23 de marzo del 2019
Ejercicio Numero 1
Parte Uno: Cargar datos.
library(readr)
library(dplyr)
library(stargazer)
datos<- read_csv("C:/Users/ejhar/Desktop/econometria/ej2.csv")
head(datos,n=7)
## # A tibble: 7 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 ## 7 3.21 6368 0.77
1. Calculos de la regresion lineal.
options(scipen = 9999) modelo_lineal<- lm(formula = Y~X1+X2, data= datos) summary(modelo_lineal)
## ## Call: ## lm(formula = Y ~ X1 + X2, data = datos) ## ## 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
1. Ejemplo de regresion multiple.
stargazer(modelo_lineal,
title = "Regresión Multiple",
type = "text", digits = 8)
## ## 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
1. Objetos dentro del modelo lineal.
options(scipen = 9999) modelo_lineal$coefficients
## (Intercept) X1 X2 ## 1.5644967711 0.2371974748 -0.0002490793
Matriz de varianza - Covarianza de los parametros \(V[\beta]\)
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
1. 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
1. valores ajustados de Y(hat)·
plot(modelo_lineal$fitted.values, main = "Valores ajustados",
ylab = "Y", xlab = "X")
modelo_lineal$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
1. Residuos del modelo e^
plot(modelo_lineal$residuals, main = "Residuos", ylab = "residuos",
xlab = "casos")
modelo_lineal$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
Ejercicio Numero 2
2. Cargar datos.
RutaYX<- read_csv("C:/Users/ejhar/Desktop/trabajo 1/matrizXY.csv")
RutaYX %>% mutate(X3=X1*X2) %>% select("Y","X1","X2","X3") -> datos2
head(datos2, n=7, 2)
## # A tibble: 7 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
2. Calculos de la regresion lineal.
options(scipen = 9999) modelo_lineal2<- lm(formula = Y~X1+X2+X3, data= datos2) summary(modelo_lineal2)
## ## Call: ## lm(formula = Y ~ X1 + X2 + X3, data = datos2) ## ## 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
2. Ejemplo de regresion multiple.
stargazer(modelo_lineal2,
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
2. Objetos dentro del modelo lineal.
options(scipen = 9999) modelo_lineal2$coefficients
## (Intercept) X1 X2 X3 ## 303.5040143 2.3292746 -25.0711288 0.2861686
Matriz de varianza - Covarianza de los parametros \(V[\beta]\)
var_covar2<-vcov(modelo_lineal2) 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
2. Intervalos de confianza.
confint(object=modelo_lineal2, 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
2. valores ajustados de Y(hat)·
plot(modelo_lineal2$fitted.values, main = "Valores ajustados",
ylab = "Y", xlab = "X")
modelo_lineal2$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
2. Residuos del modelo e^
plot(modelo_lineal2$residuals, main = "Residuos", ylab = "residuos",
xlab = "casos")
modelo_lineal2$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