residuos1 153.2398459877 6.76015401232 131.643259614 -19.6432596143 74.8973470442 -5.89734704424 75.0145372588 14.98546274125 126.6617223083 -3.66172230836 178.543287787 7.456712213

Promedio de los cuadrados F Valor crtico de F4351.7112198901 17.179821701 0.0227550502

253.3036311844

Estadstico t Probabilidad Inferior 95% Superior 95%0.5412315574 0.6259543804 -71.0615617458 100.185100270.9292270128 0.4213137073 -29.4880598594 53.809795315

5.843080918 0.009989578 13.7101580939 46.508229472

Resultados de datos de probabilidad

Residuos estndares Percentil y0.5483530423 8.3333333333 69

-1.5933721556 25 90-0.4783660531 41.6666666667 1121.2155527921 58.3333333333 123

-0.2970223111 75 1600.6048546853 91.6666666667 186

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

-40

-20

0

20

x1 Grfico de los residuales

x1

Residuos

1 1.5 2 2.5 3 3.5 4 4.5 5

-40

-20

0

20


x2

Residuos

0 10 20 30 40 50 60 70 80 90 1000

100

200

Grfico de probabilidad normal

Muestra percentil

y

Inferior 95.0% Superior 95.0%-71.0615617458 100.1851002724-29.4880598594 53.809795315113.7101580939 46.5082294725

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

-40

-20

0

20


x1

Residuos

1 1.5 2 2.5 3 3.5 4 4.5 5

-40

-20

0

20


x2

Residuos

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.40

100

200

x1 Curva de regresin ajustada

yPronstico y

x1

y

1 1.5 2 2.5 3 3.5 4 4.5 50

100

200


yPronstico y

x2

y

0 10 20 30 40 50 60 70 80 90 1000

100

200


Muestra percentil

y

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.40

100

200


yPronstico y

x1

y

1 1.5 2 2.5 3 3.5 4 4.5 50

100

200


yPronstico y

x2

y

y x2160 4112 3

69 1.690 1.2

123 3.4186 4.8

Resumen

Estadsticas de la regresinCoeficiente de corre 0.9468829213Coeficiente de dete 0.8965872666R^2 ajustado 0.8707340833Error tpico 15.6415245953Observaciones 6

ANLISIS DE VARIANZAGrados de libertad Suma de cuadrados

Regresin 1 8484.7041666667Residuos 4 978.6291666667Total 5 9463.3333333333

Coeficientes Error tpicoIntercepcin 34.1458333333 16.4360100455x2 29.7291666667 5.0482803556


Observacin Pronstico y Residuos1 153.0625 6.93752 123.3333333333 -11.33333333333 81.7125 -12.71254 69.8208333333 20.17916666675 135.225 -12.2256 176.8458333333 9.1541666667

Promedio de los cuadrados F Valor crtico de F8484.7041666667 34.6799562313 0.0041572032

244.6572916667

Estadstico t Probabilidad Inferior 95%2.0775013667 0.1063231698 -11.48784630645.8889690296 0.0041572032 15.7128933837


Residuos estndares Percentil0.4958826583 8.3333333333-0.810090589 25

-0.9086714658 41.66666666671.4423782068 58.3333333333

-0.8738256574 750.6543268471 91.6666666667

Superior 95% Inferior 95.0% Superior 95.0%79.7795129731 -11.4878463064 79.779512973143.7454399496 15.7128933837 43.7454399496


y6990

112123160186

1 1.5 2 2.5 3 3.5 4 4.5 5-20

0

20

40


x2

Residuos

1 1.5 2 2.5 3 3.5 4 4.5 50

100

200


yPronstico y

x2

y

0 10 20 30 40 50 60 70 80 90 1000

100

200


Muestra percentil

y

1 1.5 2 2.5 3 3.5 4 4.5 5-20

0

20

40


x2

Residuos

1 1.5 2 2.5 3 3.5 4 4.5 50

100

200


yPronstico y

x2

y

0 10 20 30 40 50 60 70 80 90 1000

100

200


Muestra percentil

y

x y1 98.22 91.75 81.3

10 6420 36.430 32.640 17.150 11.3

ResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumenResumen

0 10 20 30 40 50 600

10

20

x Grfico de los residuales

x

Residuos

0 10 20 30 40 50 600

100

200

x Curva de regresin ajustada

yPronstico y

x

y

0 2 4 6 8 10 120

10

20


Muestra percentil

y

x y1 98.22 91.75 81.3

10 6420 36.430 32.640 17.150 11.3

Resumen


ANLISIS DE VARIANZAGrados de libertad

Regresin 1Residuos 6Total 7

CoeficientesIntercepcin 1.9997429994x -0.0187772096


Observacin Pronstico LOG Y1 1.98096578982 1.96218858033 1.90585695154 1.81197090365 1.62419880776 1.43642671187 1.24865461598 1.0608825201

LOG Y x1.9921114878 11.9623693357 21.9100905456 5

1.806179974 101.5611013836 201.5132176001 301.2329961104 401.0530784435 50

Resumen




CoeficientesIntercepcin 1.9997429994x -0.0187772096


Observacin Pronstico LOG Y1 1.98096578982 1.96218858033 1.90585695154 1.81197090365 1.62419880776 1.43642671187 1.2486546159

8 1.0608825201

Suma de cuadrados Promedio de los cuadrados F Valor crtico de F0.8495501839 0.8495501839 492.020554 0.0000005490.0103599353 0.00172665590.8599101192

Error tpico Estadstico t Probabilidad Inferior 95%0.0222565068 89.8498139547 1.2804E-010 1.94528328910.0008465243 -22.1815363413 5.4895E-007 -0.0208485799


Residuos Residuos estndares Percentil0.0111456979 0.2897195274 6.250.0001807554 0.004698528 18.750.0042335941 0.1100473823 31.25

-0.0057909296 -0.1505285166 43.75-0.063097424 -1.6401445612 56.250.0767908883 1.9960903264 68.75

-0.0156585055 -0.4070247415 81.25-0.0078040766 -0.2028579447 93.75

Suma de cuadrados Promedio de los cuadrados F Valor crtico de F0.8495501839 0.8495501839 492.020554 0.0000005490.0103599353 0.00172665590.8599101192

Error tpico Estadstico t Probabilidad Inferior 95%0.0222565068 89.8498139547 1.2804E-010 1.94528328910.0008465243 -22.1815363413 5.4895E-007 -0.0208485799


Residuos Residuos estndares Percentil0.0111456979 0.2897195274 6.250.0001807554 0.004698528 18.750.0042335941 0.1100473823 31.25

-0.0057909296 -0.1505285166 43.75-0.063097424 -1.6401445612 56.250.0767908883 1.9960903264 68.75

-0.0156585055 -0.4070247415 81.25

-0.0078040766 -0.2028579447 93.75

Superior 95% Inferior 99.0% Superior 99.0%2.0542027098 1.9172286023 2.0822573966

-0.0167058392 -0.0219156375 -0.0156387817


LOG Y1.05307844351.23299611041.51321760011.5611013836

1.8061799741.91009054561.96236933571.9921114878

0 10 20 30 40 50 60-0.1

0

0.1


x

Residuos

0 10 20 30 40 50 600

100

200


yPronstico y

x

y

0 10 20 30 40 50 60 70 80 90 1000

2

4


Muestra percentil

y

0 10 20 30 40 50 60-0.1

0

0.1


x

Residuos

0 10 20 30 40 50 600

100

200


yPronstico y

x

y

0 10 20 30 40 50 60 70 80 90 1000

2

4


Muestra percentil

y

0 10 20 30 40 50 60-0.1

0

0.1


x

Residuos

0 10 20 30 40 50 600

2

4


LOG YPronstico LOG Y

x

LOG Y

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60-0.1

0

0.1


x

Residuos

0 10 20 30 40 50 600

2

4



x

LOG Y

0 10 20 30 40 50 60 70 80 90 1000

2

4


Muestra percentil

LOG Y

Superior 95% Inferior 99.0% Superior 99.0%2.0542027098 1.9172286023 2.0822573966

-0.0167058392 -0.0219156375 -0.0156387817


LOG Y1.05307844351.23299611041.51321760011.5611013836

1.8061799741.91009054561.9623693357

1.9921114878

0 10 20 30 40 50 60-0.1

0

0.1


x

Residuos

0 10 20 30 40 50 600

100

200


yPronstico y

x

y

0 10 20 30 40 50 60 70 80 90 1000

2

4


Muestra percentil

y

0 10 20 30 40 50 600

100

200


yPronstico y

x

y

0 10 20 30 40 50 60 70 80 90 1000

2

4


Muestra percentil

y

0 10 20 30 40 50 60-0.1

0

0.1


x

Residuos

0 10 20 30 40 50 600

100

200


yPronstico y

x

y

0 10 20 30 40 50 60 70 80 90 1000

2

4


Muestra percentil

y

0 10 20 30 40 50 60-0.1

0

0.1


x

Residuos

0 10 20 30 40 50 600

2

4



x

LOG Y

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60-0.1

0

0.1


x

Residuos

0 10 20 30 40 50 600

2

4



x

LOG Y

0 10 20 30 40 50 60 70 80 90 1000

2

4


Muestra percentil

LOG Y

0 10 20 30 40 50 60-0.1

0

0.1


x

Residuos

0 10 20 30 40 50 600

100

200


yPronstico y

x

y

0 10 20 30 40 50 60 70 80 90 1000

2

4


Muestra percentil

y

0 10 20 30 40 50 60-0.1

0

0.1


x

Residuos

x y3 1150006 1470009 239000

12 35600015 57900018 864000

Resumen


ANLISIS DE VARIANZAGrados de libertadSuma de cuadrados

Regresin 1 380070914286Residuos 4 38690419048Total 5 418761333333

Coeficientes Error tpicoIntercepcin -132466.6666667 91558.3099832x 49123.80952381 7836.66788678


Observacin Pronstico y Residuos1 14904.761904762 100095.2380952 162276.19047619 -15276.1904763 309647.61904762 -70647.6190484 457019.04761905 -101019.047625 604390.47619048 -25390.476196 751761.90476191 112238.095238

Promedio de los cuadrados F Valor crtico de F380070914286 39.29354333 0.00330519179672604761.9

Estadstico t Probabilidad Inferior 95% Superior 95% Inferior 99.0%-1.4468011335 0.221498994 -386673.28826 121739.955 -554009.812096.2684562155 0.003305192 27365.73132851 70881.8877 13043.047098


Residuos estndares Percentil y1.1378806243 8.3333333333 115000

-0.1736594216 25 147000-0.8031206918 41.6666666667 239000-1.1483824721 58.3333333333 356000-0.2886384153 75 5790001.2759203766 91.6666666667 864000

Superior 99.0%289076.47875785204.5719498

2 4 6 8 10 12 14 16 18 20-200000

0

200000


x

Residuos

2 4 6 8 10 12 14 16 18 200

500000

1000000


yPronstico y

x

y

0 10 20 30 40 50 60 70 80 90 1000

500000

1000000


Muestra percentil

y

LOG Y x5.06069784 35.16731733 6

5.3783979 95.55145 12

5.76267856 155.93651374 18

Resumen

Estadsticas de la regresinCoeficiente de 0.9971049278Coeficiente d 0.9942182371R^2 ajustado 0.9927727964Error tpico 0.0288853243Observacione 6



CoeficientesIntercepcin 4.8423543672x 0.0603639552


Observacin Pronstico LOG Y1 5.02344623282 5.20453809843 5.38562996394 5.56672182955 5.7478136956 5.9289055606

2 4 6 8 10 12 14 16 18 20-200000

0

200000


x

Residuos

2 4 6 8 10 12 14 16 18 200

500000

1000000


yPronstico y

x

y

0 10 20 30 40 50 60 70 80 90 1000

500000

1000000


Muestra percentil

y

Suma de cuadradosPromedio de los cuadradosF Valor crtico de F0.57389962 0.57389962 687.830515 0.000012560.00333745 0.000834360.57723706

Error tpico Estadstico t Probabilidad Inferior 95% Superior 95%Inferior 99.0%0.02689077 180.074938 5.7049E-009 4.76769361 4.91701512 4.71854670.00230164 26.2265231 0.00001256 0.05397358 0.06675433 0.049767


ResiduosResiduos estndares Percentil LOG Y0.03725161 1.44185895 8.33333333 5.06069784

-0.03722076 -1.44066511 25 5.16731733-0.00723206 -0.27992389 41.6666667 5.3783979-0.01527183 -0.59111078 58.3333333 5.551450.01486487 0.5753589 75 5.762678560.00760818 0.29448193 91.6666667 5.93651374

Superior 99.0%4.966162040.07096091

2 4 6 8 10 12 14 16 18 20

-0.05

0

0.05


x

Residuos

2 4 6 8 10 12 14 16 18 204

6

8



x

LOG Y

0 10 20 30 40 50 60 70 80 90 1004567


Muestra percentil

LOG Y

2 4 6 8 10 12 14 16 18 20

-0.05

0

0.05


x

Residuos

2 4 6 8 10 12 14 16 18 204

6

8



x

LOG Y

0 10 20 30 40 50 60 70 80 90 1004567


Muestra percentil

LOG Y

y x X^212 0 0

10.5 1 110 2 4

8 3 97 4 168 5 25

7.5 6 368.5 7 49

9 8 64

Resumen

Estadsticas de la regresinCoeficiente de0.65227998Coeficiente d 0.42546917R^2 ajustado0.34339334Error tpico 1.3041448Observacione 9

ANLISIS DE VARIANZAGrados de libertadSuma de cuadradosPromedio de los cuadradosF Valor crtico de F

Regresin 1 8.81666667 8.81666667 5.18385441 0.05690343Residuos 7 11.9055556 1.70079365Total 8 20.7222222

Coeficientes Error tpico Estadstico t Probabilidad Inferior 95%Intercepcin 10.4777778 0.80157473 13.0714922 3.5746E-006 8.58235473x -0.38333333 0.16836437 -2.27680794 0.05690343 -0.7814518

Anlisis de los residuales Resultados de datos de probabilidad

Observacin Pronstico y ResiduosResiduos estndares Percentil1 10.4777778 1.52222222 1.2478093 5.555555562 10.0944444 0.40555556 0.33244554 16.66666673 9.71111111 0.28888889 0.23681052 27.77777784 9.32777778 -1.32777778 -1.0884176 38.88888895 8.94444444 -1.94444444 -1.59391699 506 8.56111111 -0.56111111 -0.4599589 61.11111117 8.17777778 -0.67777778 -0.55559392 72.22222228 7.79444444 0.70555556 0.57836416 83.33333339 7.41111111 1.58888889 1.30245788 94.4444444

Valor crtico de F

Superior 95%Inferior 99.0%Superior 99.0%12.3732008 7.6726804 13.28287520.01478514 -0.97252163 0.20585496


y7

7.588

8.59

1010.5

12

0 1 2 3 4 5 6 7 8 9

-4

-2

0

2


x

Residuos

0 1 2 3 4 5 6 7 8 90

10

20


yPronstico y

x

y

0 10 20 30 40 50 60 70 80 90 1000

10

20


Muestra percentil

y

0 1 2 3 4 5 6 7 8 9

-4

-2

0

2


x

Residuos

0 1 2 3 4 5 6 7 8 90

10

20


yPronstico y

x

y

0 10 20 30 40 50 60 70 80 90 1000

10

20


Muestra percentil

y

y x X^212 0 0

10.5 1 110 2 4

8 3 97 4 168 5 25

7.5 6 368.5 7 49

9 8 64Resumen

Estadsticas de la regresinCoeficiente de0.96056429Coeficiente d 0.92268375R^2 ajustado0.89691167Error tpico 0.51674696Observacione 9

ANLISIS DE VARIANZAGrados de libertadSuma de cuadradosPromedio de los cuadrados

Regresin 2 19.1200577 9.56002886Residuos 6 1.6021645 0.26702742Total 8 20.7222222

Coeficientes Error tpico Estadstico tIntercepcin 12.1848485 0.41999992 29.0115498x -1.8465368 0.24481968 -7.54243626X^2 0.18290043 0.02944439 6.21172419


Observacin Pronstico y ResiduosResiduos estndares1 12.1848485 -0.18484848 -0.413054482 10.5212121 -0.02121212 -0.047399693 9.22337662 0.77662338 1.735409224 8.29134199 -0.29134199 -0.651020295 7.72510823 -0.72510823 -1.620295676 7.52467532 0.47532468 1.062140097 7.69004329 -0.19004329 -0.424662578 8.22121212 0.27878788 0.622967419 9.11818182 -0.11818182 -0.26408401

0 10 20 30 40 50 60 70-1

-0.50

0.51

X^2 Grfico de los residuales

X^2

Residuos

F Valor crtico de F35.8016752 0.00046218

Probabilidad Inferior 95% Superior 95%Inferior 99.0%Superior 99.0%1.1112E-007 11.1571457 13.2125513 10.627729 13.74196790.00028169 -2.44558896 -1.24748463 -2.75418812 -0.938885470.00080345 0.1108526 0.25494826 0.07373747 0.29206339


Residuos estndares Percentil y5.55555556 716.6666667 7.527.7777778 838.8888889 8

50 8.561.1111111 972.2222222 1083.3333333 10.594.4444444 12

0 1 2 3 4 5 6 7 8 9

-1-0.5

00.5

1


x

Residuos

0 10 20 30 40 50 60 70-1

-0.50

0.51

X^2 Grfico de los residuales

X^2

Residuos

0 1 2 3 4 5 6 7 8 905

1015


yPronstico y

x

y

0 10 20 30 40 50 60 7005

1015

X^2 Curva de regresin ajustada

yPronstico y

X^2

y

0 10 20 30 40 50 60 70 80 90 10005

1015


Muestra percentil

y

0 1 2 3 4 5 6 7 8 9

-1-0.5

00.5

1


x

Residuos

0 1 2 3 4 5 6 7 8 9

-1-0.5

00.5

1


x

Residuos

0 1 2 3 4 5 6 7 8 905

1015


yPronstico y

x

y

0 10 20 30 40 50 60 7005

1015

X^2 Curva de regresin ajustada

yPronstico y

X^2

y

0 10 20 30 40 50 60 70 80 90 10005

1015


Muestra percentil

y

0 1 2 3 4 5 6 7 8 9

-1-0.5

00.5

1


x

Residuos

y X1 X2 X3 Resumen0.222 7.3 0 00.395 8.7 0 0.3 Estadsticas de la regresin0.422 8.8 0.7 1 Coeficiente de0.437 8.1 4 0.2 Coeficiente d0.428 9 0.5 1 R^2 ajustado0.467 8.7 1.5 2.8 Error tpico0.444 9.3 2.1 1 Observacione0.378 7.6 5.1 3.40.494 10 0 0.3 ANLISIS DE VARIANZA0.456 8.4 3.7 4.1 Grados de libertad0.452 9.3 3.6 2 Regresin0.112 7.7 2.8 7.1 Residuos0.432 9.8 4.2 2 Total0.101 7.3 2.5 6.80.232 8.5 2 6.60.306 9.5 2.5 5 Intercepcin

0.0923 7.4 2.8 7.8 X10.116 7.8 2.8 7.7 X2

0.0764 7.7 3 8 X30.439 10.3 1.7 4.2

0.0944 7.8 3.3 8.50.117 7.1 3.9 6.6

0.0726 7.7 4.3 9.5 Anlisis de los residuales0.0412 7.4 6 10.9

0.251 7.3 2 5.2 Observacin0.00002 7.6 7.8 20.7 1

23456789

10111213141516171819

20212223242526

Estadsticas de la regresin0.930984230.866731630.848558670.06581464

26

ANLISIS DE VARIANZAGrados de libertadSuma de cuadradosPromedio de los cuadradosF Valor crtico de F

3 0.6197625 0.2065875 47.6934765 8.5353E-01022 0.09529448 0.0043315725 0.71505698

Coeficientes Error tpico Estadstico t Probabilidad Inferior 95% Superior 95%-0.36930592 0.14364551 -2.5709534 0.01742958 -0.66720848 -0.071403360.08651029 0.01600283 5.40593698 1.9830E-005 0.05332245 0.119698120.02441173 0.01022552 2.38733418 0.02599374 0.0032053 0.04561815

-0.02857704 0.00447739 -6.38252371 2.0145E-006 -0.03786257 -0.0192915

Anlisis de los residuales Resultados de datos de probabilidad

Pronstico y ResiduosResiduos estndares Percentil y0.26221918 -0.04021918 -0.65143235 1.92307692 0.000020.37476047 0.02023953 0.32782087 5.76923077 0.04120.38049578 0.04150422 0.67224625 9.61538462 0.07260.42335891 0.01364109 0.22094548 13.4615385 0.07640.39291549 0.03508451 0.56826581 17.3076923 0.09230.33993546 0.12706454 2.05807163 21.1538462 0.09440.45792734 -0.01392734 -0.22558198 25 0.1010.31551015 0.06248985 1.01215175 28.8461538 0.1120.48722384 0.00677616 0.10975383 32.6923077 0.1160.33053803 0.12546197 2.03211477 36.5384615 0.117

0.4659679 -0.0139679 -0.22623883 40.3846154 0.2220.16227916 -0.05027916 -0.81437445 44.2307692 0.2320.52387008 -0.09187008 -1.48802496 48.0769231 0.2510.12892464 -0.02792464 -0.45229697 51.9230769 0.3060.22624653 0.00575347 0.09318936 55.7692308 0.3780.37068594 -0.06468594 -1.04772188 59.6153846 0.3950.11632215 -0.02402215 -0.3890881 63.4615385 0.4220.15378397 -0.03778397 -0.61198907 67.3076923 0.4280.14144217 -0.06504217 -1.0534918 71.1538462 0.432

6.5 7 7.5 8 8.5 9 9.5 10 10.5-0.2

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0.2

X1 Grfico de los residuales

X1

Residuos

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X2

Residuos

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X3

Residuos

0.44322642 -0.00422642 -0.0684555 75 0.4370.1431282 -0.0487282 -0.78925345 78.8461538 0.439

0.15151441 -0.03451441 -0.55903185 82.6923077 0.4440.13031186 -0.05771186 -0.93476233 86.5384615 0.4520.10585086 -0.06465086 -1.04715368 90.3846154 0.4560.16244203 0.08855797 1.43437848 94.2307692 0.467

-0.11296095 0.11298095 1.82995898 98.0769231 0.494

Inferior 99.0%Superior 99.0%-0.77420758 0.035595740.04140221 0.13161836

-0.00441151 0.05323497-0.0411977 -0.01595637


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X1 Curva de regresin ajustada

yPronstico y

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y

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Muestra percentil

y

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Ejemplos de Ecuacion de Regresion

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