Ejemplo de regresion
Carga de Datos
library(dplyr)
library(readr)
ejemplo_regresion_1_ <- read_csv("C:/Users/manue/Desktop/ejemplo_regresion (1).csv")
head(ejemplo_regresion_1_,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
Regresion Lineal
library(stargazer)
options(scipen = 9999)
modelo_lineal<-lm(formula = Y~X1+X2,data =ejemplo_regresion_1_)
summary(modelo_lineal)
##
## Call:
## lm(formula = Y ~ X1 + X2, data = ejemplo_regresion_1_)
##
## 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(modelo_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 β:
options(scipen = 999)
modelo_lineal$coefficients
## (Intercept) X1 X2
## 1.5644967711 0.2371974748 -0.0002490793
Matriz de Varianza - Covarianza de los parametros V[β]
var_covar<-vcov(modelo_lineal)
print(var_covar)
## (Intercept) X1 X2
## (Intercept) 0.0063037218732 0.000240996434 -0.000000982806321
## X1 0.0002409964344 0.003086843196 -0.000001675537651
## X2 -0.0000009828063 -0.000001675538 0.000000001027106
Intervalos de confianza
confint(object = modelo_lineal,level = .95)
## 2.5 % 97.5 %
## (Intercept) 1.3998395835 1.7291539588
## X1 0.1219744012 0.3524205485
## X2 -0.0003155438 -0.0001826148
Valores Ajustados Y
plot(modelo_lineal$fitted.values,main = "Valores Ajustados",ylab = "Y",xlab = "casos")
Residuos del Modelo ϵ
plot(modelo_lineal$residuals,main = "Residuos",ylab = "Residuos",xlab = "casos")
Desarrollo practica 2
Datos
library(dplyr)
library(readr)
ejercicio_regresion_2_ <- read_csv("C:/Users/manue/Desktop/ejercicio_regresion(2).csv")
head(ejercicio_regresion_2_,n = 6)
## # A tibble: 6 x 3
## X1 X2 Y
## <dbl> <dbl> <dbl>
## 1 50 7.4 320
## 2 53 5.1 450
## 3 60 4.2 370
## 4 63 3.9 470
## 5 69 1.4 420
## 6 82 2.2 500
construccion de matriz.
ejercicio_regresion_2_%>% mutate(X3=X1*X2) %>%select("Y","X1","X2","X3")->ejercicio_regresion_2_
print(ejercicio_regresion_2_)
## # 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.
Regresion lineal
library(stargazer)
options(scipen = 9999)
modelo_lineal<-lm(formula=Y~X1+X2+X3,data=ejercicio_regresion_2_)
summary(modelo_lineal)
##
## Call:
## lm(formula = Y ~ X1 + X2 + X3, data = ejercicio_regresion_2_)
##
## 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 = "Regresión Multiple",type = "text",digits = 8)
##
## Regresión 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
Objetos dentro del modelo lineal
Vector de coeficientes estimados β:
options(scipen = 999)
modelo_lineal$coefficients
## (Intercept) X1 X2 X3
## 303.5040143 2.3292746 -25.0711288 0.2861686
Matriz de Varianza - Covarianza de los parametros V[β]:
var_covar<-vcov(modelo_lineal)
print(var_covar)
## (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
Intervalos de confianza
confint(object = modelo_lineal)
## 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 Y
plot(modelo_lineal$fitted.values,main = "Valores Ajustados",ylab = "Y",xlab = "casos")
Residuos del Modelo ϵ
plot(modelo_lineal$residuals,main = "Residuos",ylab = "Residuos",xlab = "casos")
