1. Estime el siguiente modelo:

price=+(lotsize)+{}_2(sqrft)+{}_3(bdrms)+

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("price~  lotsize + sqrft + bdrms", data = hprice1)
stargazer(modelo_estimado, title = "Modelo de precios", type = "html")

## 
## <table style="text-align:center"><caption><strong>Modelo de precios</strong></caption>
## <tr><td colspan="2" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td><em>Dependent variable:</em></td></tr>
## <tr><td></td><td colspan="1" style="border-bottom: 1px solid black"></td></tr>
## <tr><td style="text-align:left"></td><td>NA</td></tr>
## <tr><td colspan="2" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">lotsize</td><td>0.002<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(0.001)</td></tr>
## <tr><td style="text-align:left"></td><td></td></tr>
## <tr><td style="text-align:left">sqrft</td><td>0.123<sup>***</sup></td></tr>
## <tr><td style="text-align:left"></td><td>(0.013)</td></tr>
## <tr><td style="text-align:left"></td><td></td></tr>
## <tr><td style="text-align:left">bdrms</td><td>13.853</td></tr>
## <tr><td style="text-align:left"></td><td>(9.010)</td></tr>
## <tr><td style="text-align:left"></td><td></td></tr>
## <tr><td style="text-align:left">Constant</td><td>-21.770</td></tr>
## <tr><td style="text-align:left"></td><td>(29.475)</td></tr>
## <tr><td style="text-align:left"></td><td></td></tr>
## <tr><td colspan="2" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">Observations</td><td>88</td></tr>
## <tr><td style="text-align:left">R<sup>2</sup></td><td>0.672</td></tr>
## <tr><td style="text-align:left">Adjusted R<sup>2</sup></td><td>0.661</td></tr>
## <tr><td style="text-align:left">Residual Std. Error</td><td>59.833 (df = 84)</td></tr>
## <tr><td style="text-align:left">F Statistic</td><td>57.460<sup>***</sup> (df = 3; 84)</td></tr>
## <tr><td colspan="2" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"><em>Note:</em></td><td style="text-align:right"><sup>*</sup>p<0.1; <sup>**</sup>p<0.05; <sup>***</sup>p<0.01</td></tr>
## </table>

library(fitdistrplus)

## Cargando paquete requerido: MASS

## 
## Adjuntando el paquete: 'MASS'

## The following object is masked from 'package:wooldridge':
## 
##     cement

## Cargando paquete requerido: survival

fit_normal <- fitdist(data= modelo_estimado$residuals, distr= "norm")
plot(fit_normal)

2. Verique el supuesto de normalidad, a través de:

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 = 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)))

library(dplyr)

## 
## Adjuntando el paquete: '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)
library(gtExtras)

## 
## Adjuntando el paquete: 'gtExtras'

## The following object is masked from 'package:MASS':
## 
##     select

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: Elaboración 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)))

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

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^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") %>%  # Agrega un encabezado a la tabla
  tab_source_note(source_note = "Fuente: Elaboración propia")

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

## [1] 0.9413208

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

## [1] 0.0005937472

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