library(wooldridge)
data(hpricel)
## Warning in data(hpricel): data set 'hpricel' not found
head(force(hprice1),n=5)#mostrar las primeras 5 observaciones
##   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

Estimando el modelo

options(scipen = 999999)
library(wooldridge)
data(hprice1)
modelo_estimado<-lm(price~lotsize+sqrft+bdrms,data = hprice1)
summary(modelo_estimado)
## 
## Call:
## lm(formula = price ~ lotsize + sqrft + bdrms, data = hprice1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -120.026  -38.530   -6.555   32.323  209.376 
## 
## Coefficients:
##                Estimate  Std. Error t value           Pr(>|t|)    
## (Intercept) -21.7703081  29.4750419  -0.739            0.46221    
## lotsize       0.0020677   0.0006421   3.220            0.00182 ** 
## sqrft         0.1227782   0.0132374   9.275 0.0000000000000166 ***
## bdrms        13.8525217   9.0101454   1.537            0.12795    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 59.83 on 84 degrees of freedom
## Multiple R-squared:  0.6724, Adjusted R-squared:  0.6607 
## F-statistic: 57.46 on 3 and 84 DF,  p-value: < 0.00000000000000022

Verificando los supuestos de normalidad

a) La prueba JB

options(scipen = 999999)
library(tseries)
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

R/ Se puede concluir que se rechaza la Hipótesis Nula dado que 0.00000009794<0.05, por tanto los residuos no siguen una distribución normal.

Resultados forma grafica

options(scipen = 999999)
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)))

b)La prueba KS

options(scipen = 999999)
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

R/ En este caso, No se rechaza la Hipótesis Nula dado que 0.2496>0.05, por lo que los residuos siguen una distribución normal.

Resultados forma tabular

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(gt)
library(gtExtras)
residuos<-modelo_estimado$residuals
residuos%>%
  as_tibble()%>%
  mutate(posicion=row_number())%>%
  arrange(value)%>%
  mutate(dist1=row_number()/n())%>%
  mutate(dist2=(row_number()-1)/n())%>%
  mutate(zi=as.vector(scale(value,center=TRUE)))%>%
  mutate(pi=pnorm(zi,lower.tail = TRUE))%>%
  mutate(dif1=abs(dist1-pi))%>%
  mutate(dif2=abs(dist2-pi))%>%
  rename(residuales=value)->tabla_KS

#Formato
tabla_KS%>%
  gt()%>%
  tab_header("Tabla para calcular el Estadistico KS")%>%
  tab_source_note(source_note = "Fuente Elaboracion propia")%>%
  tab_style(
    style = list(
      cell_fill(color="#A569BD"),
      cell_text(style = "italic")
      ),
    locations = cells_body(
      columns=dif1,
      rows=dif1==max(dif1)
      ))%>%
  tab_style(
    style = list(
      cell_fill(color="#3498DB"),
      cell_text(style = "italic")
      ),
    locations = cells_body(
      columns=dif2,
      rows=dif2==max(dif2)
      ))
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 Elaboracion propia

c) La prueba SW

options(scipen = 999999)
library(stats)
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

R/ Se rechaza la Hipótesis Nula dado que 0.0005937<0.05, por tanto los residuos no siguen una distribución normal.

Resultados forma tabular

library(dplyr)
library(gt)
residuos<-modelo_estimado$residuals
residuos%>%
  as_tibble()%>%
  rename(residuales=value)%>%
  arrange(residuales)%>%
  mutate(pi=(row_number()-0.375)/(n()+0.25))%>%
  mutate(mi=qnorm(pi,lower.tail = TRUE))%>%
  mutate(ai=0)->tabla_SW
m<-sum(tabla_SW$mi^2)
n<-nrow(hprice1)
theta<-1/sqrt(n)
tabla_SW$ai[n]<- -2.706056*theta^5+4.434685*theta^3-0.147981*theta^2+0.2211570*theta+tabla_SW$mi[n]/sqrt(m)
tabla_SW$ai[n-1]<- -3.582633*theta^5+5.682633*theta^4-1.752461*theta^3-0.293762*theta^2+0.042981*theta+tabla_SW$mi[n-1]/sqrt(m)
tabla_SW$ai[1]<- -tabla_SW$ai[n]
tabla_SW$ai[2]<- -tabla_SW$ai[n-1]
omega<-(m-2*tabla_SW$mi[n]^2-2*tabla_SW$mi[n-1]^2)/(1-2*tabla_SW$ai[n]^2-2*tabla_SW$ai[n-1]^2)
tabla_SW$ai[3:(n-2)]<-tabla_SW$mi[3:(n-2)]/sqrt(omega)
tabla_SW%>%
  mutate(ai_ui=ai*residuales,ui2=residuales^2)->tabla_SW
tabla_SW%>%
  gt()%>%tab_header("Tabla para calcular el Estadistico W")%>%
  tab_source_note(source_note = "Fuente: Elaboracion propia")
Tabla para calcular el Estadistico W
residuales pi mi ai ai_ui ui2
-120.026447 0.007082153 -2.45306927 -0.293402275 35.216032599 14406.34799223
-115.508697 0.018413598 -2.08767462 -0.226331231 26.143225495 13342.25903657
-107.080889 0.029745042 -1.88455395 -0.200345078 21.453129005 11466.31670225
-91.243980 0.041076487 -1.73832835 -0.184799978 16.861885528 8325.46388922
-85.461169 0.052407932 -1.62194155 -0.172427012 14.735813997 7303.61136157
-77.172687 0.063739377 -1.52411994 -0.162027693 12.504112336 5955.62354189
-74.702719 0.075070822 -1.43903134 -0.152982008 11.428171985 5580.49626206
-65.502849 0.086402266 -1.36324747 -0.144925499 9.493033091 4290.62326804
-63.699108 0.097733711 -1.29457343 -0.137624830 8.766578946 4057.57641853
-62.566594 0.109065156 -1.23151500 -0.130921149 8.191290388 3914.57869135
-59.845223 0.120396601 -1.17300649 -0.124701168 7.462769211 3581.45072682
-54.466158 0.131728045 -1.11825971 -0.118881091 6.474996231 2966.56233834
-54.300415 0.143059490 -1.06667420 -0.113397086 6.157508892 2948.53511008
-52.129801 0.154390935 -1.01778137 -0.108199337 5.640409849 2717.51610406
-51.441108 0.165722380 -0.97120790 -0.103248158 5.311199604 2646.18755812
-48.704980 0.177053824 -0.92665123 -0.098511381 4.797994878 2372.17509746
-48.350295 0.188385269 -0.88386232 -0.093962535 4.543116287 2337.75102457
-47.855859 0.199716714 -0.84263354 -0.089579544 4.286906003 2290.18324033
-45.639765 0.211048159 -0.80278966 -0.085343780 3.895070072 2082.98814155
-43.142550 0.222379603 -0.76418130 -0.081239363 3.504873292 1861.27961161
-41.749618 0.233711048 -0.72667986 -0.077252621 3.225267417 1743.03058469
-40.869022 0.245042493 -0.69017366 -0.073371684 2.998628960 1670.27697055
-37.749811 0.256373938 -0.65456498 -0.069586160 2.626864381 1425.04821452
-36.663785 0.267705382 -0.61976766 -0.065886891 2.415662785 1344.23312095
-36.646568 0.279036827 -0.58570518 -0.062265742 2.281825736 1342.97093753
-33.801248 0.290368272 -0.55230918 -0.058715446 1.984655372 1142.52439130
-29.766931 0.301699717 -0.51951819 -0.055229468 1.644011789 886.07020942
-26.696234 0.313031161 -0.48727661 -0.051801897 1.382915567 712.68890388
-24.271531 0.324362606 -0.45553386 -0.048427357 1.175406112 589.10722688
-23.651448 0.335694051 -0.42424369 -0.045100930 1.066702298 559.39099788
-19.683427 0.347025496 -0.39336354 -0.041818092 0.823123358 387.43729851
-17.817835 0.358356941 -0.36285409 -0.038574662 0.687316947 317.47522771
-16.762094 0.369688385 -0.33267878 -0.035366754 0.592820839 280.96778010
-16.596960 0.381019830 -0.30280344 -0.032190736 0.534268377 275.45909399
-16.271207 0.392351275 -0.27319601 -0.029043199 0.472567902 264.75217651
-13.815798 0.403682720 -0.24382619 -0.025920922 0.358118227 190.87627634
-13.462160 0.415014164 -0.21466524 -0.022820850 0.307217946 181.22976154
-12.081520 0.426345609 -0.18568573 -0.019740068 0.238490014 145.96311543
-11.629207 0.437677054 -0.15686137 -0.016675778 0.193926071 135.23845458
-11.312669 0.449008499 -0.12816677 -0.013625283 0.154138322 127.97648221
-8.236558 0.460339943 -0.09957734 -0.010585969 0.087191945 67.84088513
-7.662789 0.471671388 -0.07106908 -0.007555284 0.057894545 58.71832836
-6.752801 0.483002833 -0.04261848 -0.004530728 0.030595109 45.60032533
-6.707262 0.494334278 -0.01420234 -0.001509837 0.010126869 44.98736398
-6.402439 0.505665722 0.01420234 0.001509837 -0.009666636 40.99122172
-5.446904 0.516997167 0.04261848 0.004530728 -0.024678442 29.66876028
-3.537785 0.528328612 0.07106908 0.007555284 -0.026728971 12.51592288
-2.824941 0.539660057 0.09957734 0.010585969 -0.029904742 7.98029397
-2.745208 0.550991501 0.12816677 0.013625283 -0.037404243 7.53616965
-0.195089 0.562322946 0.15686137 0.016675778 -0.003253260 0.03805971
1.399296 0.573654391 0.18568573 0.019740068 0.027622188 1.95802794
5.363331 0.584985836 0.21466524 0.022820850 0.122395774 28.76531940
6.700640 0.596317280 0.24382619 0.025920922 0.173686769 44.89857663
7.386314 0.607648725 0.27319601 0.029043199 0.214522195 54.55763860
9.099900 0.618980170 0.30280344 0.032190736 0.292932472 82.80817401
12.433611 0.630311615 0.33267878 0.035366754 0.439736453 154.59467612
16.718018 0.641643059 0.36285409 0.038574662 0.644891897 279.49212715
18.093192 0.652974504 0.39336354 0.041818092 0.756622761 327.36359375
18.801816 0.664305949 0.42424369 0.045100930 0.847979378 353.50828232
19.168108 0.675637394 0.45553386 0.048427357 0.928260810 367.41636183
19.219211 0.686968839 0.48727661 0.051801897 0.995591588 369.37806665
20.334434 0.698300283 0.51951819 0.055229468 1.123059997 413.48922446
24.909926 0.709631728 0.55230918 0.058715446 1.462597386 620.50439009
26.236229 0.720963173 0.58570518 0.062265742 1.633618255 688.33970624
30.924022 0.732294618 0.61976766 0.065886891 2.037487625 956.29510728
32.253952 0.743626062 0.65456498 0.069586160 2.244428679 1040.31742689
32.529367 0.754957507 0.69017366 0.073371684 2.386734412 1058.15970869
32.675968 0.766288952 0.72667986 0.077252621 2.524304208 1067.71890359
33.275839 0.777620397 0.76418130 0.081239363 2.703307993 1107.28147309
36.031430 0.788951841 0.80278966 0.085343780 3.075058468 1298.26396526
37.147186 0.800283286 0.84263354 0.089579544 3.327627926 1379.91339592
40.320875 0.811614731 0.88386232 0.093962535 3.788651606 1625.77293960
44.334467 0.822946176 0.92665123 0.098511381 4.367449560 1965.54494196
46.907165 0.834277620 0.97120790 0.103248158 4.843078418 2200.28216686
54.418366 0.845609065 1.01778137 0.108199337 5.888031095 2961.35853839
55.091131 0.856940510 1.06667420 0.113397086 6.247173760 3035.03273452
55.470305 0.868271955 1.11825971 0.118881091 6.594370299 3076.95468678
62.939597 0.879603399 1.17300649 0.124701168 7.848641202 3961.39282116
66.478628 0.890934844 1.23151500 0.130921149 8.703458353 4419.40796540
67.426518 0.902266289 1.29457343 0.137624830 9.279563066 4546.33534619
67.603959 0.913597734 1.36324747 0.144925499 9.797537528 4570.29533539
69.707122 0.924929178 1.43903134 0.152982008 10.663935560 4859.08292257
69.843246 0.936260623 1.52411994 0.162027693 11.316540065 4878.07906512
74.848732 0.947592068 1.62194155 0.172427012 12.905943238 5602.33268291
112.729191 0.958923513 1.73832835 0.184799978 20.832352140 12707.87061041
163.795081 0.970254958 1.88455395 0.200345078 32.815538239 26828.82842547
198.660139 0.981586402 2.08767462 0.226331231 44.962993843 39465.85101402
209.375830 0.992917847 2.45306927 0.293402275 61.431344750 43838.23810785
Fuente: Elaboracion propia

Resultados forma grafica

options(scipen = 999999)
Wn_salida<-qnorm(salida_SW$p.value,lower.tail = FALSE)
print(Wn_salida)
## [1] 3.241867
library(fastGraph)
shadeDist(Wn_salida,ddist = "dnorm",lower.tail = FALSE)