REGRESIÓN LINEAL MÚLTIPLE
Ing. Eco. Máximo Pasache Ramos e-mail:
[email protected]
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Regresión Lineal Múltiple Definición: El Modelo de Regresión Lineal Múltiple, utiliza mas de una variable explicativa, haciendo posible incrementar el poder explicativo y la utilidad del modelo en la toma de muchas decisiones de negocio. Este modelo permite incorporar dos o más variables explicativas independientes.
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Regresión Lineal Múltiple Modelo de Regresión Múltiple Estimado
En donde: es el valor estimado para la variable dependiente y bi son los estimados para los los coeficientes poblacionales βi
Los bi se denominan coeficientes parciales (o netos) de regresión y tienen la misma interpretación que en la
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Regresión Lineal Múltiple Ejemplo con 2 variables Independientes:
En donde: es el valor proyectado de los pasajeros expresado en miles X1 Publicidad expresada en miles de dólares X2 Ingreso Nacional en millones de dólares
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Regresión Lineal Múltiple Gráfico:
Plano de Regresión, los coeficientes de las dos variables
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Supuestos en la Regresión Lineal Múltiple 1) Mode Modello de de Re Regr gre esió ión n Lineal, o lineal en los parámetros 2) Valores de de “X” independientes del término del error. Esto significa que se requiere covarianza cero entre u i y cada variable de X… Cov(u i ,X 1 ) = Cov(u i ,X 2 ) = 0 3) Valor medio de la perturbación u i igual a cero E(u i | X 1 , X 2 ) = 0
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Supuestos en la Regresión Lineal Múltiple 6) El número de observaciones de parámetros por estimar.
“n” debe
ser mayor que el
7) Debe haber variación en los valores de las variables
“X”
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Regresión Lineal Múltiple Ejemplo: 1
Y
X1
X2
123.4
300.5
4.3
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Regresión Lineal Múltiple Cálculo de Coeficientes a través de Sistema de Ecuaciones :
… (1)
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Regresión Lineal Múltiple Y
X1
X2
Y.X Y.X1
Y.X2
X21
X22
X1.X2
1
123.4
300.5
4.3
37081.7
530.62
90300.25
18.49
1292.15 1292.15
2
135.7
325.9
5.5
44224.63
746.35
106210.81
30.25
1792.45
3
115.9
298.6
7.8
34607.74
904.02
89161.96
60.84
2329.08
4
100.6
200.9
4.9
20210.54
492.94
40360.81
24.01
984.41
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Regresión Lineal Múltiple Resolviendo el Sistema de Ecuaciones: Y* = 56.221 + 0.158X 0.158X1 + 3.652X2
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Regresión Lineal Múltiple
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Regresión Lineal Múltiple