Datos

library(dplyr)
library(readr)
ejercicio_doss <- read_csv("E:/ejercicio_doss.csv")
head(ejercicio_doss,n = 6)

## # A tibble: 6 x 3
##      X1    X2     Y
##   <dbl> <dbl> <dbl>
## 1     5  7.14    32
## 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

Regresion Lineal

library(stargazer)
options(scipen = 9999)
modelo_lineal2<-lm(formula = Y~X1+X2,data = ejercicio_doss)
summary(modelo_lineal2)

## 
## Call:
## lm(formula = Y ~ X1 + X2, data = ejercicio_doss)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -151.194  -49.312    1.857   60.555  226.223 
## 
## Coefficients:
##             Estimate Std. Error t value        Pr(>|t|)    
## (Intercept)  61.0133    57.4367   1.062           0.303    
## X1            4.0919     0.2752  14.866 0.0000000000357 ***
## X2           14.2466     5.9759   2.384           0.029 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 97.09 on 17 degrees of freedom
## Multiple R-squared:  0.9316, Adjusted R-squared:  0.9236 
## F-statistic: 115.8 on 2 and 17 DF,  p-value: 0.0000000001251

stargazer(modelo_lineal2,title = "Ejercicio de Regresión Multiple",type = "text",digits = 8)

## 
## Ejercicio de Regresión Multiple
## ================================================
##                         Dependent variable:     
##                     ----------------------------
##                                  Y              
## ------------------------------------------------
## X1                         4.09185700***        
##                             (0.27524100)        
##                                                 
## X2                         14.24664000**        
##                             (5.97585600)        
##                                                 
## Constant                    61.01329000         
##                            (57.43673000)        
##                                                 
## ------------------------------------------------
## Observations                     20             
## R2                           0.93161220         
## Adjusted R2                  0.92356660         
## Residual Std. Error    97.08614000 (df = 17)    
## F Statistic         115.79120000*** (df = 2; 17)
## ================================================
## Note:                *p<0.1; **p<0.05; ***p<0.01

Objetos Dentro Del Modelo Lineal

Vector de Coeficientes estimados

options(scipen = 999)
modelo_lineal2$coefficients

## (Intercept)          X1          X2 
##   61.013290    4.091857   14.246644

Matriz de Varianza - Covarianza de los parametros V[β]

var_covar<-vcov(modelo_lineal2)
print(var_covar)

##             (Intercept)           X1            X2
## (Intercept)  3298.97753 -10.75297606 -201.68414674
## X1            -10.75298   0.07575761   -0.09534885
## X2           -201.68415  -0.09534885   35.71085958

Intervalos de Confianza

confint(object = modelo_lineal2,level = .95)

##                  2.5 %     97.5 %
## (Intercept) -60.167610 182.194190
## X1            3.511150   4.672565
## X2            1.638689  26.854599

Valores Ajustados

plot(modelo_lineal2$fitted.values,main = "Valores Ajustados",ylab = "Y",xlab = "casos")

modelo_lineal2$fitted.values %>% as.matrix()

##         [,1]
## 1   183.1936
## 2   350.5396
## 3   366.3606
## 4   374.3622
## 5   363.2967
## 6   427.8882
## 7   569.9255
## 8   567.7723
## 9   710.0242
## 10  826.5997
## 11  747.4498
## 12  842.9547
## 13  951.6784
## 14 1037.2755
## 15 1043.6379
## 16 1077.2510
## 17 1125.1432
## 18 1197.0725
## 19 1223.7769
## 20 1195.7976

Residuos del modelo

plot(modelo_lineal2$residuals,main = "Residuos",ylab = "Residuos",xlab = "casos")

modelo_lineal2$residuals %>% matrix()

##                [,1]
##  [1,] -151.19361215
##  [2,]   99.46039163
##  [3,]    3.63936998
##  [4,]   95.63779125
##  [5,]   56.70325673
##  [6,]   72.11179721
##  [7,]    0.07447666
##  [8,]   72.22768431
##  [9,]  -40.02419425
## [10,]  -46.59969203
## [11,]  -57.44976423
## [12,] -142.95472376
## [13,]  -41.67835643
## [14,] -107.27550981
## [15,] -103.63786615
## [16,]   -7.25098127
## [17,]   34.85683775
## [18,]   12.92749838
## [19,]  226.22314707
## [20,]   24.20244912