Pruebas de normalidad
KEVIN ALBERTO LANDAVER FRANDO
2024-05-05
library(wooldridge)
data(hprice1)
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 7.829630Estimación del 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=stargazermodelo_estimado<-lm(price~lotsize+sqrft+bdrms,data = hprice1)
head(modelo_estimado)## $coefficients
## (Intercept) lotsize sqrft bdrms
## -21.770308148 0.002067707 0.122778185 13.852521744
##
## $residuals
## 1 2 3 4 5 6
## -45.639765 74.848732 -8.236558 -12.081520 18.093192 62.939597
## 7 8 9 10 11 12
## 40.320875 69.843246 -43.142550 -17.817835 -47.855859 -85.461169
## 13 14 15 16 17 18
## -54.466158 -54.300415 -52.129801 -29.766931 -51.441108 32.675968
## 19 20 21 22 23 24
## 67.603959 33.275839 -16.596960 -26.696234 -24.271531 -107.080889
## 25 26 27 28 29 30
## 30.924022 5.363331 -40.869022 46.907165 -48.350295 44.334467
## 31 32 33 34 35 36
## -6.707262 -77.172687 19.168108 -37.749811 55.091131 -59.845223
## 37 38 39 40 41 42
## -33.801248 18.801816 -65.502849 26.236229 9.099900 198.660139
## 43 44 45 46 47 48
## -3.537785 55.470305 32.253952 12.433611 -48.704980 -91.243980
## 49 50 51 52 53 54
## 32.529367 66.478628 -11.629207 36.031430 6.700640 -74.702719
## 55 56 57 58 59 60
## 1.399296 -13.815798 -41.749618 -16.271207 20.334434 -16.762094
## 61 62 63 64 65 66
## -2.824941 16.718018 67.426518 69.707122 -0.195089 112.729191
## 67 68 69 70 71 72
## -6.752801 -2.745208 -63.699108 -7.662789 -36.663785 19.219211
## 73 74 75 76 77 78
## 163.795081 -11.312669 -13.462160 209.375830 -115.508697 24.909926
## 79 80 81 82 83 84
## -36.646568 7.386314 -120.026447 -5.446904 -62.566594 37.147186
## 85 86 87 88
## -6.402439 -23.651448 54.418366 -19.683427
##
## $effects
## (Intercept) lotsize sqrft bdrms
## -2753.7058885 -332.5616495 705.7416406 91.9901445 24.5834978
##
## 66.8527560 44.8832440 76.5989953 -36.2017162 -8.2714140
##
## -41.3451966 -80.3333083 -52.1490911 -47.6962279 -45.4396010
##
## -21.4606182 -44.9756580 38.6921166 74.7127636 37.4752905
##
## -9.1467971 -21.1247447 -17.3328476 -100.1217461 34.9310630
##
## 12.2638846 -34.4604306 51.8314167 -45.2788593 47.6377835
##
## 0.5400987 -78.0011614 26.2598840 -31.7170779 59.0374055
##
## -51.4777607 -31.1935976 17.2480483 -59.4795824 31.3027063
##
## 15.7472963 186.5292347 1.8843622 62.7904146 37.6090149
##
## 17.8596096 -37.3104404 -86.0209705 39.5186686 72.2168253
##
## -5.1473111 35.8444169 14.2293000 -67.7612398 6.3361415
##
## -7.1769528 -35.1247118 -10.3524247 27.2772785 -9.8686202
##
## 2.7580175 23.4354132 72.9339571 67.5762995 4.6416417
##
## 114.4137877 -2.4100430 -3.6676503 -61.0775917 -1.0282994
##
## -34.3312543 26.0846967 149.4864995 -2.7756414 -17.8966533
##
## 216.6223093 -180.7567259 30.1896218 -30.2227630 3.5758697
##
## -112.3861904 2.2509979 -57.6987297 44.0646274 0.6634092
##
## -17.0550424 61.4863214 -12.4893671
##
## $rank
## [1] 4
##
## $fitted.values
## 1 2 3 4 5 6 7 8
## 345.6398 295.1513 199.2366 207.0815 354.9068 403.3354 292.1791 245.1568
## 9 10 11 12 13 14 15 16
## 249.1425 257.8178 332.8559 385.4612 459.4662 266.3004 317.1298 257.1669
## 17 18 19 20 21 22 23 24
## 291.4411 252.3240 200.3960 276.7242 282.5970 296.6962 249.2715 257.0809
## 25 26 27 28 29 30 31 32
## 216.0760 269.6367 270.8690 296.0928 525.8503 305.6655 236.7073 412.1727
## 33 34 35 36 37 38 39 40
## 231.8319 272.7498 305.9089 249.8452 393.8012 556.1982 274.5039 198.7638
## 41 42 43 44 45 46 47 48
## 236.9001 514.8399 251.5378 174.5297 342.7460 252.5664 361.7050 508.7440
## 49 50 51 52 53 54 55 56
## 220.4706 248.5214 275.6292 218.9686 203.2994 254.7027 248.6007 263.8158
## 57 58 59 60 61 62 63 64
## 250.7496 274.2712 268.6656 332.7621 227.8249 249.2820 242.5735 401.5429
## 65 66 67 68 69 70 71 72
## 335.1951 382.2708 286.2528 382.7452 388.6991 227.6628 251.6638 220.7808
## 73 74 75 76 77 78 79 80
## 561.2049 241.3127 319.4622 215.6242 433.5087 305.0901 282.6466 217.6137
## 81 82 83 84 85 86 87 88
## 231.0264 273.5719 306.5666 257.8528 242.4024 226.1514 164.5816 261.6834
##
## $assign
## [1] 0 1 2 3Ajuste de los residuos a la Distribución Normal
library(fitdistrplus)## Loading required package: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:wooldridge':
##
## cement## Loading required package: survivalfit_normal<-fitdist(data = modelo_estimado$residuals,distr = "norm")
plot(fit_normal)
summary(fit_normal)## Fitting of the distribution ' norm ' by maximum likelihood
## Parameters :
## estimate Std. Error
## mean -2.321494e-15 6.231624
## sd 5.845781e+01 4.406423
## Loglikelihood: -482.8775 AIC: 969.7549 BIC: 974.7096
## Correlation matrix:
## mean sd
## mean 1 0
## sd 0 1- Verifique el supuesto de normalidad, a través de:
- La prueba JB (Cálculo manual)
library(tseries)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoosalida_JB<-jarque.bera.test(modelo_estimado$residuals)
salida_JB##
## Jarque Bera Test
##
## data: modelo_estimado$residuals
## X-squared = 32.278, df = 2, p-value = 9.794e-08library(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)))
- La prueba KS
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, unionlibrary(gt) # Carga la librería gt para crear tablas de datos
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 = "#A569BD"), # 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 | |||||||
Cálculo del estadístico D:
D<-max(max(tabla_KS$dif1),max(tabla_KS$dif2))
print(D)## [1] 0.0754392Valor crítico de la tabla de Lilliefors
Conclusión
En este caso dado que 0.0754392 > 0.009953375 se rechaza la hipótesis nula: ε ≁ N 0, σε, por lo que los residuos no siguen una distribución normal
library(nortest)
prueba_KS<-lillie.test(modelo_estimado$residuals)
prueba_KS##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: modelo_estimado$residuals
## D = 0.075439, p-value = 0.2496p.value<-prueba_KS$p.value- La prueba SW
library(dplyr)
library(gt)
residuos<-modelo_estimado$residuals
residuos %>%
as_tibble() %>%
rename(residuales=value) %>%
arrange(residuales) %>%
mutate(pi=(row_number()-0.375)/(n()+0.25)) %>%
mutate(mi=qnorm(pi,lower.tail = TRUE)) %>%
mutate(ai=0)->tabla_SWsalida_SW<-shapiro.test(modelo_estimado$residuals)
print(salida_SW)##
## Shapiro-Wilk normality test
##
## data: modelo_estimado$residuals
## W = 0.94132, p-value = 0.0005937Wn_salida<-qnorm(salida_SW$p.value,lower.tail = FALSE)
print(Wn_salida)## [1] 3.241867library(fastGraph)
shadeDist(Wn_salida,ddist = "dnorm",lower.tail = FALSE)