Tabla 3.3 - Transformación de variables e interpretación de β1
Tabla 3.3 - Transformación de variables e interpretación de β1
|
Modelo
|
Regresión
|
Variable dependiente
|
Variable independiente
|
Interpretación de β1
|
|
Lin-Lin
|
Yi = β0 + β1Xi + εi
|
Y
|
X
|
ΔY = β1ΔX
|
|
Lin-Log
|
Yi = β0 + β1log(Xi) + εi
|
Y
|
log(X)
|
ΔY = (β1/100)%ΔX
|
|
Log-Lin
|
log(Yi) = β0 + β1Xi + εi
|
log(Y)
|
X
|
%ΔY = (100β1)ΔX
|
|
Log-Log
|
log(Yi) = β0 + β1log(Xi) + εi
|
log(Y)
|
log(X)
|
%ΔY = β1%ΔX
|
library(paqueteMETODOS)
## Cargando paquete requerido: dplyr
##
## Adjuntando el paquete: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
## Cargando paquete requerido: ggplot2
library(nortest)
data(biomasa)
head(biomasa)
## # A tibble: 6 × 8
## finca mg bio_aerea bio_sub bio_total area_foliar diametro altura
## <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 FINCA_1 GENOTIPO_1 12.8 0.93 13.7 44.5 4.7 5
## 2 FINCA_1 GENOTIPO_1 13.9 0.69 14.6 39.7 5.3 5.6
## 3 FINCA_1 GENOTIPO_1 15.1 0.78 15.9 45.6 4.8 5.8
## 4 FINCA_1 GENOTIPO_1 8.08 0.91 8.99 29.5 3.2 4.3
## 5 FINCA_1 GENOTIPO_1 5.58 1.41 6.99 22.5 2.2 3.3
## 6 FINCA_1 GENOTIPO_2 18.5 0.84 19.3 34.2 6.3 7.9
modelo1=lm(bio_total ~ diametro, data=biomasa) # Lin - Lin
modelo2=lm(bio_total ~ log(diametro), data=biomasa) # Lin - Log
modelo3=lm(log(bio_total) ~ diametro, data=biomasa) # Log - Lin
modelo4=lm(log(bio_total) ~ log(diametro), data=biomasa) # Log - Log
u=modelo1$residuals
shapiro.test(u) # Normalidad
##
## Shapiro-Wilk normality test
##
## data: u
## W = 0.95356, p-value = 0.002793
lmtest::bptest(modelo1) # Homoscedasticidad
##
## studentized Breusch-Pagan test
##
## data: modelo1
## BP = 11.76, df = 1, p-value = 0.0006052
lmtest::dwtest(modelo1) # No autocorrelación
##
## Durbin-Watson test
##
## data: modelo1
## DW = 1.0719, p-value = 1.035e-06
## alternative hypothesis: true autocorrelation is greater than 0
boxplot (u) # Outliers
u2=modelo2$residuals
shapiro.test(u2) # Normalidad
##
## Shapiro-Wilk normality test
##
## data: u2
## W = 0.90336, p-value = 5.741e-06
lmtest::bptest(modelo2) # Homoscedasticidad
##
## studentized Breusch-Pagan test
##
## data: modelo2
## BP = 3.8361, df = 1, p-value = 0.05016
lmtest::dwtest(modelo2) # No autocorrelación
##
## Durbin-Watson test
##
## data: modelo2
## DW = 1.1852, p-value = 2.018e-05
## alternative hypothesis: true autocorrelation is greater than 0
boxplot (u2) # Outliers
u3=modelo3$residuals
shapiro.test(u3) # Normalidad
##
## Shapiro-Wilk normality test
##
## data: u3
## W = 0.98394, p-value = 0.3338
lmtest::bptest(modelo3) # Homoscedasticidad
##
## studentized Breusch-Pagan test
##
## data: modelo3
## BP = 3.879, df = 1, p-value = 0.04889
lmtest::dwtest(modelo3) # No autocorrelación
##
## Durbin-Watson test
##
## data: modelo3
## DW = 0.67803, p-value = 1.716e-13
## alternative hypothesis: true autocorrelation is greater than 0
boxplot (u3) # Outliers
u4=modelo4$residuals
shapiro.test(u4) # Normalidad
##
## Shapiro-Wilk normality test
##
## data: u4
## W = 0.98194, p-value = 0.2459
lmtest::bptest(modelo4) # Homoscedasticidad
##
## studentized Breusch-Pagan test
##
## data: modelo4
## BP = 0.79099, df = 1, p-value = 0.3738
lmtest::dwtest(modelo4) # No autocorrelación
##
## Durbin-Watson test
##
## data: modelo4
## DW = 0.91146, p-value = 6.207e-09
## alternative hypothesis: true autocorrelation is greater than 0
boxplot (u4) # Outliers
stargazer::stargazer(modelo1, modelo2, modelo3, modelo4, type="text", df=FALSE)
##
## ===============================================================
## Dependent variable:
## -------------------------------------------
## bio_total log(bio_total)
## (1) (2) (3) (4)
## ---------------------------------------------------------------
## diametro 5.103*** 0.278***
## (0.251) (0.011)
##
## log(diametro) 23.369*** 1.344***
## (1.564) (0.058)
##
## Constant -9.020*** -19.909*** 1.328*** 0.618***
## (1.413) (2.629) (0.060) (0.098)
##
## ---------------------------------------------------------------
## Observations 90 90 90 90
## R2 0.825 0.717 0.887 0.858
## Adjusted R2 0.823 0.714 0.885 0.857
## Residual Std. Error 3.435 4.362 0.145 0.162
## F Statistic 413.961*** 223.224*** 687.562*** 532.232***
## ===============================================================
## Note: *p<0.1; **p<0.05; ***p<0.01
Tabla de Transformaciones
Tabla de Transformaciones
|
λ
|
-2
|
-1
|
-0.5
|
0
|
0.5
|
1
|
2
|
|
Transformación
|
1/y2
|
1/y
|
1/√y
|
log(y)
|
√y
|
y
|
y2
|
modelo1=lm(bio_total ~ diametro, data=biomasa)
summary(modelo1)
##
## Call:
## lm(formula = bio_total ~ diametro, data = biomasa)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.3775 -2.6594 0.0237 1.8758 11.9876
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.0203 1.4129 -6.384 7.86e-09 ***
## diametro 5.1026 0.2508 20.346 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.435 on 88 degrees of freedom
## Multiple R-squared: 0.8247, Adjusted R-squared: 0.8227
## F-statistic: 414 on 1 and 88 DF, p-value: < 2.2e-16
par(mfrow = c(1,2))
library(MASS)
##
## Adjuntando el paquete: 'MASS'
## The following object is masked from 'package:dplyr':
##
## select
boxcox(lm(mpg ~ wt, data = mtcars))
boxcox(lm(biomasa$bio_total ~ biomasa$diametro, data=biomasa), lambda = -3:3)
#Se repite el proceso pero esta vez entrechando el rango de valores de lambda
bc<-boxcox(lm(biomasa$bio_total ~ biomasa$diametro), lambda = -1:1)
(lambda <- bc$x[which.max(bc$y)])
## [1] 0.07070707