Clase Regresion y Correlacion

Regresin y Correlacin

Relaciones entre variablesFrancis GaltonPrimo de DarwinEstadstico y aventureroFundador (con otros) de la estadstica moderna para explicar las teoras de Darwin.

El trmino regresin fue introducido por Galton en su libro Natural inheritance (1889) refirindose a la ley de la regresin universalCada peculiaridad en un hombre es compartida por sus descendientes, pero en promedio , en un grado menor. Regresin a la media

Conclusin

Padres muy altos tienen tendencia a tener hijos que heredan parte de esta altura, aunque tienen tendencia a acercarse (regresar) a la media. Lo mismo puede decirse de los padres muy bajos.

Hoy en da el sentido de regresin es el de prediccin de una medida basndonos en el conocimiento de otra.

Modelo de Regresin Lineal El Modelo es la expresin terica del comportamiento de la poblacin

ParmetrosError ResidualParte sistemtica

Elementos del Modelo= Es el valor medio terico que asume la variable Y cuando x=0= Es el valor medio terico del aumento o decremento de la variable Y cuando x varia una unidad.= Es el trmino de error en l se incluyen los errores casuales, de medicin, deficiencias del modelo, etc.

Supuestos del ModeloLa variable "explicativa" X toma valores predeterminados por el investigador.

Para cada valor fijo de X , la variable Y se distribuye Normal .

La relacin entre las variables X e Y es lineal , es decir, la regresin del promedio es lineal Simblicamente : E(Y/X) = + .X , ya que E() = 0

Los valores de la variable Y son independientes entre si ya que existe Homocedasticidad ,significa que la variancia de los errores es constante , no depende del valor de X. La variancia de Y no depende del valor que tome la variable X

CALCULO DE LA RECTA DE REGRESIN ( x1 , y1 ) , ( x2 , y2 ) , ... , ( xn , yn ) Recta de EstimacinModelo de Regresin

Regresin Lineal Algebra de la Muestra.El anlisis de regresin sirve para predecir una medida en funcin de otra medida (o varias).Y = Variable dependientePredichaExplicada

X = Variable independientePredictoraExplicativa

Estudio conjunto de dos variables

fila = datos de un individuo

columna =representa los valores que toma una variable sobre los mismos.

Las individuos no muestran ningn orden particular.

Las observaciones se representan en un diagrama de dispersin. Objetivo ser intentar reconocer a partir del mismo si hay relacin entre las variables, de qu tipo, y si es posible predecir el valor de una de ellas en funcin de la otra.

Diagramas de dispersin o nube de puntosMide 187 cm.Mide 161 cm.Pesa 76 kg.Pesa 50 kg.Alturas y pesos de 30 individuos representados en un diagrama de dispersin.

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U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY

0.32107709790.43902892560.5950575838-0.15343165490.240574730317010168605630.82-10517.216560887365

0.5095050130.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.8036134967r real68.827586206912.801047816861

0.06005948070.05769547650.9438398223-1.57441758131.587849599815464.760

0.05548652570.83860121620.662221620.98872529190.41853406418063.378

0.14449624920.11387091140.8898571326-1.20619659021.225769024915864.462

0.30899055740.53754795820.49822607190.0942580074-0.004446566317162.566

0.80759120930.4698249680.2895794741-0.0757096811-0.554613554216961.460

0.56459358020.3623377610.1713417684-0.3522171708-0.94887622916660.954

0.08487780230.73047812450.95883435740.61425949151.737316244417664.884

0.79622382230.23698741340.9235514845-0.71602651771.429373400616364.668

0.92548599490.66471351180.41045670910.425361854-0.22637041217462.167

0.40928312970.36272675970.3066671094-0.351179888-0.505319802116661.557

0.78094424680.55083439150.98900851930.12776961942.290661080417164.983

0.86477479320.95588578090.26399508291.7048173074-0.631076828718761.377

0.16457131620.96558168580.90703611441.81948976781.322722601118864.593

0.46622302180.18906278910.2130066129-0.8813550865-0.796032136316161.150

0.98762363060.99697854840.14927259042.7454502187-1.039558342319760.784

0.66300341160.53765111760.21743730330.0945177443-0.780877165217161.160

0.56783209570.48295272630.6630831527-0.04274403060.420892443517063.368

0.89033912970.29005181210.3509696513-0.5532332659-0.382704066516461.856

0.23191944980.81017356710.08427214430.8785359286-1.376896737117960.464

0.892243320.92592929540.84805634671.44612792141.028132991718464.286

0.93297289510.76293712660.97270838780.71578211881.922178021417764.986

0.93813002260.01684722430.1804037537-2.1237079846-0.913827366714960.937

0.58627896790.66791730920.95659177340.43416954991.712435064817464.881

0.05707053280.82722099210.8991330750.94324021231.276627697317964.583

0.70102967010.34869066750.5972566326-0.38885794170.24625268491666363

0.0237166550.70237231980.86871606940.53123577421.120342661417564.378

0.13259568530.20987961530.8718443876-0.80683880891.13515322216264.465

Hoja1

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r=0,8

Hoja2

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Relacin entre variables.El peso aumenta con la altura

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0.32107709790.43902892560.5950575838-0.15343165490.240574730317010168605630.82-10517.216560887365

0.5095050130.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.8036134967r real68.827586206912.801047816861

0.06005948070.05769547650.9438398223-1.57441758131.587849599815464.760

0.05548652570.83860121620.662221620.98872529190.41853406418063.378

0.14449624920.11387091140.8898571326-1.20619659021.225769024915864.462

0.30899055740.53754795820.49822607190.0942580074-0.004446566317162.566

0.80759120930.4698249680.2895794741-0.0757096811-0.554613554216961.460

0.56459358020.3623377610.1713417684-0.3522171708-0.94887622916660.954

0.08487780230.73047812450.95883435740.61425949151.737316244417664.884

0.79622382230.23698741340.9235514845-0.71602651771.429373400616364.668

0.92548599490.66471351180.41045670910.425361854-0.22637041217462.167

0.40928312970.36272675970.3066671094-0.351179888-0.505319802116661.557

0.78094424680.55083439150.98900851930.12776961942.290661080417164.983

0.86477479320.95588578090.26399508291.7048173074-0.631076828718761.377

0.16457131620.96558168580.90703611441.81948976781.322722601118864.593

0.46622302180.18906278910.2130066129-0.8813550865-0.796032136316161.150

0.98762363060.99697854840.14927259042.7454502187-1.039558342319760.784

0.66300341160.53765111760.21743730330.0945177443-0.780877165217161.160

0.56783209570.48295272630.6630831527-0.04274403060.420892443517063.368

0.89033912970.29005181210.3509696513-0.5532332659-0.382704066516461.856

0.23191944980.81017356710.08427214430.8785359286-1.376896737117960.464

0.892243320.92592929540.84805634671.44612792141.028132991718464.286

0.93297289510.76293712660.97270838780.71578211881.922178021417764.986

0.93813002260.01684722430.1804037537-2.1237079846-0.913827366714960.937

0.58627896790.66791730920.95659177340.43416954991.712435064817464.881

0.05707053280.82722099210.8991330750.94324021231.276627697317964.583

0.70102967010.34869066750.5972566326-0.38885794170.24625268491666363

0.0237166550.70237231980.86871606940.53123577421.120342661417564.378

0.13259568530.20987961530.8718443876-0.80683880891.13515322216264.465

Hoja1

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r=0,8

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Prediccin de una variable en funcin de la otra. El peso aumenta 10Kg por cada 10 cm de altura... o sea,el peso aumenta en una unidad por cada unidad de altura.10 cm.10 kg.

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0.09869029090.43902892560.5950575838-0.15343165490.240574730317010168605630.82-10517.216560887365

0.44867371570.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.8036134967r real68.827586206912.801047816861

0.63588908070.05769547650.9438398223-1.57441758131.587849599815464.760

0.27798826210.83860121620.662221620.98872529190.41853406418063.378

0.33404890920.11387091140.8898571326-1.20619659021.225769024915864.462

0.9056646350.53754795820.49822607190.0942580074-0.004446566317162.566

0.74370709850.4698249680.2895794741-0.0757096811-0.554613554216961.460

0.15874117880.3623377610.1713417684-0.3522171708-0.94887622916660.954

0.20844385880.73047812450.95883435740.61425949151.737316244417664.884

0.33846401810.23698741340.9235514845-0.71602651771.429373400616364.668

0.26644882880.66471351180.41045670910.425361854-0.22637041217462.167

0.00527476350.36272675970.3066671094-0.351179888-0.505319802116661.557

0.01477920190.55083439150.98900851930.12776961942.290661080417164.983

0.35786894770.95588578090.26399508291.7048173074-0.631076828718761.377

0.84226238580.96558168580.90703611441.81948976781.322722601118864.593

0.0702175880.18906278910.2130066129-0.8813550865-0.796032136316161.150

0.81825903790.99697854840.14927259042.7454502187-1.039558342319760.784

0.3333380880.53765111760.21743730330.0945177443-0.780877165217161.160

0.92468923360.48295272630.6630831527-0.04274403060.420892443517063.368

0.58428988110.29005181210.3509696513-0.5532332659-0.382704066516461.856

0.52224880180.81017356710.08427214430.8785359286-1.376896737117960.464

0.21680985320.92592929540.84805634671.44612792141.028132991718464.286

0.50089487940.76293712660.97270838780.71578211881.922178021417764.986

0.49993764190.01684722430.1804037537-2.1237079846-0.913827366714960.937

0.09890800340.66791730920.95659177340.43416954991.712435064817464.881

0.58682803540.82722099210.8991330750.94324021231.276627697317964.583

0.44946246160.34869066750.5972566326-0.38885794170.24625268491666363

0.38216211350.70237231980.86871606940.53123577421.120342661417564.378

0.4254435070.20987961530.8718443876-0.80683880891.13515322216264.465

Hoja1

r=0,8

Hoja2

Hoja3

EstimacinExisten dos mtodos para hallar los estimadores de y que dan los mismos resultados.Mtodo de Mxima VerosimilitudMtodo de los Mnimos Cuadrados

Covarianza de X e YLa covarianza entre dos variables, Cov(x,y), nos indica si la posible relacin entre dos variables es directa o inversa.

Directa: Cov(x,y), >0

Inversa: Cov(x,y),

Relacin directa e inversa.Para valores de X por encima de la media tenemos valores de Y por encima y por debajo en cantidades similares. No existe relacinPara los valores de X mayores que la media le corresponden valores de Y menores. Esto es relacin inversa o decreciente.Para los valores de X mayores que la media le corresponden valores de Y mayores tambin.

Para los valores de X menores que la media le corresponden valores de Y menores tambin.

Esto se llama relacin directa o creciente entre X e Y.

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0.72274696750.43902892560.5950575838-0.15343165490.240574730317010168605630.9-10515.007333035264

0.30929477570.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.8913679189r real68.034482758611.651499115160

0.79531870370.05769547650.9438398223-1.57441758131.587849599815464.757

0.03631570220.83860121620.662221620.98872529190.41853406418063.377

0.86783875080.11387091140.8898571326-1.20619659021.225769024915864.459

0.25569832020.53754795820.49822607190.0942580074-0.004446566317162.566

0.42452929760.4698249680.2895794741-0.0757096811-0.554613554216961.461

0.51355848860.3623377610.1713417684-0.3522171708-0.94887622916660.956

0.86924383120.73047812450.95883435740.61425949151.737316244417664.880

0.05499280660.23698741340.9235514845-0.71602651771.429373400616364.665

0.29568106190.66471351180.41045670910.425361854-0.22637041217462.168

0.09503555380.36272675970.3066671094-0.351179888-0.505319802116661.558

0.55550039980.55083439150.98900851930.12776961942.290661080417164.977

0.78075372260.95588578090.26399508291.7048173074-0.631076828718761.379

0.99363693410.96558168580.90703611441.81948976781.322722601118864.590

0.7196567650.18906278910.2130066129-0.8813550865-0.796032136316161.152

0.96041622320.99697854840.14927259042.7454502187-1.039558342319760.787

0.45905465920.53765111760.21743730330.0945177443-0.780877165217161.162

0.58713460480.48295272630.6630831527-0.04274403060.420892443517063.367

0.46028098910.29005181210.3509696513-0.5532332659-0.382704066516461.857

0.6309204810.81017356710.08427214430.8785359286-1.376896737117960.467

0.48137093620.92592929540.84805634671.44612792141.028132991718464.284

0.75529142650.76293712660.97270838780.71578211881.922178021417764.982

0.92842640410.01684722430.1804037537-2.1237079846-0.913827366714960.939

0.28704184340.66791730920.95659177340.43416954991.712435064817464.878

0.24927133750.82722099210.8991330750.94324021231.276627697317964.580

0.30513292940.34869066750.5972566326-0.38885794170.24625268491666362

0.92182696590.70237231980.86871606940.53123577421.120342661417564.376

0.47395941310.20987961530.8718443876-0.80683880891.13515322216264.463

Hoja1

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r=0,9

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0.95511587380.43902892560.5950575838-0.15343165490.240574730317010168605630.7200-110.547735582135

0.40432403190.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.6-0.6931993739r real33.103448275915.166534911244

0.07764431680.05769547650.9438398223-1.57441758131.587849599815464.763

0.75616212090.83860121620.662221620.98872529190.41853406418063.324

0.47951644790.11387091140.8898571326-1.20619659021.225769024915864.455

0.54236160040.53754795820.49822607190.0942580074-0.004446566317162.529

0.74460489890.4698249680.2895794741-0.0757096811-0.554613554216961.425

0.97603928060.3623377610.1713417684-0.3522171708-0.94887622916660.924

0.89310171160.73047812450.95883435740.61425949151.737316244417664.842

0.36323618850.23698741340.9235514845-0.71602651771.429373400616364.652

0.55393406360.66471351180.41045670910.425361854-0.22637041217462.124

0.3977652670.36272675970.3066671094-0.351179888-0.505319802116661.529

0.66401449160.55083439150.98900851930.12776961942.290661080417164.953

0.49764920920.95588578090.26399508291.7048173074-0.631076828718761.36

0.62421102440.96558168580.90703611441.81948976781.322722601118864.526

0.58779807340.18906278910.2130066129-0.8813550865-0.796032136316161.131

0.97620559960.99697854840.14927259042.7454502187-1.039558342319760.7-8

0.52652096570.53765111760.21743730330.0945177443-0.780877165217161.121

0.17373138460.48295272630.6630831527-0.04274403060.420892443517063.334

0.42725479060.29005181210.3509696513-0.5532332659-0.382704066516461.832

0.28062513320.81017356710.08427214430.8785359286-1.376896737117960.46

0.23075976050.92592929540.84805634671.44612792141.028132991718464.227

0.50293534710.76293712660.97270838780.71578211881.922178021417764.943

0.53937074980.01684722430.1804037537-2.1237079846-0.913827366714960.941

0.37146074590.66791730920.95659177340.43416954991.712435064817464.844

0.32731235210.82722099210.8991330750.94324021231.276627697317964.534

0.74593711990.34869066750.5972566326-0.38885794170.24625268491666337

0.05978134840.70237231980.86871606940.53123577421.120342661417564.337

0.32394984420.20987961530.8718443876-0.80683880891.13515322216264.450

Hoja1

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r=-0,7

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Supuestos de los errores

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Columna 1Columna 2

Columna 11

Columna 20.77912905931

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513Estadsticas de la regresin

514Coeficiente de correlacin mltiple0.7791290593

Coeficiente de determinacin R^20.6070420911

R^2 ajustado0.5930078801

Error tpico2.3519817563

Observaciones30

ANLISIS DE VARIANZA

Grados de libertadSuma de cuadradosPromedio de los cuadradosFValor crtico de F

Regresin1239.2757575758239.275757575843.25445083540.0000003933

Residuos28154.89090909095.5318181818

Total29394.1666666667

CoeficientesError tpicoEstadstico tProbabilidadInferior 95%Superior 95%Inferior 95,0%Superior 95,0%

Intercepcin-0.21.487523873-0.13445162370.8940072761-3.24705794672.8470579467-3.24705794672.8470579467

Variable X 12.55454545450.38841700356.5768116010.00000039331.75890839723.35018251191.75890839723.3501825119

Anlisis de los residuales

ObservacinPronstico para YResiduos

14.9090909091-1.9090909091

24.9090909091-0.9090909091

34.90909090910.0909090909

44.90909090911.0909090909

54.90909090912.0909090909

64.90909090913.0909090909

77.4636363636-3.4636363636

87.4636363636-2.4636363636

97.4636363636-1.4636363636

107.4636363636-0.4636363636

117.46363636360.5363636364

127.46363636361.5363636364

137.46363636362.5363636364

1410.0181818182-4.0181818182

1510.0181818182-3.0181818182

1610.0181818182-2.0181818182

1710.0181818182-1.0181818182

1810.0181818182-0.0181818182

1910.01818181820.9818181818

2010.01818181821.9818181818

2110.01818181822.9818181818

2212.5727272727-3.5727272727

2312.5727272727-2.5727272727

2412.5727272727-1.5727272727

2512.5727272727-0.5727272727

2612.57272727270.4272727273

2712.57272727271.4272727273

2812.57272727272.4272727273

2912.57272727273.4272727273

3012.57272727274.4272727273

Hoja1

Variable X 1

Residuos

Variable X 1 Grfico de los residuales

Hoja2

Hoja3

e1enei

Grfico3

65

61

60

78

62

66

60

54

84

68

67

57

83

77

93

50

84

60

68

56

64

86

86

37

81

83

63

78

65

Hoja1


0.44845734590.43902892560.5950575838-0.15343165490.240574730317010168605630.82-10517.216560887365

0.51092118810.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.8036134967r real68.827586206912.801047816861

0.96831566310.05769547650.9438398223-1.57441758131.587849599815464.760

0.03945399770.83860121620.662221620.98872529190.41853406418063.378

0.68903886490.11387091140.8898571326-1.20619659021.225769024915864.462

0.26201953460.53754795820.49822607190.0942580074-0.004446566317162.566

0.50517675590.4698249680.2895794741-0.0757096811-0.554613554216961.460

0.55224700360.3623377610.1713417684-0.3522171708-0.94887622916660.954

0.82914983470.73047812450.95883435740.61425949151.737316244417664.884

0.29185339480.23698741340.9235514845-0.71602651771.429373400616364.668

0.50351750310.66471351180.41045670910.425361854-0.22637041217462.167

0.25672516830.36272675970.3066671094-0.351179888-0.505319802116661.557

0.50920465980.55083439150.98900851930.12776961942.290661080417164.983

0.11029053250.95588578090.26399508291.7048173074-0.631076828718761.377

0.37464656880.96558168580.90703611441.81948976781.322722601118864.593

0.61527939130.18906278910.2130066129-0.8813550865-0.796032136316161.150

0.87022878050.99697854840.14927259042.7454502187-1.039558342319760.784

0.72818053210.53765111760.21743730330.0945177443-0.780877165217161.160

0.6723332410.48295272630.6630831527-0.04274403060.420892443517063.368

0.19608680910.29005181210.3509696513-0.5532332659-0.382704066516461.856

0.97987903860.81017356710.08427214430.8785359286-1.376896737117960.464

0.60336506320.92592929540.84805634671.44612792141.028132991718464.286

0.85961264230.76293712660.97270838780.71578211881.922178021417764.986

0.46708749840.01684722430.1804037537-2.1237079846-0.913827366714960.937

0.47764860560.66791730920.95659177340.43416954991.712435064817464.881

0.19828251210.82722099210.8991330750.94324021231.276627697317964.583

0.54387847510.34869066750.5972566326-0.38885794170.24625268491666363

0.64183095710.70237231980.86871606940.53123577421.120342661417564.378

0.63315675220.20987961530.8718443876-0.80683880891.13515322216264.465

Hoja1

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

r=0,8

Hoja2

Hoja3

Interpretacin de los coeficientesa = ordenada al origen cuando x=0 ; y=a

b= pendiente de la recta

b>0 :existe una relacin lineal directa entre las variables

b

Otros modelos de RegresinSe pueden considerar otros tipos de modelos, en funcin del aspecto que presente el diagrama de dispersin (regresin no lineal)

Incluso se puede considerar el que una variable dependa de varias (regresin mltiple).

Grfico11

68

51

92

227

66

89

62

35

183

67

120

43

131

366

428

25

669

76

88

37

177

322

202

95

155

224

56

158

60

recta o parbola?

Hoja1

U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorYYNLb2

0.82827150790.43902892560.5950575838-0.15343165490.240574730317010168605630.5200-117.907411494836680.5

0.66580588720.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.6-0.494717264r real36.034482758621.39204292714951

0.09094520610.05769547650.9438398223-1.57441758131.587849599815464.77492

0.38419582620.83860121620.662221620.98872529190.41853406418063.327227

0.39853652680.11387091140.8898571326-1.20619659021.225769024915864.46466

0.23855711690.53754795820.49822607190.0942580074-0.004446566317162.52989

0.0807724210.4698249680.2895794741-0.0757096811-0.554613554216961.42162

0.47727346210.3623377610.1713417684-0.3522171708-0.94887622916660.91735

0.51399794250.73047812450.95883435740.61425949151.737316244417664.855183

0.185120210.23698741340.9235514845-0.71602651771.429373400616364.66367

0.27690945840.66471351180.41045670910.425361854-0.22637041217462.122120

0.73911763210.36272675970.3066671094-0.351179888-0.505319802116661.52543

0.08559200750.55083439150.98900851930.12776961942.290661080417164.970131

0.81043304870.95588578090.26399508291.7048173074-0.631076828718761.32366

0.47429788370.96558168580.90703611441.81948976781.322722601118864.536428

0.29084249060.18906278910.2130066129-0.8813550865-0.796032136316161.12525

0.57542750070.99697854840.14927259042.7454502187-1.039558342319760.7-16669

0.4848115980.53765111760.21743730330.0945177443-0.780877165217161.11576

0.54603101930.48295272630.6630831527-0.04274403060.420892443517063.33888

0.78196795340.29005181210.3509696513-0.5532332659-0.382704066516461.82937

0.91859773020.81017356710.08427214430.8785359286-1.376896737117960.4-4177

0.75963493550.92592929540.84805634671.44612792141.028132991718464.234322

0.58602831080.76293712660.97270838780.71578211881.922178021417764.957202

0.59536752150.01684722430.1804037537-2.1237079846-0.913827366714960.93595

0.31575595690.66791730920.95659177340.43416954991.712435064817464.857155

0.25058008890.82722099210.8991330750.94324021231.276627697317964.544224

0.15838036630.34869066750.5972566326-0.38885794170.2462526849166633856

0.66490467320.70237231980.86871606940.53123577421.120342661417564.345158

0.24012203090.20987961530.8718443876-0.80683880891.13515322216264.45860

Hoja1

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

Parablico?

Hoja2

Hoja3

Grfico12

59804

57801

43490

63827

52952

59833

59817

59561

60719

58491

60078

59569

59874

79454

83164

56909

138516

59819

59838

58965

62712

70810

61229

22791

60113

62760

59582

60345

59874

recta o cbica?

Hoja1

U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorYYNLb2

0.44521822660.43902892560.5950575838-0.15343165490.240574730317010168605630.560000-117.907411494859836598044

0.69953027470.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.6-0.494717264r real59836.034482758621.39204292715984957801

0.29815526350.05769547650.9438398223-1.57441758131.587849599815464.75987443490

0.39416940050.83860121620.662221620.98872529190.41853406418063.35982763827

0.34900926860.11387091140.8898571326-1.20619659021.225769024915864.45986452952

0.83135368960.53754795820.49822607190.0942580074-0.004446566317162.55982959833

0.93591247460.4698249680.2895794741-0.0757096811-0.554613554216961.45982159817

0.80773956360.3623377610.1713417684-0.3522171708-0.94887622916660.95981759561

0.02158149480.73047812450.95883435740.61425949151.737316244417664.85985560719

0.16318699890.23698741340.9235514845-0.71602651771.429373400616364.65986358491

0.87084296920.66471351180.41045670910.425361854-0.22637041217462.15982260078

0.76012732520.36272675970.3066671094-0.351179888-0.505319802116661.55982559569

0.42178730780.55083439150.98900851930.12776961942.290661080417164.95987059874

0.58447688160.95588578090.26399508291.7048173074-0.631076828718761.35980279454

0.35878109760.96558168580.90703611441.81948976781.322722601118864.55983683164

0.80048620940.18906278910.2130066129-0.8813550865-0.796032136316161.15982556909

0.78638977490.99697854840.14927259042.7454502187-1.039558342319760.759784138516

0.34530652460.53765111760.21743730330.0945177443-0.780877165217161.15981559819

0.46670555680.48295272630.6630831527-0.04274403060.420892443517063.35983859838

0.72660037220.29005181210.3509696513-0.5532332659-0.382704066516461.85982958965

0.15358275210.81017356710.08427214430.8785359286-1.376896737117960.45979662712

0.5475353840.92592929540.84805634671.44612792141.028132991718464.25983470810

0.55633311220.76293712660.97270838780.71578211881.922178021417764.95985761229

0.95882179270.01684722430.1804037537-2.1237079846-0.913827366714960.95983522791

0.80015355320.66791730920.95659177340.43416954991.712435064817464.85985760113

0.51937276890.82722099210.8991330750.94324021231.276627697317964.55984462760

0.9712908260.34869066750.5972566326-0.38885794170.2462526849166635983859582

0.25852924330.70237231980.86871606940.53123577421.120342661417564.35984560345

0.227025450.20987961530.8718443876-0.80683880891.13515322216264.45985859874

Hoja1

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

Cbico?

Hoja2

Hoja3

Interpretacin de la variabilidad en YYEn primer lugar olvidemos que existe la variable X. Veamos cul es la variabilidad en el eje Y.

La franja sombreada indica la zona donde varan los valores de Y.

Proyeccin sobre el eje Y = olvidar X

Interpretacin del residuoYAhora en los errores de prediccin (lneas verticales). Los proyectamos sobre el eje Y.Se observa que los errores de prediccin, residuos, estn menos dispersos que la variable Y original.

Cuanto menos dispersos sean los residuos, mejor ser la bondad del ajuste.

Coeficiente de Determinacin = r2Error totalError no ExplicadoError Explicado

Grfico3

65

61

60

78

62

66

60

54

84

68

67

57

83

77

93

50

84

60

68

56

64

86

86

37

81

83

63

78

65

Hoja1


0.32107709790.43902892560.5950575838-0.15343165490.240574730317010168605630.82-10517.216560887365

0.5095050130.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.8036134967r real68.827586206912.801047816861

0.06005948070.05769547650.9438398223-1.57441758131.587849599815464.760

0.05548652570.83860121620.662221620.98872529190.41853406418063.378

0.14449624920.11387091140.8898571326-1.20619659021.225769024915864.462

0.30899055740.53754795820.49822607190.0942580074-0.004446566317162.566

0.80759120930.4698249680.2895794741-0.0757096811-0.554613554216961.460

0.56459358020.3623377610.1713417684-0.3522171708-0.94887622916660.954

0.08487780230.73047812450.95883435740.61425949151.737316244417664.884

0.79622382230.23698741340.9235514845-0.71602651771.429373400616364.668

0.92548599490.66471351180.41045670910.425361854-0.22637041217462.167

0.40928312970.36272675970.3066671094-0.351179888-0.505319802116661.557

0.78094424680.55083439150.98900851930.12776961942.290661080417164.983

0.86477479320.95588578090.26399508291.7048173074-0.631076828718761.377

0.16457131620.96558168580.90703611441.81948976781.322722601118864.593

0.46622302180.18906278910.2130066129-0.8813550865-0.796032136316161.150

0.98762363060.99697854840.14927259042.7454502187-1.039558342319760.784

0.66300341160.53765111760.21743730330.0945177443-0.780877165217161.160

0.56783209570.48295272630.6630831527-0.04274403060.420892443517063.368

0.89033912970.29005181210.3509696513-0.5532332659-0.382704066516461.856

0.23191944980.81017356710.08427214430.8785359286-1.376896737117960.464

0.892243320.92592929540.84805634671.44612792141.028132991718464.286

0.93297289510.76293712660.97270838780.71578211881.922178021417764.986

0.93813002260.01684722430.1804037537-2.1237079846-0.913827366714960.937

0.58627896790.66791730920.95659177340.43416954991.712435064817464.881

0.05707053280.82722099210.8991330750.94324021231.276627697317964.583

0.70102967010.34869066750.5972566326-0.38885794170.24625268491666363

0.0237166550.70237231980.86871606940.53123577421.120342661417564.378

0.13259568530.20987961530.8718443876-0.80683880891.13515322216264.465

Hoja1

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

r=0,8

Hoja2

Hoja3

Coeficiente de DeterminacinResumiendo:

La dispersin del error residual ser una fraccin de la dispersin original de Y

Cuanto menor sea la dispersin del error residual mejor ser el ajuste de regresin.

Eso hace que definamos como medida de bondad de un ajuste de regresin, o coeficiente de determinacin a:Y

Resumen sobre bondad de un ajusteLa bondad de un ajuste de un modelo de regresin se mide usando el coeficiente de determinacin r2

r2 es una medida adimensional que slo puede tomar valores en [0, 1]

Cuando un ajuste es bueno, r2 ser cercano a uno.

Cuando un ajuste es malo r2 ser cercano a cero.

A r2 tambin se le denomina porcentaje de variabilidad explicado por el modelo de regresin.

Coef. de correlacin lineal de PearsonLa coeficiente de correlacin lineal de Pearson de dos variables, r, nos indica si los puntos tienen una tendencia a disponerse alineadamente (excluyendo rectas horizontales y verticales).

tiene el mismo signo que cov(x,y) por tanto de su signo obtenemos el que la posible relacin sea directa o inversa.

r es til para determinar si hay relacin lineal entre dos variables, pero no servir para otro tipo de relaciones (cuadrtica, logartmica,...)

Coeficiente de Correlacin :rX e Y son variables aleatorias . Luego, no existe una variable explicativa y otra explicada.

La poblacin de la cual se extrae la muestra es Normal Bivariada .

Existe una relacin lineal entre las variables, la cual est medida por el coeficiente de correlacin poblacional definido como :

r =-1 *Existe relacin inversa y perfecta entre las variables

r =1 *Existe relacin directa y perfecta entre variables

r =0 *No existe relacin lineal entre las variables -Variables no correlacionadas

-1 < r < 0 *Existe relacin inversa entre las variables

0 < r < 1 * Existe relacin directa entre las variables

Correlaciones Negativas

Grfico7

36

49

74

27

64

29

21

17

55

63

22

25

70

2

36

25

-16

15

38

29

-4

34

57

35

57

44

38

45

58

r=-0,5

Hoja1


0.54579486640.43902892560.5950575838-0.15343165490.240574730317010168605630.5200-117.907411494836

0.46270990120.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.6-0.494717264r real36.034482758621.392042927149

0.4852670590.05769547650.9438398223-1.57441758131.587849599815464.774

0.01911357040.83860121620.662221620.98872529190.41853406418063.327

0.92570201880.11387091140.8898571326-1.20619659021.225769024915864.464

0.53085394810.53754795820.49822607190.0942580074-0.004446566317162.529

0.72795158260.4698249680.2895794741-0.0757096811-0.554613554216961.421

0.42381971760.3623377610.1713417684-0.3522171708-0.94887622916660.917

0.54477323810.73047812450.95883435740.61425949151.737316244417664.855

0.42929836280.23698741340.9235514845-0.71602651771.429373400616364.663

0.35054786040.66471351180.41045670910.425361854-0.22637041217462.122

0.94186433010.36272675970.3066671094-0.351179888-0.505319802116661.525

0.2609131380.55083439150.98900851930.12776961942.290661080417164.970

0.63925548160.95588578090.26399508291.7048173074-0.631076828718761.32

0.33941188040.96558168580.90703611441.81948976781.322722601118864.536

0.57540454350.18906278910.2130066129-0.8813550865-0.796032136316161.125

0.25934828650.99697854840.14927259042.7454502187-1.039558342319760.7-16

0.27084887330.53765111760.21743730330.0945177443-0.780877165217161.115

0.21811201870.48295272630.6630831527-0.04274403060.420892443517063.338

0.28946248620.29005181210.3509696513-0.5532332659-0.382704066516461.829

0.02240351990.81017356710.08427214430.8785359286-1.376896737117960.4-4

0.23629557340.92592929540.84805634671.44612792141.028132991718464.234

0.87015346130.76293712660.97270838780.71578211881.922178021417764.957

0.98847085750.01684722430.1804037537-2.1237079846-0.913827366714960.935

0.98361841310.66791730920.95659177340.43416954991.712435064817464.857

0.32776158820.82722099210.8991330750.94324021231.276627697317964.544

0.15788477550.34869066750.5972566326-0.38885794170.24625268491666338

0.79770698560.70237231980.86871606940.53123577421.120342661417564.345

0.49163245750.20987961530.8718443876-0.80683880891.13515322216264.458

Hoja1

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

r=-0,5

Hoja2

Hoja3

Grfico8

35

44

63

24

55

29

25

24

42

52

24

29

53

6

26

31

-8

21

34

32

6

27

43

41

44

34

37

37

50

r=-0,7

Hoja1


0.61729822170.43902892560.5950575838-0.15343165490.240574730317010168605630.7200-110.547735582135

0.69716267940.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.6-0.6931993739r real33.103448275915.166534911244

0.04600106330.05769547650.9438398223-1.57441758131.587849599815464.763

0.98776995690.83860121620.662221620.98872529190.41853406418063.324

0.10007391080.11387091140.8898571326-1.20619659021.225769024915864.455

0.03720506460.53754795820.49822607190.0942580074-0.004446566317162.529

0.60226685980.4698249680.2895794741-0.0757096811-0.554613554216961.425

0.07415733990.3623377610.1713417684-0.3522171708-0.94887622916660.924

0.51056231240.73047812450.95883435740.61425949151.737316244417664.842

0.44379665160.23698741340.9235514845-0.71602651771.429373400616364.652

0.73824211370.66471351180.41045670910.425361854-0.22637041217462.124

0.48712595590.36272675970.3066671094-0.351179888-0.505319802116661.529

0.27533967760.55083439150.98900851930.12776961942.290661080417164.953

0.32230035970.95588578090.26399508291.7048173074-0.631076828718761.36

0.52315988260.96558168580.90703611441.81948976781.322722601118864.526

0.16453416770.18906278910.2130066129-0.8813550865-0.796032136316161.131

0.1013879550.99697854840.14927259042.7454502187-1.039558342319760.7-8

0.94243312090.53765111760.21743730330.0945177443-0.780877165217161.121

0.84700707470.48295272630.6630831527-0.04274403060.420892443517063.334

0.66780761830.29005181210.3509696513-0.5532332659-0.382704066516461.832

0.74994647940.81017356710.08427214430.8785359286-1.376896737117960.46

0.43570087950.92592929540.84805634671.44612792141.028132991718464.227

0.22966503720.76293712660.97270838780.71578211881.922178021417764.943

0.75165687450.01684722430.1804037537-2.1237079846-0.913827366714960.941

0.23349169450.66791730920.95659177340.43416954991.712435064817464.844

0.33325891160.82722099210.8991330750.94324021231.276627697317964.534

0.14709819710.34869066750.5972566326-0.38885794170.24625268491666337

0.86272090460.70237231980.86871606940.53123577421.120342661417564.337

0.99333068680.20987961530.8718443876-0.80683880891.13515322216264.450

Hoja1

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

r=-0,7

Hoja2

Hoja3

Grfico9

33

40

51

21

46

29

29

31

30

42

25

32

37

11

16

36

-1

26

31

35

16

19

30

48

32

25

35

29

42

r=-0,95

Hoja1


0.19371888780.43902892560.5950575838-0.15343165490.240574730317010168605630.95200-13.398215281933

0.72452379970.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.6-0.9456008699r real30.206896551711.059024432740

0.75956365750.05769547650.9438398223-1.57441758131.587849599815464.751

0.8860076550.83860121620.662221620.98872529190.41853406418063.321

0.69250676470.11387091140.8898571326-1.20619659021.225769024915864.446

0.32026330950.53754795820.49822607190.0942580074-0.004446566317162.529

0.5172898010.4698249680.2895794741-0.0757096811-0.554613554216961.429

0.51446254920.3623377610.1713417684-0.3522171708-0.94887622916660.931

0.7480229540.73047812450.95883435740.61425949151.737316244417664.830

0.54475818930.23698741340.9235514845-0.71602651771.429373400616364.642

0.28150412250.66471351180.41045670910.425361854-0.22637041217462.125

0.86331364820.36272675970.3066671094-0.351179888-0.505319802116661.532

0.81466563140.55083439150.98900851930.12776961942.290661080417164.937

0.0424927570.95588578090.26399508291.7048173074-0.631076828718761.311

0.5326931490.96558168580.90703611441.81948976781.322722601118864.516

0.7907436020.18906278910.2130066129-0.8813550865-0.796032136316161.136

0.10424189380.99697854840.14927259042.7454502187-1.039558342319760.7-1

0.97096570350.53765111760.21743730330.0945177443-0.780877165217161.126

0.06550125910.48295272630.6630831527-0.04274403060.420892443517063.331

0.49919217590.29005181210.3509696513-0.5532332659-0.382704066516461.835

0.77768660630.81017356710.08427214430.8785359286-1.376896737117960.416

0.87148717120.92592929540.84805634671.44612792141.028132991718464.219

0.08683559720.76293712660.97270838780.71578211881.922178021417764.930

0.02372694720.01684722430.1804037537-2.1237079846-0.913827366714960.948

0.23367547340.66791730920.95659177340.43416954991.712435064817464.832

0.13815154190.82722099210.8991330750.94324021231.276627697317964.525

0.99762046750.34869066750.5972566326-0.38885794170.24625268491666335

0.8419379530.70237231980.86871606940.53123577421.120342661417564.329

0.88396354460.20987961530.8718443876-0.80683880891.13515322216264.442

Hoja1

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

r=-0,95

Hoja2

Hoja3

Grfico10

32

38

47

20

43

29

31

34

25

38

26

34

30

13

13

39

3

29

30

36

20

16

24

51

27

22

34

26

39

r=-0,999

Hoja1


0.30919189280.43902892560.5950575838-0.15343165490.240574730317010168605630.999200-10.462714484832

0.78490643980.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.6-0.9986429307r real29.27586206910.395279272538

0.77747221160.05769547650.9438398223-1.57441758131.587849599815464.747

0.76591717580.83860121620.662221620.98872529190.41853406418063.320

0.28391026010.11387091140.8898571326-1.20619659021.225769024915864.443

0.49399174920.53754795820.49822607190.0942580074-0.004446566317162.529

0.70429608740.4698249680.2895794741-0.0757096811-0.554613554216961.431

0.10320091660.3623377610.1713417684-0.3522171708-0.94887622916660.934

0.74752938910.73047812450.95883435740.61425949151.737316244417664.825

0.69745751490.23698741340.9235514845-0.71602651771.429373400616364.638

0.94158042580.66471351180.41045670910.425361854-0.22637041217462.126

0.47268893190.36272675970.3066671094-0.351179888-0.505319802116661.534

0.48932701720.55083439150.98900851930.12776961942.290661080417164.930

0.89196259980.95588578090.26399508291.7048173074-0.631076828718761.313

0.17601936970.96558168580.90703611441.81948976781.322722601118864.513

0.89755704180.18906278910.2130066129-0.8813550865-0.796032136316161.139

0.11903461790.99697854840.14927259042.7454502187-1.039558342319760.73

0.25030891630.53765111760.21743730330.0945177443-0.780877165217161.129

0.49519415370.48295272630.6630831527-0.04274403060.420892443517063.330

0.51311001040.29005181210.3509696513-0.5532332659-0.382704066516461.836

0.4647394070.81017356710.08427214430.8785359286-1.376896737117960.420

0.41704355860.92592929540.84805634671.44612792141.028132991718464.216

0.99611579630.76293712660.97270838780.71578211881.922178021417764.924

0.06456219630.01684722430.1804037537-2.1237079846-0.913827366714960.951

0.2766573180.66791730920.95659177340.43416954991.712435064817464.827

0.26284736910.82722099210.8991330750.94324021231.276627697317964.522

0.63533924570.34869066750.5972566326-0.38885794170.24625268491666334

0.87805949470.70237231980.86871606940.53123577421.120342661417564.326

0.63362402120.20987961530.8718443876-0.80683880891.13515322216264.439

Hoja1

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

r=-0,999

Hoja2

Hoja3

correlaciones positivas

Grfico8

66

65

71

81

70

66

56

48

95

78

66

54

98

73

101

45

78

55

71

54

55

93

98

31

93

92

64

85

73

r=0,6

Hoja1


0.47658417240.43902892560.5950575838-0.15343165490.240574730317010168605630.6-105113.78513179666

0.74448372440.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.5787624846r real71.551724137917.633405223865

0.78598472230.05769547650.9438398223-1.57441758131.587849599815464.771

0.36728426210.83860121620.662221620.98872529190.41853406418063.381

0.31006492160.11387091140.8898571326-1.20619659021.225769024915864.470

0.35892228560.53754795820.49822607190.0942580074-0.004446566317162.566

0.18709417150.4698249680.2895794741-0.0757096811-0.554613554216961.456

0.6631853020.3623377610.1713417684-0.3522171708-0.94887622916660.948

0.35417802860.73047812450.95883435740.61425949151.737316244417664.895

0.59374579760.23698741340.9235514845-0.71602651771.429373400616364.678

0.38880562150.66471351180.41045670910.425361854-0.22637041217462.166

0.6713353260.36272675970.3066671094-0.351179888-0.505319802116661.554

0.39556336160.55083439150.98900851930.12776961942.290661080417164.998

0.03910091760.95588578090.26399508291.7048173074-0.631076828718761.373

0.22143921140.96558168580.90703611441.81948976781.322722601118864.5101

0.96582185260.18906278910.2130066129-0.8813550865-0.796032136316161.145

0.5477411710.99697854840.14927259042.7454502187-1.039558342319760.778

0.57736722140.53765111760.21743730330.0945177443-0.780877165217161.155

0.53480884180.48295272630.6630831527-0.04274403060.420892443517063.371

0.56896278160.29005181210.3509696513-0.5532332659-0.382704066516461.854

0.99480469650.81017356710.08427214430.8785359286-1.376896737117960.455

0.18825176740.92592929540.84805634671.44612792141.028132991718464.293

0.03193493210.76293712660.97270838780.71578211881.922178021417764.998

0.84429527160.01684722430.1804037537-2.1237079846-0.913827366714960.931

0.03518975050.66791730920.95659177340.43416954991.712435064817464.893

0.809866180.82722099210.8991330750.94324021231.276627697317964.592

0.90708055210.34869066750.5972566326-0.38885794170.24625268491666364

0.64942946720.70237231980.86871606940.53123577421.120342661417564.385

0.25812389660.20987961530.8718443876-0.80683880891.13515322216264.473

Hoja1

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

r=0,6

Hoja2

Hoja3

Grfico9

85

114

197

114

168

66

12

-28

233

192

48

14

280

23

207

-18

-5

-7

104

23

-55

175

252

-41

229

193

84

175

163

r=0,1

Hoja1


0.62157410810.43902892560.5950575838-0.15343165490.240574730317010168605630.11-105193.419167674285

0.69064233210.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.0954028081r real103.344827586297.513668666114

0.00967073250.05769547650.9438398223-1.57441758131.587849599815464.7197

0.18759116220.83860121620.662221620.98872529190.41853406418063.3114

0.54413110950.11387091140.8898571326-1.20619659021.225769024915864.4168

0.12295343450.53754795820.49822607190.0942580074-0.004446566317162.566

0.73700693650.4698249680.2895794741-0.0757096811-0.554613554216961.412

0.35645030210.3623377610.1713417684-0.3522171708-0.94887622916660.9-28

0.90974405250.73047812450.95883435740.61425949151.737316244417664.8233

0.80766615480.23698741340.9235514845-0.71602651771.429373400616364.6192

0.30063374260.66471351180.41045670910.425361854-0.22637041217462.148

0.73531267810.36272675970.3066671094-0.351179888-0.505319802116661.514

0.71713863590.55083439150.98900851930.12776961942.290661080417164.9280

0.22986979150.95588578090.26399508291.7048173074-0.631076828718761.323

0.76254946560.96558168580.90703611441.81948976781.322722601118864.5207

0.20962820130.18906278910.2130066129-0.8813550865-0.796032136316161.1-18

0.96989194320.99697854840.14927259042.7454502187-1.039558342319760.7-5

0.52010091390.53765111760.21743730330.0945177443-0.780877165217161.1-7

0.12240219960.48295272630.6630831527-0.04274403060.420892443517063.3104

0.32332934940.29005181210.3509696513-0.5532332659-0.382704066516461.823

0.62886776380.81017356710.08427214430.8785359286-1.376896737117960.4-55

0.32163576720.92592929540.84805634671.44612792141.028132991718464.2175

0.99619655770.76293712660.97270838780.71578211881.922178021417764.9252

0.85771995550.01684722430.1804037537-2.1237079846-0.913827366714960.9-41

0.87901027940.66791730920.95659177340.43416954991.712435064817464.8229

0.97128092290.82722099210.8991330750.94324021231.276627697317964.5193

0.16127075980.34869066750.5972566326-0.38885794170.24625268491666384

0.05145907510.70237231980.86871606940.53123577421.120342661417564.3175

0.5909037020.20987961530.8718443876-0.80683880891.13515322216264.4163

Hoja1

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

r=0,1

Hoja2

Hoja3

Grfico1

68

71

84

84

80

66

52

40

110

90

64

50

117

68

113

38

69

49

74

50

43

102

115

24

107

103

67

95

82

r=0,4

Hoja1


0.96278561480.43902892560.5950575838-0.15343165490.240574730317010168605630.42-105122.33989176268

0.72884958310.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.4019895599r real7525.272310048271

0.24308268250.05769547650.9438398223-1.57441758131.587849599815464.784

0.52635142170.83860121620.662221620.98872529190.41853406418063.384

0.50863950040.11387091140.8898571326-1.20619659021.225769024915864.480

0.55985996350.53754795820.49822607190.0942580074-0.004446566317162.566

0.59602864420.4698249680.2895794741-0.0757096811-0.554613554216961.452

0.80864153810.3623377610.1713417684-0.3522171708-0.94887622916660.940

0.87987313340.73047812450.95883435740.61425949151.737316244417664.8110

0.44536999780.23698741340.9235514845-0.71602651771.429373400616364.690

0.19007548650.66471351180.41045670910.425361854-0.22637041217462.164

0.94267983280.36272675970.3066671094-0.351179888-0.505319802116661.550

0.26996493790.55083439150.98900851930.12776961942.290661080417164.9117

0.53698251330.95588578090.26399508291.7048173074-0.631076828718761.368

0.91658998760.96558168580.90703611441.81948976781.322722601118864.5113

0.04159517760.18906278910.2130066129-0.8813550865-0.796032136316161.138

0.71756587380.99697854840.14927259042.7454502187-1.039558342319760.769

0.4257736250.53765111760.21743730330.0945177443-0.780877165217161.149

0.7340984470.48295272630.6630831527-0.04274403060.420892443517063.374

0.79217515180.29005181210.3509696513-0.5532332659-0.382704066516461.850

0.16349300190.81017356710.08427214430.8785359286-1.376896737117960.443

0.87609902720.92592929540.84805634671.44612792141.028132991718464.2102

0.37987287540.76293712660.97270838780.71578211881.922178021417764.9115

0.94283623360.01684722430.1804037537-2.1237079846-0.913827366714960.924

0.80597712590.66791730920.95659177340.43416954991.712435064817464.8107

0.71268062690.82722099210.8991330750.94324021231.276627697317964.5103

0.44776339980.34869066750.5972566326-0.38885794170.24625268491666367

0.69567684650.70237231980.86871606940.53123577421.120342661417564.395

0.45363680980.20987961530.8718443876-0.80683880891.13515322216264.482

Hoja1

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

r=0,4

Hoja2

Hoja3

Grfico3

65

61

60

78

62

66

60

54

84

68

67

57

83

77

93

50

84

60

68

56

64

86

86

37

81

83

63

78

65

r=0,8

Hoja1


0.82764210480.43902892560.5950575838-0.15343165490.240574730317010168605630.82-10517.216560887365

0.48443779890.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.8036134967r real68.827586206912.801047816861

0.87494951180.05769547650.9438398223-1.57441758131.587849599815464.760

0.09048222120.83860121620.662221620.98872529190.41853406418063.378

0.83722174980.11387091140.8898571326-1.20619659021.225769024915864.462

0.56613209760.53754795820.49822607190.0942580074-0.004446566317162.566

0.19465737450.4698249680.2895794741-0.0757096811-0.554613554216961.460

0.94140210750.3623377610.1713417684-0.3522171708-0.94887622916660.954

0.72142453560.73047812450.95883435740.61425949151.737316244417664.884

0.32169090690.23698741340.9235514845-0.71602651771.429373400616364.668

0.53772385560.66471351180.41045670910.425361854-0.22637041217462.167

0.19731314950.36272675970.3066671094-0.351179888-0.505319802116661.557

0.02376851410.55083439150.98900851930.12776961942.290661080417164.983

0.64190367980.95588578090.26399508291.7048173074-0.631076828718761.377

0.34736649610.96558168580.90703611441.81948976781.322722601118864.593

0.69768502570.18906278910.2130066129-0.8813550865-0.796032136316161.150

0.17596406410.99697854840.14927259042.7454502187-1.039558342319760.784

0.35440034640.53765111760.21743730330.0945177443-0.780877165217161.160

0.77712879430.48295272630.6630831527-0.04274403060.420892443517063.368

0.3932159450.29005181210.3509696513-0.5532332659-0.382704066516461.856

0.98512241010.81017356710.08427214430.8785359286-1.376896737117960.464

0.0985164190.92592929540.84805634671.44612792141.028132991718464.286

0.74107843230.76293712660.97270838780.71578211881.922178021417764.986

0.34261101850.01684722430.1804037537-2.1237079846-0.913827366714960.937

0.99414000130.66791730920.95659177340.43416954991.712435064817464.881

0.66027963270.82722099210.8991330750.94324021231.276627697317964.583

0.8175993160.34869066750.5972566326-0.38885794170.24625268491666363

0.8542092950.70237231980.86871606940.53123577421.120342661417564.378

0.4008132320.20987961530.8718443876-0.80683880891.13515322216264.465

Hoja1

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

r=0,8

Hoja2

Hoja3

casi perfectas y positivas

Grfico6

63

57

49

75

53

66

64

61

71

58

69

61

66

82

83

56

92

66

65

59

74

79

72

44

69

74

61

70

57

r=1

Hoja1


0.47700924580.43902892560.5950575838-0.15343165490.240574730317010168605630.9999-10510.146224369663

0.91912983670.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.61r real66.068965517210.33884884757

0.98545306580.05769547650.9438398223-1.57441758131.587849599815464.749

0.34588573090.83860121620.662221620.98872529190.41853406418063.375

0.15509038990.11387091140.8898571326-1.20619659021.225769024915864.453

0.35404648080.53754795820.49822607190.0942580074-0.004446566317162.566

0.30181521020.4698249680.2895794741-0.0757096811-0.554613554216961.464

0.3385061590.3623377610.1713417684-0.3522171708-0.94887622916660.961

0.68031426020.73047812450.95883435740.61425949151.737316244417664.871

0.5776764880.23698741340.9235514845-0.71602651771.429373400616364.658

0.57211611240.66471351180.41045670910.425361854-0.22637041217462.169

0.9636665390.36272675970.3066671094-0.351179888-0.505319802116661.561

0.38040682790.55083439150.98900851930.12776961942.290661080417164.966

0.18678390630.95588578090.26399508291.7048173074-0.631076828718761.382

0.61607118640.96558168580.90703611441.81948976781.322722601118864.583

0.64644911010.18906278910.2130066129-0.8813550865-0.796032136316161.156

0.98803732760.99697854840.14927259042.7454502187-1.039558342319760.792

0.72592174690.53765111760.21743730330.0945177443-0.780877165217161.166

0.48880282950.48295272630.6630831527-0.04274403060.420892443517063.365

0.74391508850.29005181210.3509696513-0.5532332659-0.382704066516461.859

0.20141147680.81017356710.08427214430.8785359286-1.376896737117960.474

0.27344082720.92592929540.84805634671.44612792141.028132991718464.279

0.67369119640.76293712660.97270838780.71578211881.922178021417764.972

0.53256668360.01684722430.1804037537-2.1237079846-0.913827366714960.944

0.54872629620.66791730920.95659177340.43416954991.712435064817464.869

0.25228187850.82722099210.8991330750.94324021231.276627697317964.574

0.87165544830.34869066750.5972566326-0.38885794170.24625268491666361

0.73948508560.70237231980.86871606940.53123577421.120342661417564.370

0.69435243490.20987961530.8718443876-0.80683880891.13515322216264.457

Hoja1

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

r=1

Hoja2

Hoja3

Grfico2

64

60

57

77

59

66

61

56

80

65

68

58

77

79

90

52

87

62

67

57

67

84

82

39

78

80

62

76

63

r=0,9

Hoja1


0.35503405380.43902892560.5950575838-0.15343165490.240574730317010168605630.9-10515.007333035264

0.00076888730.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.8913679189r real68.034482758611.651499115160

0.76256905750.05769547650.9438398223-1.57441758131.587849599815464.757

0.40204064980.83860121620.662221620.98872529190.41853406418063.377

0.65254883690.11387091140.8898571326-1.20619659021.225769024915864.459

0.89345411450.53754795820.49822607190.0942580074-0.004446566317162.566

0.82418578990.4698249680.2895794741-0.0757096811-0.554613554216961.461

0.53996918230.3623377610.1713417684-0.3522171708-0.94887622916660.956

0.24866681330.73047812450.95883435740.61425949151.737316244417664.880

0.36810036930.23698741340.9235514845-0.71602651771.429373400616364.665

0.32505406060.66471351180.41045670910.425361854-0.22637041217462.168

0.56725610310.36272675970.3066671094-0.351179888-0.505319802116661.558

0.23351551310.55083439150.98900851930.12776961942.290661080417164.977

0.56718144480.95588578090.26399508291.7048173074-0.631076828718761.379

0.5002961790.96558168580.90703611441.81948976781.322722601118864.590

0.6201006280.18906278910.2130066129-0.8813550865-0.796032136316161.152

0.21959439850.99697854840.14927259042.7454502187-1.039558342319760.787

0.84791492850.53765111760.21743730330.0945177443-0.780877165217161.162

0.58384005610.48295272630.6630831527-0.04274403060.420892443517063.367

0.10451772330.29005181210.3509696513-0.5532332659-0.382704066516461.857

0.67988775130.81017356710.08427214430.8785359286-1.376896737117960.467

0.38893237210.92592929540.84805634671.44612792141.028132991718464.284

0.9161537510.76293712660.97270838780.71578211881.922178021417764.982

0.7573156110.01684722430.1804037537-2.1237079846-0.913827366714960.939

0.80794229020.66791730920.95659177340.43416954991.712435064817464.878

0.01255949510.82722099210.8991330750.94324021231.276627697317964.580

0.55812846440.34869066750.5972566326-0.38885794170.24625268491666362

0.5909763310.70237231980.86871606940.53123577421.120342661417564.376

0.18987388850.20987961530.8718443876-0.80683880891.13515322216264.463

Hoja1

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

r=0,9

Hoja2

Hoja3

Grfico5

63

58

51

76

55

66

63

60

74

60

69

60

69

81

85

55

90

65

66

58

72

81

75

43

72

76

61

72

59

r=0,99

Hoja1


0.44659047840.43902892560.5950575838-0.15343165490.240574730317010168605630.99-10511.473206171963

0.17641518270.21452462770.7282081777-0.79081939810.607402612171.068965517210.33884884716262.99655172411.548410254563.60.9881633659r real66.72413793110.451518786658

0.78483671350.05769547650.9438398223-1.57441758131.587849599815464.751

0.09269008530.83860121620.662221620.98872529190.41853406418063.376

0.52065465670.11387091140.8898571326-1.20619659021.225769024915864.455

0.56071040160.53754795820.49822607190.0942580074-0.004446566317162.566

0.94818143880.4698249680.2895794741-0.0757096811-0.554613554216961.463

0.3012378920.3623377610.1713417684-0.3522171708-0.94887622916660.960

0.66866410.73047812450.95883435740.61425949151.737316244417664.874

0.16145271740.23698741340.9235514845-0.71602651771.429373400616364.660

0.83846469610.66471351180.41045670910.425361854-0.22637041217462.169

0.77310779410.36272675970.3066671094-0.351179888-0.505319802116661.560

0.90297267980.55083439150.98900851930.12776961942.290661080417164.969

0.30601530410.95588578090.26399508291.7048173074-0.631076828718761.381

0.58762811740.96558168580.90703611441.81948976781.322722601118864.585

0.30706795530.18906278910.2130066129-0.8813550865-0.796032136316161.155

0.92571621180.99697854840.14927259042.7454502187-1.039558342319760.790

0.67024332860.53765111760.21743730330.0945177443-0.780877165217161.165

0.67105706480.48295272630.6630831527-0.04274403060.420892443517063.366

0.66276025750.29005181210.3509696513-0.5532332659-0.382704066516461.858

0.17981586580.81017356710.08427214430.8785359286-1.376896737117960.472

0.18294537140.92592929540.84805634671.44612792141.028132991718464.281

0.91781929230.76293712660.97270838780.71578211881.922178021417764.975

0.11459626870.01684722430.1804037537-2.1237079846-0.913827366714960.943

0.66128154380.66791730920.95659177340.43416954991.712435064817464.872

0.65736863710.82722099210.8991330750.94324021231.276627697317964.576

0.22871230540.34869066750.5972566326-0.38885794170.24625268491666361

0.39487873970.70237231980.86871606940.53123577421.120342661417564.372

0.31542994930.20987961530.8718443876-0.80683880891.13515322216264.459

Hoja1

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

r=0,95

Hoja2

Hoja3

Animacin: Residuos del modelo de regresin

INFERENCIA SOBRE EL COEFICIENTE DE CORRELACINDistribucin del coeficiente de correlacin muestral rH0 : = 0 H1 : 0 H0 : X e Y son independientes H1 : X e Y no son independientes

DISTRIBUCIN DE LOS ESTIMADORES DE y

VARIANCIA DE LA RECTA DE REGRESIN

ESTIMACIN DE LA MEDIA DE Yi Correspondiente a un valor conocido de xi

ESTIMACION DE UN FUTURO VALOR Yi PARA Xi FIJO

Clase Regresion y Correlacion

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Transcript of Clase Regresion y Correlacion