library(wooldridge)
data("hprice1")
head(force(hprice1),n=5)
##   price assess bdrms lotsize sqrft colonial   lprice  lassess llotsize   lsqrft
## 1   300  349.1     4    6126  2438        1 5.703783 5.855359 8.720297 7.798934
## 2   370  351.5     3    9903  2076        1 5.913503 5.862210 9.200593 7.638198
## 3   191  217.7     3    5200  1374        0 5.252274 5.383118 8.556414 7.225482
## 4   195  231.8     3    4600  1448        1 5.273000 5.445875 8.433811 7.277938
## 5   373  319.1     4    6095  2514        1 5.921578 5.765504 8.715224 7.829630

#Estimacion de modelo

library(stargazer)
## 
## Please cite as:
##  Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.
##  R package version 5.2.3. https://CRAN.R-project.org/package=stargazer
modelo_estimado<-lm(formula = price~lotsize+sqrft+bdrms,data = hprice1)
options(scipen = 9999)
stargazer(modelo_estimado,title = "Modelo Estimado",type = "text",digits=5)
## 
## Modelo Estimado
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                                price           
## -----------------------------------------------
## lotsize                     0.00207***         
##                              (0.00064)         
##                                                
## sqrft                       0.12278***         
##                              (0.01324)         
##                                                
## bdrms                        13.85252          
##                              (9.01015)         
##                                                
## Constant                     -21.77031         
##                             (29.47504)         
##                                                
## -----------------------------------------------
## Observations                    88             
## R2                            0.67236          
## Adjusted R2                   0.66066          
## Residual Std. Error     59.83348 (df = 84)     
## F Statistic          57.46023*** (df = 3; 84)  
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01
library(fitdistrplus)
## Loading required package: MASS
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:wooldridge':
## 
##     cement
## Loading required package: survival
fit_normal<-fitdist(modelo_estimado$residuals,distr = "norm")
plot(fit_normal)

summary(fit_normal)
## Fitting of the distribution ' norm ' by maximum likelihood 
## Parameters : 
##                       estimate Std. Error
## mean  0.0000000000000009992007   6.231624
## sd   58.4578135693031910591344   4.406424
## Loglikelihood:  -482.8775   AIC:  969.7549   BIC:  974.7096 
## Correlation matrix:
##      mean sd
## mean    1  0
## sd      0  1

#Prueba JB

library(tseries)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
salida_JB<-jarque.bera.test(modelo_estimado$residuals)
salida_JB
## 
##  Jarque Bera Test
## 
## data:  modelo_estimado$residuals
## X-squared = 32.278, df = 2, p-value = 0.00000009794
library(fastGraph)
alpha_sig<-0.05
JB<-salida_JB$statistic
gl<-salida_JB$parameter
VC<-qchisq(1-alpha_sig,gl,lower.tail = TRUE)
shadeDist(JB,ddist = "dchisq",
          parm1 = gl,
          lower.tail = FALSE,xmin = 0,
          sub=paste("VC:",round(VC,2),"","JB",round(JB,2)))

#Prueba KS

library(nortest)
prueba_KS<-lillie.test(modelo_estimado$residuals)
prueba_KS
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  modelo_estimado$residuals
## D = 0.075439, p-value = 0.2496
p.value<-prueba_KS$p.value

#Forma Manual

library(dplyr)  # Carga la librería dplyr para manipulación de datos
## 
## Attaching package: 'dplyr'
## The following object is masked from 'package:MASS':
## 
##     select
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(gt)  # Carga la librería gt para crear tablas de datos
library(gtExtras)  # Carga la librería gtExtras para agregar funcionalidades a las tablas creadas con gt
## 
## Attaching package: 'gtExtras'
## The following object is masked from 'package:MASS':
## 
##     select
residuos<-modelo_estimado$residuals  # Crea un vector con los residuos del modelo estimado
residuos %>%  # Utiliza el operador %>% para encadenar las operaciones siguientes al vector residuos
  as_tibble() %>%  # Convierte el vector residuos en una tibble (tabla) de una columna
  mutate(posicion=row_number()) %>%  # Agrega una columna llamada "posicion" con el número de fila
  arrange(value) %>%  # Ordena la tabla por los valores de residuos en orden ascendente
  mutate(dist1=row_number()/n()) %>%  # Agrega una columna "dist1" con los percentiles según su posición en la tabla (usando la función row_number() y n() para obtener el número de filas)
  mutate(dist2=(row_number()-1)/n()) %>%  # Agrega una columna "dist2" con los percentiles según su posición en la tabla, pero ajustando en una unidad para evitar problemas con los extremos de la distribución
  mutate(zi=as.vector(scale(value,center=TRUE))) %>%  # Agrega una columna "zi" con los valores de residuos escalados para tener media cero y varianza uno
  mutate(pi=pnorm(zi,lower.tail = TRUE)) %>%  # Agrega una columna "pi" con los valores de la función de distribución acumulada (CDF) de una distribución normal estándar evaluada en los valores de zi
  mutate(dif1=abs(dist1-pi)) %>%  # Agrega una columna "dif1" con las diferencias absolutas entre los percentiles según la posición y los valores de pi
  mutate(dif2=abs(dist2-pi)) %>%  # Agrega una columna "dif2" con las diferencias absolutas entre los percentiles ajustados según la posición y los valores de pi
  rename(residuales=value) -> tabla_KS  # Renombra la columna "value" como "residuales" y asigna la tabla resultante a la variable tabla_KS


#Formato
 tabla_KS %>%  # Utiliza el operador %>% para encadenar las operaciones siguientes a la tabla tabla_KS
  gt() %>%  # Crea una tabla con la función gt()
  tab_header("Tabla para calcular el Estadistico KS") %>%  # Agrega un encabezado a la tabla
  tab_source_note(source_note = "Fuente: Elaboración propia") %>%  # Agrega una nota de fuente a la tabla
  tab_style(  # Cambia el estilo de algunas celdas de la tabla
    style = list(
      cell_fill(color = "#FF5733"),  # Cambia el color de fondo de las celdas a un tono de morado
      cell_text(style = "italic")  # Cambia el estilo de texto de las celdas a itálico
      ),
    locations = cells_body(  # Aplica el estilo a las celdas del cuerpo de la tabla que cumplan las siguientes condiciones:
      columns = dif1,  # Que pertenezcan a la columna "dif1"
      rows = dif1==max(dif1)  # Que pertenezcan a la fila donde el valor de "dif1" es máximo
    )) %>%
   tab_style(  # Cambia el estilo de algunas celdas de la tabla
    style = list(
      cell_fill(color = "#3498DB"),  # Cambia el color de fondo de las celdas a un tono de azul
      cell_text(style = "italic")  # Cambia el estilo de texto de las celdas a itálico
      ),
    locations = cells_body(  # Aplica el estilo a las celdas del cuerpo de la tabla que cumplan las siguientes condiciones:
      columns = dif2,  # Que pertenezcan a la columna "dif2"
      rows = dif2==max(dif2)  # Que pertenezcan a la fila donde el valor de "dif2" es máximo
    ))
Tabla para calcular el Estadistico KS
residuales posicion dist1 dist2 zi pi dif1 dif2
-120.026447 81 0.01136364 0.00000000 -2.041515459 0.02059981 0.0092361731 0.0205998094
-115.508697 77 0.02272727 0.01136364 -1.964673586 0.02472601 0.0019987418 0.0133623781
-107.080889 24 0.03409091 0.02272727 -1.821326006 0.03427866 0.0001877487 0.0115513850
-91.243980 48 0.04545455 0.03409091 -1.551957925 0.06033615 0.0148816002 0.0262452366
-85.461169 12 0.05681818 0.04545455 -1.453598781 0.07302879 0.0162106057 0.0275742421
-77.172687 32 0.06818182 0.05681818 -1.312620980 0.09465535 0.0264735301 0.0378371665
-74.702719 54 0.07954545 0.06818182 -1.270609602 0.10193378 0.0223883300 0.0337519664
-65.502849 39 0.09090909 0.07954545 -1.114130117 0.13261169 0.0417025941 0.0530662305
-63.699108 69 0.10227273 0.09090909 -1.083450505 0.13930425 0.0370315271 0.0483951634
-62.566594 83 0.11363636 0.10227273 -1.064187703 0.14362184 0.0299854747 0.0413491110
-59.845223 36 0.12500000 0.11363636 -1.017900230 0.15436269 0.0293626861 0.0407263225
-54.466158 13 0.13636364 0.12500000 -0.926408352 0.17711690 0.0407532663 0.0521169027
-54.300415 14 0.14772727 0.13636364 -0.923589260 0.17785010 0.0301228311 0.0414864675
-52.129801 15 0.15909091 0.14772727 -0.886669532 0.18762842 0.0285375141 0.0399011505
-51.441108 17 0.17045455 0.15909091 -0.874955638 0.19079902 0.0203444766 0.0317081129
-48.704980 47 0.18181818 0.17045455 -0.828417174 0.20371714 0.0218989601 0.0332625965
-48.350295 29 0.19318182 0.18181818 -0.822384375 0.20542908 0.0122472664 0.0236109028
-47.855859 11 0.20454545 0.19318182 -0.813974573 0.20782976 0.0032843043 0.0146479407
-45.639765 1 0.21590909 0.20454545 -0.776281294 0.21879146 0.0028823668 0.0142460032
-43.142550 9 0.22727273 0.21590909 -0.733806463 0.23153335 0.0042606233 0.0156242596
-41.749618 57 0.23863636 0.22727273 -0.710114247 0.23881665 0.0001802823 0.0115439187
-40.869022 27 0.25000000 0.23863636 -0.695136302 0.24348494 0.0065150566 0.0048485798
-37.749811 34 0.26136364 0.25000000 -0.642082009 0.26040997 0.0009536682 0.0104099682
-36.663785 71 0.27272727 0.26136364 -0.623609925 0.26644190 0.0062853771 0.0050782592
-36.646568 79 0.28409091 0.27272727 -0.623317083 0.26653809 0.0175528221 0.0061891857
-33.801248 37 0.29545455 0.28409091 -0.574921384 0.28267223 0.0127823120 0.0014186757
-29.766931 16 0.30681818 0.29545455 -0.506302171 0.30632227 0.0004959124 0.0108677240
-26.696234 22 0.31818182 0.30681818 -0.454073044 0.32488813 0.0067063089 0.0180699452
-24.271531 23 0.32954545 0.31818182 -0.412831567 0.33986501 0.0103195566 0.0216831929
-23.651448 86 0.34090909 0.32954545 -0.402284648 0.34373728 0.0028281851 0.0141918214
-19.683427 88 0.35227273 0.34090909 -0.334793052 0.36889060 0.0166178738 0.0279815102
-17.817835 10 0.36363636 0.35227273 -0.303061413 0.38092153 0.0172851663 0.0286488027
-16.762094 60 0.37500000 0.36363636 -0.285104441 0.38778206 0.0127820638 0.0241457002
-16.596960 21 0.38636364 0.37500000 -0.282295711 0.38885839 0.0024947507 0.0138583870
-16.271207 58 0.39772727 0.38636364 -0.276755010 0.39098411 0.0067431583 0.0046204781
-13.815798 56 0.40909091 0.39772727 -0.234991254 0.40710776 0.0019831485 0.0093804879
-13.462160 75 0.42045455 0.40909091 -0.228976273 0.40944368 0.0110108666 0.0003527698
-12.081520 4 0.43181818 0.42045455 -0.205493119 0.41859344 0.0132247451 0.0018611087
-11.629207 51 0.44318182 0.43181818 -0.197799788 0.42160086 0.0215809622 0.0102173258
-11.312669 74 0.45454545 0.44318182 -0.192415834 0.42370825 0.0308372092 0.0194735728
-8.236558 3 0.46590909 0.45454545 -0.140094626 0.44429261 0.0216164775 0.0102528411
-7.662789 70 0.47727273 0.46590909 -0.130335452 0.44815052 0.0291222111 0.0177585748
-6.752801 67 0.48863636 0.47727273 -0.114857588 0.45427900 0.0343573625 0.0229937262
-6.707262 31 0.50000000 0.48863636 -0.114083016 0.45458599 0.0454140074 0.0340503710
-6.402439 85 0.51136364 0.50000000 -0.108898313 0.45664157 0.0547220642 0.0433584278
-5.446904 82 0.52272727 0.51136364 -0.092645733 0.46309251 0.0596347676 0.0482711313
-3.537785 43 0.53409091 0.52272727 -0.060173762 0.47600862 0.0580822876 0.0467186512
-2.824941 61 0.54545455 0.53409091 -0.048049090 0.48083856 0.0646159857 0.0532523493
-2.745208 68 0.55681818 0.54545455 -0.046692922 0.48137899 0.0754391961 0.0640755598
-0.195089 65 0.56818182 0.55681818 -0.003318245 0.49867621 0.0695056040 0.0581419676
1.399296 55 0.57954545 0.56818182 0.023800450 0.50949411 0.0700513452 0.0586877088
5.363331 26 0.59090909 0.57954545 0.091224254 0.53634280 0.0545662924 0.0432026561
6.700640 53 0.60227273 0.59090909 0.113970383 0.54536936 0.0569033628 0.0455397265
7.386314 80 0.61363636 0.60227273 0.125632935 0.54998875 0.0636476093 0.0522839730
9.099900 41 0.62500000 0.61363636 0.154779103 0.56150227 0.0634977329 0.0521340965
12.433611 46 0.63636364 0.62500000 0.211481796 0.58374433 0.0526193043 0.0412556680
16.718018 62 0.64772727 0.63636364 0.284354766 0.61193074 0.0357965328 0.0244328965
18.093192 5 0.65909091 0.64772727 0.307744934 0.62086179 0.0382291219 0.0268654856
18.801816 38 0.67045455 0.65909091 0.319797835 0.62543921 0.0450153400 0.0336517036
19.168108 33 0.68181818 0.67045455 0.326028052 0.62779843 0.0540197476 0.0426561112
19.219211 72 0.69318182 0.68181818 0.326897255 0.62812720 0.0650546167 0.0536909803
20.334434 59 0.70454545 0.69318182 0.345865960 0.63527827 0.0692671805 0.0579035442
24.909926 78 0.71590909 0.70454545 0.423689939 0.66410402 0.0518050676 0.0404414312
26.236229 40 0.72727273 0.71590909 0.446248874 0.67229126 0.0549814685 0.0436178321
30.924022 25 0.73863636 0.72727273 0.525982978 0.70054998 0.0380863808 0.0267227444
32.253952 45 0.75000000 0.73863636 0.548603608 0.70836125 0.0416387548 0.0302751184
32.529367 49 0.76136364 0.75000000 0.553288104 0.70996693 0.0513967091 0.0400330727
32.675968 18 0.77272727 0.76136364 0.555781630 0.71081993 0.0619073452 0.0505437088
33.275839 20 0.78409091 0.77272727 0.565984762 0.71429793 0.0697929786 0.0584293423
36.031430 52 0.79545455 0.78409091 0.612854281 0.73001365 0.0654408934 0.0540772571
37.147186 84 0.80681818 0.79545455 0.631832029 0.73625168 0.0705665028 0.0592028664
40.320875 7 0.81818182 0.80681818 0.685812928 0.75358446 0.0645973596 0.0532337232
44.334467 30 0.82954545 0.81818182 0.754079634 0.77459930 0.0549461574 0.0435825211
46.907165 28 0.84090909 0.82954545 0.797838357 0.78751785 0.0533912405 0.0420276041
54.418366 87 0.85227273 0.84090909 0.925595465 0.82267187 0.0296008528 0.0182372164
55.091131 35 0.86363636 0.85227273 0.937038450 0.82563061 0.0380057535 0.0266421172
55.470305 44 0.87500000 0.86363636 0.943487765 0.82728426 0.0477157353 0.0363520989
62.939597 6 0.88636364 0.87500000 1.070532059 0.85781006 0.0285535797 0.0171899433
66.478628 50 0.89772727 0.88636364 1.130727018 0.87091500 0.0268122757 0.0154486394
67.426518 63 0.90909091 0.89772727 1.146849569 0.87427810 0.0348128083 0.0234491719
67.603959 19 0.92045455 0.90909091 1.149867648 0.87490081 0.0455537393 0.0341901029
69.707122 64 0.93181818 0.92045455 1.185640095 0.88211777 0.0497004123 0.0383367759
69.843246 8 0.94318182 0.93181818 1.187955411 0.88257451 0.0606073068 0.0492436705
74.848732 2 0.95454545 0.94318182 1.273093116 0.89850750 0.0560379553 0.0446743189
112.729191 66 0.96590909 0.95454545 1.917397313 0.97240626 0.0064971714 0.0178608078
163.795081 73 0.97727273 0.96590909 2.785970904 0.99733162 0.0200588896 0.0314225260
198.660139 42 0.98863636 0.97727273 3.378986513 0.99963623 0.0109998685 0.0223635048
209.375830 76 1.00000000 0.98863636 3.561248407 0.99981545 0.0001845478 0.0111790885
Fuente: Elaboración propia 
#n=88 alpha=0.05
#por lo tanto el nivel de significancia es 0.09337093393 ya que n es mayor que 50
#0.875897/9.38083152=0.09337093393


#en conclusion en este caso 0.09337093393 > 0.075439 se rechaza la hipotesis Nula

#Prueba SW

salida_SW<-shapiro.test(modelo_estimado$residuals)
print(salida_SW)
## 
##  Shapiro-Wilk normality test
## 
## data:  modelo_estimado$residuals
## W = 0.94132, p-value = 0.0005937
Wn_salida<-qnorm(salida_SW$p.value,lower.tail = FALSE)
print(Wn_salida)
## [1] 3.241867
#En este caso que 0.05 > 0.0005937472 se rechaza la Hipótesis Nula: ϵ∼N(0,σ2),por lo que los residuos no siguen una distribución normal.