PARTE 1
Carga de datos
library(readr)
library(dplyr)
ejemplo_regresion <- read_csv("C:/Users/ariel/Downloads/ejemplo_regresion.csv")
head(ejemplo_regresion,n = 6)
## # A tibble: 6 x 3
## X1 X2 Y
## <dbl> <dbl> <dbl>
## 1 3.92 7298 0.75
## 2 3.61 6855 0.71
## 3 3.32 6636 0.66
## 4 3.07 6506 0.61
## 5 3.06 6450 0.7
## 6 3.11 6402 0.72
Ejemplo de regresión lineal
library(stargazer)
options(scipen = 9999)
mod_lineal<-lm(formula = Y~X1+X2,data = ejemplo_regresion)
summary(mod_lineal)
##
## Call:
## lm(formula = Y ~ X1 + X2, data = ejemplo_regresion)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.085090 -0.039102 -0.003341 0.030236 0.105692
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.56449677 0.07939598 19.705 0.00000000000000182 ***
## X1 0.23719747 0.05555937 4.269 0.000313 ***
## X2 -0.00024908 0.00003205 -7.772 0.00000009508790794 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0533 on 22 degrees of freedom
## Multiple R-squared: 0.8653, Adjusted R-squared: 0.8531
## F-statistic: 70.66 on 2 and 22 DF, p-value: 0.000000000265
stargazer(mod_lineal,title = "Ejemplo de Regresión Multiple",type = "text",digits = 8)
##
## Ejemplo de Regresión Multiple
## ===============================================
## Dependent variable:
## ---------------------------
## Y
## -----------------------------------------------
## X1 0.23719750***
## (0.05555937)
##
## X2 -0.00024908***
## (0.00003205)
##
## Constant 1.56449700***
## (0.07939598)
##
## -----------------------------------------------
## Observations 25
## R2 0.86529610
## Adjusted R2 0.85305030
## Residual Std. Error 0.05330222 (df = 22)
## F Statistic 70.66057000*** (df = 2; 22)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
Objetos dentro del modelo lineal
Vector de Coeficientes estimados:
options(scipen = 999)
mod_lineal$coefficients
## (Intercept) X1 X2
## 1.5644967711 0.2371974748 -0.0002490793
Matriz de Varianza - Covarianza de los parámetros
var_covar1<-vcov(mod_lineal)
print(var_covar1)
## (Intercept) X1 X2
## (Intercept) 0.0063037218732 0.000240996434 -0.000000982806321
## X1 0.0002409964344 0.003086843196 -0.000001675537651
## X2 -0.0000009828063 -0.000001675538 0.000000001027106
Intérvalos de confianza
confint(object = mod_lineal,level = .95)
## 2.5 % 97.5 %
## (Intercept) 1.3998395835 1.7291539588
## X1 0.1219744012 0.3524205485
## X2 -0.0003155438 -0.0001826148
Valores Ajustados
plot(mod_lineal$fitted.values,main = "Valores Ajustados",ylab = "Y",xlab = "casos")
mod_lineal$fitted.values %>% as.matrix()
## [,1]
## 1 0.6765303
## 2 0.7133412
## 3 0.6991023
## 4 0.6721832
## 5 0.6837597
## 6 0.7075753
## 7 0.7397638
## 8 0.7585979
## 9 0.7943078
## 10 0.7935605
## 11 0.7984347
## 12 0.8272778
## 13 0.8021665
## 14 0.7992462
## 15 0.7544349
## 16 0.7339716
## 17 0.7048866
## 18 0.6930338
## 19 0.6350898
## 20 0.6127185
## 21 0.5701215
## 22 0.4796371
## 23 0.4374811
## 24 0.3953981
## 25 0.3773799
Residuos del Modelo
plot(mod_lineal$residuals,main = "Residuos",ylab = "Residuos",xlab = "casos")
mod_lineal$residuals %>% matrix()
## [,1]
## [1,] 0.073469743
## [2,] -0.003341163
## [3,] -0.039102258
## [4,] -0.062183196
## [5,] 0.016240338
## [6,] 0.012424659
## [7,] 0.030236216
## [8,] -0.018597878
## [9,] 0.105692240
## [10,] 0.026439478
## [11,] -0.048434733
## [12,] -0.057277771
## [13,] -0.022166535
## [14,] 0.040753758
## [15,] 0.035565142
## [16,] -0.033971640
## [17,] -0.024886579
## [18,] 0.026966239
## [19,] -0.085089833
## [20,] 0.017281530
## [21,] -0.010121525
## [22,] -0.069637086
## [23,] 0.072518915
## [24,] 0.074601871
## [25,] -0.057379932
PARTE 1.1 PRUEBAS DE NORMALIDAD
Ajuste de los residuos a la distribución normal
library(fitdistrplus)
library(stargazer)
fit_normal<-fitdist(data = mod_lineal$residuals,distr = "norm")
plot(fit_normal)
summary(fit_normal)
## Fitting of the distribution ' norm ' by maximum likelihood
## Parameters :
## estimate Std. Error
## mean 0.000000000000000007770748 0.010000382
## sd 0.050001911895951975384200 0.007058615
## Loglikelihood: 39.41889 AIC: -74.83778 BIC: -72.40002
## Correlation matrix:
## mean sd
## mean 1 0
## sd 0 1
Prueba de Normalidad de Jarque - Bera
library(normtest)
library(psych)
jb.norm.test(mod_lineal$residuals)
##
## Jarque-Bera test for normality
##
## data: mod_lineal$residuals
## JB = 0.93032, p-value = 0.5035
Se rechaza Ho por lo que los residuos no tienen distribucion normal
qqnorm(mod_lineal$residuals)
qqline(mod_lineal$residuals)
hist(mod_lineal$residuals,main = "Histograma de los residuos",xlab = "Residuos",ylab = "frecuencia")
Prueba de Normalidad de Kolmogorov - Smirnov
library(nortest)
lillie.test(mod_lineal$residuals)
##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: mod_lineal$residuals
## D = 0.082345, p-value = 0.9328
No se rechaza Ho por lo que los residuos tienen distribucion normal
qqnorm(mod_lineal$residuals)
qqline(mod_lineal$residuals)
hist(mod_lineal$residuals,main = "Histograma de los residuos",xlab = "Residuos",ylab = "frecuencia")
PARTE 2
Carga de datos
library(readr)
library(dplyr)
options(scipen=9999)
regresion <- read_csv("C:/Users/ariel/OneDrive/Documentos/matriz_1.csv")
head(regresion,n = 6)
## # A tibble: 6 x 3
## Y X1 X2
## <dbl> <dbl> <dbl>
## 1 320 50 7.4
## 2 450 53 5.1
## 3 370 60 4.2
## 4 470 63 3.9
## 5 420 69 1.4
## 6 500 82 2.2
Construcción de matriz añadiendo X3
regresion %>% mutate(X3=X1*X2) %>% dplyr ::select("Y","X1","X2","X3")->regresion
regresion
## # A tibble: 20 x 4
## Y X1 X2 X3
## <dbl> <dbl> <dbl> <dbl>
## 1 320 50 7.4 370
## 2 450 53 5.1 270.
## 3 370 60 4.2 252
## 4 470 63 3.9 246.
## 5 420 69 1.4 96.6
## 6 500 82 2.2 180.
## 7 570 100 7 700
## 8 640 104 5.7 593.
## 9 670 113 13.1 1480.
## 10 780 130 16.4 2132
## 11 690 150 5.1 765
## 12 700 181 2.9 525.
## 13 910 202 4.5 909
## 14 930 217 6.2 1345.
## 15 940 229 3.2 733.
## 16 1070 240 2.4 576
## 17 1160 243 4.9 1191.
## 18 1210 247 8.8 2174.
## 19 1450 249 10.1 2515.
## 20 1220 254 6.7 1702.
Ingreso Modelo lineal
library(stargazer)
options(scipen=9999)
modelo_lineal<-lm(formula=Y~X1+X2+X3, data=regresion)
summary(modelo_lineal)
##
## Call:
## lm(formula = Y ~ X1 + X2 + X3, data = regresion)
##
## Residuals:
## Min 1Q Median 3Q Max
## -108.527 -37.595 -2.745 52.292 102.808
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 303.50401 71.54695 4.242 0.000621 ***
## X1 2.32927 0.47698 4.883 0.000166 ***
## X2 -25.07113 11.48487 -2.183 0.044283 *
## X3 0.28617 0.07681 3.726 0.001840 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 67.68 on 16 degrees of freedom
## Multiple R-squared: 0.9634, Adjusted R-squared: 0.9566
## F-statistic: 140.4 on 3 and 16 DF, p-value: 0.00000000001054
stargazer(modelo_lineal, title = "Regresion multiple",xlab="Casos", ylab="Y", type = "text", digits = 8)
##
## Regresion multiple
## ================================================
## Dependent variable:
## ----------------------------
## Y
## ------------------------------------------------
## X1 2.32927500***
## (0.47698220)
##
## X2 -25.07113000**
## (11.48487000)
##
## X3 0.28616860***
## (0.07681293)
##
## Constant 303.50400000***
## (71.54695000)
##
## ------------------------------------------------
## Observations 20
## R2 0.96341370
## Adjusted R2 0.95655370
## Residual Std. Error 67.67775000 (df = 16)
## F Statistic 140.44060000*** (df = 3; 16)
## ================================================
## Note: *p<0.1; **p<0.05; ***p<0.01
##
## Regresion multiple
## =====
## Casos
## -----
##
## Regresion multiple
## =
## Y
## -
Objetos dentro del modelo lineal
Vector de Coeficientes estimados:
options(scipen = 999)
modelo_lineal$coefficients
## (Intercept) X1 X2 X3
## 303.5040143 2.3292746 -25.0711288 0.2861686
Matriz de Varianza - Covarianza de los parámetros
var_covarz<-vcov(modelo_lineal)
print(var_covarz)
## (Intercept) X1 X2 X3
## (Intercept) 5118.96645 -31.10997447 -722.8989902 4.493190281
## X1 -31.10997 0.22751204 4.5755139 -0.033223456
## X2 -722.89899 4.57551391 131.9021598 -0.822206343
## X3 4.49319 -0.03322346 -0.8222063 0.005900226
Intérvalos de confianza
confint(object = modelo_lineal,level = .95)
## 2.5 % 97.5 %
## (Intercept) 151.8312499 455.1767786
## X1 1.3181175 3.3404318
## X2 -49.4179582 -0.7242993
## X3 0.1233324 0.4490047
Valores Ajustados
plot(modelo_lineal$fitted.values,main = "Valores Ajustados",ylab = "Y",xlab = "casos")
modelo_lineal$fitted.values %>% as.matrix()
## [,1]
## 1 340.3238
## 2 376.4442
## 3 410.0762
## 4 422.7825
## 5 456.7683
## 6 490.9729
## 7 561.2516
## 8 572.4839
## 9 661.8956
## 10 805.2546
## 11 743.9514
## 12 802.6063
## 13 921.3246
## 14 1038.5268
## 15 966.3846
## 16 967.1923
## 17 1087.4101
## 18 1280.2249
## 19 1349.9604
## 20 1214.1649
Residuos del Modelo
plot(modelo_lineal$residuals,main = "Residuos",ylab = "Residuos",xlab = "casos")
modelo_lineal$residuals %>% matrix()
## [,1]
## [1,] -20.323767
## [2,] 73.555820
## [3,] -40.076233
## [4,] 47.217467
## [5,] -36.768268
## [6,] 9.027138
## [7,] 8.748419
## [8,] 67.516125
## [9,] 8.104393
## [10,] -25.254613
## [11,] -53.951414
## [12,] -102.606335
## [13,] -11.324647
## [14,] -108.526815
## [15,] -26.384626
## [16,] 102.807683
## [17,] 72.589856
## [18,] -70.224936
## [19,] 100.039646
## [20,] 5.835106
Parte 2.1
library(fitdistrplus)
library(stargazer)
fit_normal<-fitdist(data = modelo_lineal$residuals,distr = "norm")
plot(fit_normal)
summary(fit_normal)
## Fitting of the distribution ' norm ' by maximum likelihood
## Parameters :
## estimate Std. Error
## mean -0.0000000000000004440892 13.535551
## sd 60.5328216633827125292555 9.571082
## Loglikelihood: -110.4425 AIC: 224.885 BIC: 226.8764
## Correlation matrix:
## mean sd
## mean 1 0
## sd 0 1
Prueba de Normalidad de Jarque - Bera
library(normtest)
library(psych)
jb.norm.test(modelo_lineal$residuals)
##
## Jarque-Bera test for normality
##
## data: modelo_lineal$residuals
## JB = 0.58681, p-value = 0.652
No se rechaza Ho por lo que los residuos tienen distribucion normal
qqnorm(modelo_lineal$residuals)
qqline(modelo_lineal$residuals)
hist(modelo_lineal$residuals,main = "Histograma de los residuos",xlab = "Residuos",ylab = "frecuencia")
Prueba de Normalidad de Kolmogorov - Smirnov
library(nortest)
lillie.test(modelo_lineal$residuals)
##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: modelo_lineal$residuals
## D = 0.14222, p-value = 0.3594
No se rechaza Ho por lo que los residuos tienen distribucion normal
qqnorm(modelo_lineal$residuals)
qqline(modelo_lineal$residuals)
hist(modelo_lineal$residuals,main = "Histograma de los residuos",xlab = "Residuos",ylab = "frecuencia")