Clase Regresion y Correlacion
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Transcript of Clase Regresion y Correlacion
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Regresin y Correlacin
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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
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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.
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Modelo de Regresin Lineal El Modelo es la expresin terica del comportamiento de la poblacin
ParmetrosError ResidualParte sistemtica
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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.
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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
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CALCULO DE LA RECTA DE REGRESIN ( x1 , y1 ) , ( x2 , y2 ) , ... , ( xn , yn ) Recta de EstimacinModelo de Regresin
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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
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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.
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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.
Grfico3
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68
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68
56
64
86
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81
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63
78
65
Hoja1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
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0
r=0,8
Hoja2
Hoja3
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Relacin entre variables.El peso aumenta con la altura
Grfico3
65
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78
62
66
60
54
84
68
67
57
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77
93
50
84
60
68
56
64
86
86
37
81
83
63
78
65
Hoja1
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
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
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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.
Grfico3
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54
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86
86
37
81
83
63
78
65
Hoja1
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
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EstimacinExisten dos mtodos para hallar los estimadores de y que dan los mismos resultados.Mtodo de Mxima VerosimilitudMtodo de los Mnimos Cuadrados
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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),
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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.
Grfico2
64
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57
77
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66
61
56
80
65
68
58
77
79
90
52
87
62
67
57
67
84
82
39
78
80
62
76
63
Hoja1
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
0
0
0
0
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0
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0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
r=0,9
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
Hoja1
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
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
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Supuestos de los errores
Grfico2
3
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10
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6
7
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11
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14
Hoja4
Columna 1Columna 2
Columna 11
Columna 20.77912905931
Hoja1
23
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28
34
35
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39
310
45
46
47
48
49
410
411
412
56
57
58
59
510
511Resumen
512
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
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
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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
U1UF1UF2Z1Z2med1dt1N1med2dt2N2rabCerrorY
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