### definir directorio
#setwd("~/AESpecialist/Regresion")
mtcars## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
## Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
## Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
## Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
## Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
## Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
## Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
## Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
## Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
## Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
## Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
## Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
## Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
## Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
## Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
## Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
## Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
## AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
## Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
## Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
## Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
## Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
## Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
## Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
## Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
## Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
## Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2library(readxl)
library(MASS)
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(nortest)
library(MVN)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2## sROC 0.1-2 loadedattach(mtcars)## exploracion y resumen datos
head(mtcars)## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000dim(mtcars)## [1] 32 11realizamos prueba de Mardia \[ H_0: \text{elvector aleatorio distribuye normal bivariado }\\H_a: \text{el vector aleatorio No distribuye normal bivariado}\]
mvn(mtcars)## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 394.609460003421 2.11444606575459e-05 NO
## 2 Mardia Kurtosis 0.0383039985304523 0.969445302761312 YES
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk mpg 0.9476 0.1229 YES
## 2 Shapiro-Wilk cyl 0.7533 <0.001 NO
## 3 Shapiro-Wilk disp 0.9200 0.0208 NO
## 4 Shapiro-Wilk hp 0.9334 0.0488 NO
## 5 Shapiro-Wilk drat 0.9459 0.1101 YES
## 6 Shapiro-Wilk wt 0.9433 0.0927 YES
## 7 Shapiro-Wilk qsec 0.9733 0.5935 YES
## 8 Shapiro-Wilk vs 0.6323 <0.001 NO
## 9 Shapiro-Wilk am 0.6251 <0.001 NO
## 10 Shapiro-Wilk gear 0.7728 <0.001 NO
## 11 Shapiro-Wilk carb 0.8511 4e-04 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## mpg 32 20.090625 6.0269481 19.200 10.400 33.900 15.42500 22.80
## cyl 32 6.187500 1.7859216 6.000 4.000 8.000 4.00000 8.00
## disp 32 230.721875 123.9386938 196.300 71.100 472.000 120.82500 326.00
## hp 32 146.687500 68.5628685 123.000 52.000 335.000 96.50000 180.00
## drat 32 3.596563 0.5346787 3.695 2.760 4.930 3.08000 3.92
## wt 32 3.217250 0.9784574 3.325 1.513 5.424 2.58125 3.61
## qsec 32 17.848750 1.7869432 17.710 14.500 22.900 16.89250 18.90
## vs 32 0.437500 0.5040161 0.000 0.000 1.000 0.00000 1.00
## am 32 0.406250 0.4989909 0.000 0.000 1.000 0.00000 1.00
## gear 32 3.687500 0.7378041 4.000 3.000 5.000 3.00000 4.00
## carb 32 2.812500 1.6152000 2.000 1.000 8.000 2.00000 4.00
## Skew Kurtosis
## mpg 0.6106550 -0.37276603
## cyl -0.1746119 -1.76211977
## disp 0.3816570 -1.20721195
## hp 0.7260237 -0.13555112
## drat 0.2659039 -0.71470062
## wt 0.4231465 -0.02271075
## qsec 0.3690453 0.33511422
## vs 0.2402577 -2.00193762
## am 0.3640159 -1.92474143
## gear 0.5288545 -1.06975068
## carb 1.0508738 1.25704307cor.test(disp,wt, data="mtcars")## coeficiente pearson ##
## Pearson's product-moment correlation
##
## data: disp and wt
## t = 10.576, df = 30, p-value = 1.222e-11
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.7811586 0.9442902
## sample estimates:
## cor
## 0.8879799Para este test la hipotesis sera la siguiente \[ H_0: \rho= 0\\H_a:\rho \not= 0\] EL test de mardia confirma la normalidad de los datos de mt cars pero esta no es normalidad bivariada, el test confirma normalidad univariada ya que el skewness no se cumple en los datos mtcars. La correlacion de pearson nos da valor de 0.8, la corrimos sin embargo ya que la prueba de mardia resulto en univariada el coeficiente de correlacion mas apropiado es el de spearman, no es necesario interpretar.
La decisión se toma a partir del valor p, en este caso con un alfa de 0.01
cor.test(disp, wt, data="mtcars", method = "spearman")## coeficiente spearman ## Warning in cor.test.default(disp, wt, data = "mtcars", method = "spearman"):
## Cannot compute exact p-value with ties##
## Spearman's rank correlation rho
##
## data: disp and wt
## S = 558.11, p-value = 3.346e-12
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## 0.8977064La decisión se toma a partir del valor p, en este caso con un alfa de 0.01, se rechaza H_0 El coeficiente de spearman da 0.9, puedo decir qu existe una relacion positiva y significativa entre dist y wt a medida qye aumenta una aumenta la otra.