análisis de regresión y correlación lineal
DESCRIPTION
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Análisis de regresión y Correlación Lineal
El objetivo primordial del análisis de Regresión es estimar el valor de las variablealeato0ria (variable independiente).
El termino de análisis de regresión indica que el valor de una variable dependiente se estima con base en una variable independiente o de Predicción.
Diagrama de Disposición
Es una grafica en la que cada punto trazado representa un par de valores observados de las variables independientes y dependientes.
Método de mínimos cuadrados
Para el ajuste de una línea de regresión
y=b0+b1 x
Calculo de b1 y b0
b1=εxy−nx yε x2−nx2
b0=Y−b1 x
Modelo #1
Prueba#1 Se toma una muestra aleatoria de 10 embarques de una compañía Y y se registra el tiempo de entrega (y) en días y la distancia recorrida (x) en millas.
1. Calcule la ecuación de regresión y estime el tiempo que tarda un embarque al recorrer X=1000 millas.
Millas Xy x2 y2
1 825 3.5 2887.5 680625 12.252 215 1.0 215 46225 13 1070 4.0 4280 1144900 164 550 2.0 1100 302500 45 480 1.0 480 230400 16 920 3.0 2760 846400 97 1350 4.5 6075 1822500 20.258 325 1.5 487.5 105625 2.259 670 3.0 2010 448900 9
10 1215 5.0 6075 1476225 25Total 7620 28.5 26370 7104300 99.75
Embarque Muestreal
Tiempo de entrega (y)
b1=26370−10 (7620 )(2.85)7104300−10 (762)2
= 0.0036
b0=2.25−0.0036(762)= 0.11
Sustitución en la ecuación de Regresion
a)Ŷ=0.11+.0036(x)
Y 1000=.11+.0036(1000)
Y 1000=3.71dias
El camión tarda 3.71 dias en recorrer la distancia x=1000 millas.
b) Calcule x=1500
Y 1500=0.11+.0036 (1500 )
Y 1500=5.51dias
El camión tarda 5.51 dias en recorrer la distancia X=1500 millas
c) Calcule x=500Y 500=0.11+ .0036 (500 )
Y 500=1.91diasEl camión tarda 1.91 dias en recorrer la distancia X=500 millas
d) Caqlcule x=820Y 82 0=0.11+.0036 (820 )Y 820=3.062dias
El camión tarde 3.062 dias en recorrer la distancia x=820