Datos

library(wooldridge)
data(hprice1)
head(force(hprice1),n=5) #mostrar las primeras 5 observaciones

price	assess	bdrms	lotsize	sqrft	colonial	lprice	lassess	llotsize	lsqrft
300	349.1	4	6126	2438	1	5.703783	5.855359	8.720297	7.798934
370	351.5	3	9903	2076	1	5.913503	5.862210	9.200593	7.638198
191	217.7	3	5200	1374	0	5.252274	5.383118	8.556414	7.225481
195	231.8	3	4600	1448	1	5.273000	5.445875	8.433811	7.277938
373	319.1	4	6095	2514	1	5.921578	5.765504	8.715224	7.829630

Modelo Estimado

library(stargazer)
price<-lm(formula = price ~ lotsize + sqrft + bdrms, data = hprice1)
stargazer(price,title = "Modelo precio", type = "text",digits = 8)

## 
## Modelo precio
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                                price           
## -----------------------------------------------
## lotsize                    0.00206771***       
##                            (0.00064213)        
##                                                
## sqrft                      0.12277820***       
##                            (0.01323741)        
##                                                
## bdrms                       13.85252000        
##                            (9.01014500)        
##                                                
## Constant                   -21.77031000        
##                            (29.47504000)       
##                                                
## -----------------------------------------------
## Observations                    88             
## R2                          0.67236220         
## Adjusted R2                 0.66066090         
## Residual Std. Error    59.83348000 (df = 84)   
## F Statistic         57.46023000*** (df = 3; 84)
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

Verificación de Supuestos

Prueba de Normalidad de Jarque Bera

library(tseries)
salida_JB<-jarque.bera.test(price$residuals)
print(salida_JB)

## 
##  Jarque Bera Test
## 
## data:  price$residuals
## X-squared = 32.278, df = 2, p-value = 9.794e-08

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)))

Análisis

En este caso se muestra un valor de p-value muy pequeño, lo que significa que se rechaza la hipótesis nula, concluyendo que los residuos no siguen una distribución normal.

Prueba de Kolmogorov Smirnov - Lilliefors

library(dplyr)  
library(gt)  
library(gtExtras)

residuos_KS<-price$residuals  
residuos_KS %>%  
  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 de la tabla
tabla_KS %>% 
  gt() %>% 
  tab_header("Tabla para calcular el Estadistico KS") %>%  
  tab_source_note(source_note = "Fuente: Elaboración propia") %>%  
  tab_style(  
    style = list(
      cell_fill(color = "#698B69"), 
      cell_text(style = "italic")  
      ),
    locations = cells_body(  
      columns = dif1, 
      rows = dif1==max(dif1) 
    )) %>%
   tab_style(  
    style = list(
      cell_fill(color = "#79CDCD"),  
      cell_text(style = "italic")  
      ),
    locations = cells_body(  
      columns = dif2, 
      rows = dif2==max(dif2)  
    ))

residuales	posicion	dist1	dist2	zi	pi	dif1	dif2
Tabla para calcular el Estadistico KS
-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 estadístico D

D<-max(max(tabla_KS$dif1),max(tabla_KS$dif2))
print(D)

## [1] 0.0754392

# Tamaño de la muestra
n <- 88
# Nivel de significancia
alpha <- 0.05
# Calcular el valor crítico
valor_critico <- sqrt(-0.5 * log(alpha / 2)) / sqrt(n)
print(valor_critico)

## [1] 0.1447741

Análisis

En este caso dado que 0.0754392<0.1447741. No se rechaza la hipótesis nula, por lo que los residuos siguen una distribución normal.

Prueba de Shapiro - Wilk

residuos_SW<-price$residuals
residuos_SW %>%  
  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^4-2.071190*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: Elaboración propia")

residuales	pi	mi	ai	ai_ui	ui2
Tabla para calcular el Estadistico W
-120.026447	0.007082153	-2.45306927	-0.286093929	34.338837782	1.440635e+04
-115.508697	0.018413598	-2.08767462	-0.226331231	26.143225495	1.334226e+04
-107.080889	0.029745042	-1.88455395	-0.201511408	21.578020632	1.146632e+04
-91.243980	0.041076487	-1.73832835	-0.185875811	16.960048752	8.325464e+03
-85.461169	0.052407932	-1.62194155	-0.173430814	14.821600075	7.303611e+03
-77.172687	0.063739377	-1.52411994	-0.162970954	12.576906330	5.955624e+03
-74.702719	0.075070822	-1.43903134	-0.153872609	11.494702279	5.580496e+03
-65.502849	0.086402266	-1.36324747	-0.145769197	9.548297773	4.290623e+03
-63.699108	0.097733711	-1.29457343	-0.138426027	8.817614500	4.057576e+03
-62.566594	0.109065156	-1.23151500	-0.131683320	8.238976839	3.914579e+03
-59.845223	0.120396601	-1.17300649	-0.125427129	7.506214499	3.581451e+03
-54.466158	0.131728045	-1.11825971	-0.119573169	6.512691096	2.966562e+03
-54.300415	0.143059490	-1.06667420	-0.114057239	6.193355472	2.948535e+03
-52.129801	0.154390935	-1.01778137	-0.108829231	5.673246083	2.717516e+03
-51.441108	0.165722380	-0.97120790	-0.103849228	5.342119306	2.646188e+03
-48.704980	0.177053824	-0.92665123	-0.099084876	4.825926905	2.372175e+03
-48.350295	0.188385269	-0.88386232	-0.094509548	4.569564512	2.337751e+03
-47.855859	0.199716714	-0.84263354	-0.090101040	4.311862673	2.290183e+03
-45.639765	0.211048159	-0.80278966	-0.085840618	3.917745629	2.082988e+03
-43.142550	0.222379603	-0.76418130	-0.081712307	3.525277277	1.861280e+03
-41.749618	0.233711048	-0.72667986	-0.077702356	3.244043648	1.743031e+03
-40.869022	0.245042493	-0.69017366	-0.073798824	3.016085791	1.670277e+03
-37.749811	0.256373938	-0.65456498	-0.069991263	2.642156946	1.425048e+03
-36.663785	0.267705382	-0.61976766	-0.066270458	2.429725818	1.344233e+03
-36.646568	0.279036827	-0.58570518	-0.062628228	2.295109622	1.342971e+03
-33.801248	0.290368272	-0.55230918	-0.059057264	1.996209250	1.142524e+03
-29.766931	0.301699717	-0.51951819	-0.055550992	1.653582575	8.860702e+02
-26.696234	0.313031161	-0.48727661	-0.052103467	1.390966354	7.126889e+02
-24.271531	0.324362606	-0.45553386	-0.048709282	1.182248861	5.891072e+02
-23.651448	0.335694051	-0.42424369	-0.045363489	1.072912217	5.593910e+02
-19.683427	0.347025496	-0.39336354	-0.042061540	0.827915257	3.874373e+02
-17.817835	0.358356941	-0.36285409	-0.038799229	0.691318234	3.174752e+02
-16.762094	0.369688385	-0.33267878	-0.035572645	0.596272007	2.809678e+02
-16.596960	0.381019830	-0.30280344	-0.032378138	0.537378676	2.754591e+02
-16.271207	0.392351275	-0.27319601	-0.029212277	0.475319006	2.647522e+02
-13.815798	0.403682720	-0.24382619	-0.026071824	0.360203050	1.908763e+02
-13.462160	0.415014164	-0.21466524	-0.022953704	0.309006447	1.812298e+02
-12.081520	0.426345609	-0.18568573	-0.019854987	0.239878409	1.459631e+02
-11.629207	0.437677054	-0.15686137	-0.016772858	0.195055032	1.352385e+02
-11.312669	0.449008499	-0.12816677	-0.013704604	0.155035654	1.279765e+02
-8.236558	0.460339943	-0.09957734	-0.010647596	0.087699542	6.784089e+01
-7.662789	0.471671388	-0.07106908	-0.007599268	0.058231584	5.871833e+01
-6.752801	0.483002833	-0.04261848	-0.004557105	0.030773222	4.560033e+01
-6.707262	0.494334278	-0.01420234	-0.001518626	0.010185824	4.498736e+01
-6.402439	0.505665722	0.01420234	0.001518626	-0.009722911	4.099122e+01
-5.446904	0.516997167	0.04261848	0.004557105	-0.024822110	2.966876e+01
-3.537785	0.528328612	0.07106908	0.007599268	-0.026884576	1.251592e+01
-2.824941	0.539660057	0.09957734	0.010647596	-0.030078835	7.980294e+00
-2.745208	0.550991501	0.12816677	0.013704604	-0.037621996	7.536170e+00
-0.195089	0.562322946	0.15686137	0.016772858	-0.003272200	3.805971e-02
1.399296	0.573654391	0.18568573	0.019854987	0.027782994	1.958028e+00
5.363331	0.584985836	0.21466524	0.022953704	0.123108313	2.876532e+01
6.700640	0.596317280	0.24382619	0.026071824	0.174697904	4.489858e+01
7.386314	0.607648725	0.27319601	0.029212277	0.215771059	5.455764e+01
9.099900	0.618980170	0.30280344	0.032378138	0.294637808	8.280817e+01
12.433611	0.630311615	0.33267878	0.035572645	0.442296424	1.545947e+02
16.718018	0.641643059	0.36285409	0.038799229	0.648646203	2.794921e+02
18.093192	0.652974504	0.39336354	0.042061540	0.761027520	3.273636e+02
18.801816	0.664305949	0.42424369	0.045363489	0.852915978	3.535083e+02
19.168108	0.675637394	0.45553386	0.048709282	0.933664777	3.674164e+02
19.219211	0.686968839	0.48727661	0.052103467	1.001387528	3.693781e+02
20.334434	0.698300283	0.51951819	0.055550992	1.129598008	4.134892e+02
24.909926	0.709631728	0.55230918	0.059057264	1.471112049	6.205044e+02
26.236229	0.720963173	0.58570518	0.062628228	1.643128534	6.883397e+02
30.924022	0.732294618	0.61976766	0.066270458	2.049349072	9.562951e+02
32.253952	0.743626062	0.65456498	0.069991263	2.257494854	1.040317e+03
32.529367	0.754957507	0.69017366	0.073798824	2.400629035	1.058160e+03
32.675968	0.766288952	0.72667986	0.077702356	2.538999708	1.067719e+03
33.275839	0.777620397	0.76418130	0.081712307	2.719045583	1.107281e+03
36.031430	0.788951841	0.80278966	0.085840618	3.092960242	1.298264e+03
37.147186	0.800283286	0.84263354	0.090101040	3.347000059	1.379913e+03
40.320875	0.811614731	0.88386232	0.094509548	3.810707636	1.625773e+03
44.334467	0.822946176	0.92665123	0.099084876	4.392875123	1.965545e+03
46.907165	0.834277620	0.97120790	0.103849228	4.871272904	2.200282e+03
54.418366	0.845609065	1.01778137	0.108829231	5.922308882	2.961359e+03
55.091131	0.856940510	1.06667420	0.114057239	6.283542333	3.035033e+03
55.470305	0.868271955	1.11825971	0.119573169	6.632760113	3.076955e+03
62.939597	0.879603399	1.17300649	0.125427129	7.894332885	3.961393e+03
66.478628	0.890934844	1.23151500	0.131683320	8.754126443	4.419408e+03
67.426518	0.902266289	1.29457343	0.138426027	9.333585010	4.546335e+03
67.603959	0.913597734	1.36324747	0.145769197	9.854574914	4.570295e+03
69.707122	0.924929178	1.43903134	0.153872609	10.726016772	4.859083e+03
69.843246	0.936260623	1.52411994	0.162970954	11.382420482	4.878079e+03
74.848732	0.947592068	1.62194155	0.173430814	12.981076532	5.602333e+03
112.729191	0.958923513	1.73832835	0.185875811	20.953629849	1.270787e+04
163.795081	0.970254958	1.88455395	0.201511408	33.006577315	2.682883e+04
198.660139	0.981586402	2.08767462	0.226331231	44.962993843	3.946585e+04
209.375830	0.992917847	2.45306927	0.286093929	59.901153719	4.383824e+04
Fuente: Elaboración propia

Cálculo del Estadistico W

W<-(sum(tabla_SW$ai_ui)^2)/sum(tabla_SW$ui2)
print(W)

## [1] 0.9413208

Cálculo del Wn y su p-value

#Wn
mu<-0.0038915*log(n)^3-0.083751*log(n)^2-0.31082*log(n)-1.5861
sigma<-exp(0.0030302*log(n)^2-0.082676*log(n)-0.4803)
Wn<-(log(1-W)-mu)/sigma
print(Wn)

## [1] 3.241867

#P-value
p.value<-pnorm(Wn,lower.tail = FALSE)
print(p.value)

## [1] 0.0005937472

library(fastGraph)
shadeDist(Wn,ddist = "dnorm",lower.tail = FALSE)

Análisis

Basándonos en el valor p obtenido es 0.0005937472<0.05, se rechaza la hipótesis nula, por lo que se concluye que los residuos no siguen una distribución normal según la prueba.

Ejercicio pruebas de normalidad

JAZMIN GUADALUPE FLORES GARCIA - FG20019

2024-05-03

Datos

Modelo Estimado

Verificación de Supuestos

Prueba de Normalidad de Jarque Bera

Análisis

Prueba de Kolmogorov Smirnov - Lilliefors

Cálculo estadístico D

Análisis

Prueba de Shapiro - Wilk

Cálculo del Estadistico W

Cálculo del Wn y su p-value

Análisis