taller 1
Martin Alejandro Bernal Mazabuel
2022-10-18
Instalamos la base de datos
library(readr)
library(haven)
library(tidyselect)
library(haven)
Taller_1<-read_dta("C:/Users/Martin Alejandro/OneDrive/Documentos/econometria/eco II/Taller_1.dta")
View(Taller_1)procedemos a observar los distintos datos
summary(Taller_1)## price sqft beds baths age
## Min. : 50000 Min. : 704 Min. :1.00 Min. :1.000 Min. : 0.00
## 1st Qu.: 79900 1st Qu.:1201 1st Qu.:3.00 1st Qu.:2.000 1st Qu.: 8.00
## Median : 99950 Median :1516 Median :3.00 Median :2.000 Median :18.00
## Mean :112811 Mean :1612 Mean :3.17 Mean :2.055 Mean :24.56
## 3rd Qu.:128000 3rd Qu.:1874 3rd Qu.:4.00 3rd Qu.:2.000 3rd Qu.:38.00
## Max. :500000 Max. :4300 Max. :6.00 Max. :5.000 Max. :96.00
## stories vacant
## Min. :1.000 Min. :0.0000
## 1st Qu.:1.000 1st Qu.:0.0000
## Median :1.000 Median :1.0000
## Mean :1.207 Mean :0.5284
## 3rd Qu.:1.000 3rd Qu.:1.0000
## Max. :2.000 Max. :1.0000library(modeest)
mfv(Taller_1$price) #Moda de la variable## [1] 75000mfv(Taller_1$sqft)## [1] 1064mfv(Taller_1$beds)## [1] 3mfv(Taller_1$baths)## [1] 2mfv(Taller_1$age)## [1] 16mfv(Taller_1$stories)## [1] 1mfv(Taller_1$vacant)## [1] 1library(moments) #Se activa el paquete moments para encontrar la curtosis y la asimetria ##
## Attaching package: 'moments'## The following object is masked from 'package:modeest':
##
## skewnessskewness(Taller_1$price) # Coeficiente de asimetria de la variable## [1] 2.707592skewness(Taller_1$sqft)## [1] 1.149429skewness(Taller_1$beds)## [1] 0.5459253skewness(Taller_1$baths)## [1] 0.351758skewness(Taller_1$age)## [1] 1.099061skewness(Taller_1$stories)## [1] 1.447726skewness(Taller_1$vacant)## [1] -0.1138202kurtosis(Taller_1)## price sqft beds baths age stories vacant
## 14.772683 4.940148 3.941886 3.624871 3.825866 3.095910 1.012955Se propone un modelo con las variables que se encuentran en la base de datos
(metros cuadrados, numero de baños, numero de camas, años, numero de pisos, y la dicotomica “vacante”)
price<-Taller_1$price
sqft<-Taller_1$sqft
beds<-Taller_1$beds
baths<-Taller_1$baths
age<-Taller_1$age
stories<-Taller_1$stories
vacant<-Taller_1$vacant#variable price sera la variable dependiente, las demas seran las explicativas
modelo1<- lm(price ~ sqft + beds + baths + age + stories + vacant)
res<-residuals(modelo1)
summary(modelo1)##
## Call:
## lm(formula = price ~ sqft + beds + baths + age + stories + vacant)
##
## Residuals:
## Min 1Q Median 3Q Max
## -90740 -17215 -1734 13923 167282
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36741.177 5529.365 6.645 5.34e-11 ***
## sqft 96.054 2.979 32.248 < 2e-16 ***
## beds -17786.861 1956.722 -9.090 < 2e-16 ***
## baths -1009.123 2651.334 -0.381 0.7036
## age -331.464 53.565 -6.188 9.36e-10 ***
## stories -5743.812 3206.128 -1.792 0.0736 .
## vacant -9895.778 1938.365 -5.105 4.06e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 28030 on 873 degrees of freedom
## Multiple R-squared: 0.7202, Adjusted R-squared: 0.7183
## F-statistic: 374.5 on 6 and 873 DF, p-value: < 2.2e-16Supuestos
Media Cero
hist(res)
mean(res)## [1] 2.766841e-12Exogeneidad
estimated_price <- fitted.values(modelo1)
cor(res, estimated_price)## [1] 4.084423e-18plot(modelo1,which = 1)
Normalidad
library(ggplot2)
SampleQuantiles <- rstandard(modelo1)
(ggplot(modelo1,aes(qqnorm(SampleQuantiles)[[1]],SampleQuantiles))
+ geom_point(na.rm = TRUE,col="red")
+ geom_abline()
+ scale_x_continuous(name = "Theorical Quantiles")
+ scale_y_continuous(name = "Sample Quantiles"))
Varianza Constante
(ggplot(modelo1, aes(fitted.values(modelo1),res))
+ geom_point(col=I("red"))
+ stat_smooth(method = "loess")
+ stat_binhex(bins = 100)
+ scale_fill_gradient(low = "blue",high = "black")
+ geom_hline(yintercept = 0,col ="black", linetype = "dashed")
+ xlab("Fitted Values")
+ ylab("Residuals"))## `geom_smooth()` using formula 'y ~ x'
No Autocorrelación
residualesrezagados<-dplyr::lag(res)
plot(res,residualesrezagados)
punto b
predicción
se predice el precio de dos casas las cuales toman valores para la primera: sqft1: 1400 y age1: 20; para la segunda: sqft2: 1800 y age2: 20
Modelo2 <- lm(price ~ sqft + age, data = Taller_1)
library(tibble)
### Primera forma
## Predicción del precio de una casa de 1400 pies cuadrados ##
cvalues1 <- tibble(sqft = 1400,
age = 20)
predict(Modelo2, cvalues1, interval = "prediction")## fit lwr upr
## 1 96710.01 37695.21 155724.8## Predicción del precio de una casa con 1800 pies cuadrados ##
cvalues2 <- tibble(sqft = 1800,
age = 20)
predict(Modelo2, cvalues2, interval = "prediction")## fit lwr upr
## 1 128675 69663.77 187686.2### Segunda forma
library(tibble)
library(broom)
tidy(Modelo2, quick=TRUE)## # A tibble: 3 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -11490. 3741. -3.07 2.20e- 3
## 2 sqft 79.9 1.95 41.0 2.61e-206
## 3 age -184. 50.2 -3.67 2.62e- 4nuevo <- data.frame(sqft=c(1400, 1800),
age=c(20))
predict(object=Modelo2, newdata=nuevo, interval = "prediction")## fit lwr upr
## 1 96710.01 37695.21 155724.8
## 2 128674.98 69663.77 187686.2Punto C
Pruebas Formales
para verificar si el modelo se encuentra con problemas de heteroceasticidad, se realizaran diferentes pruebas, como la de Breush-Pagan, la de White, la de Goldfeld-Quant, entre otras que son las mas reconocidas, con una que indique heteroceasticidad se presume que el modelo presenta problemas.
### Prueba de Breusch-Pagan
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericbptest(modelo1,studentize = FALSE)##
## Breusch-Pagan test
##
## data: modelo1
## BP = 785.04, df = 6, p-value < 2.2e-16bptest(modelo1)##
## studentized Breusch-Pagan test
##
## data: modelo1
## BP = 218.16, df = 6, p-value < 2.2e-16library(car)## Loading required package: carDatancvTest(modelo1)## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 715.1047, Df = 1, p = < 2.22e-16### Prueba de White
library(readr)
bptest(modelo1, ~ fitted(modelo1) + I(fitted(modelo1)^2),studentize = FALSE)##
## Breusch-Pagan test
##
## data: modelo1
## BP = 1183.4, df = 2, p-value < 2.2e-16ncvTest(modelo1, ~ fitted(modelo1) + I(fitted(modelo1)^2))## Non-constant Variance Score Test
## Variance formula: ~ fitted(modelo1) + I(fitted(modelo1)^2)
## Chisquare = 1183.431, Df = 2, p = < 2.22e-16### Prueba de Goldfeld-Quandt
gqtest(modelo1)##
## Goldfeld-Quandt test
##
## data: modelo1
## GQ = 1.3854, df1 = 433, df2 = 433, p-value = 0.0003592
## alternative hypothesis: variance increases from segment 1 to 2gqtest(modelo1,order.by = ~ sqft + beds + baths + age + stories + vacant, data = Taller_1)##
## Goldfeld-Quandt test
##
## data: modelo1
## GQ = 0.53517, df1 = 433, df2 = 433, p-value = 1
## alternative hypothesis: variance increases from segment 1 to 2### Prueba de Park
Residuales2 <- (res^2)
Park1 <- lm(log(Residuales2) ~ log(sqft))
summary(Park1)##
## Call:
## lm(formula = log(Residuales2) ~ log(sqft))
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.9026 -0.8179 0.4323 1.4269 4.3576
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.4936 1.7024 2.052 0.0405 *
## log(sqft) 2.1022 0.2319 9.066 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.142 on 878 degrees of freedom
## Multiple R-squared: 0.08561, Adjusted R-squared: 0.08456
## F-statistic: 82.2 on 1 and 878 DF, p-value: < 2.2e-16Park2 <- lm(log(Residuales2) ~ log(beds))
summary(Park2)##
## Call:
## lm(formula = log(Residuales2) ~ log(beds))
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.3315 -0.8803 0.4325 1.4715 5.1633
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.0892 0.3921 46.132 <2e-16 ***
## log(beds) 0.7304 0.3406 2.145 0.0323 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.234 on 878 degrees of freedom
## Multiple R-squared: 0.005211, Adjusted R-squared: 0.004078
## F-statistic: 4.599 on 1 and 878 DF, p-value: 0.03226Park3 <- lm(log(Residuales2) ~ log(baths))
summary(Park3)##
## Call:
## lm(formula = log(Residuales2) ~ log(baths))
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.2372 -0.9064 0.4209 1.4609 4.6879
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.1294 0.1572 115.358 < 2e-16 ***
## log(baths) 1.1860 0.2093 5.666 1.98e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.2 on 878 degrees of freedom
## Multiple R-squared: 0.03528, Adjusted R-squared: 0.03418
## F-statistic: 32.1 on 1 and 878 DF, p-value: 1.981e-08Park4 <- lm(log(Residuales2) ~ log(age + 0.0001))
summary(Park4)##
## Call:
## lm(formula = log(Residuales2) ~ log(age + 1e-04))
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.1166 -0.9061 0.3690 1.4582 5.0738
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.04980 0.09224 206.521 <2e-16 ***
## log(age + 1e-04) -0.06260 0.02468 -2.536 0.0114 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.232 on 878 degrees of freedom
## Multiple R-squared: 0.007273, Adjusted R-squared: 0.006143
## F-statistic: 6.433 on 1 and 878 DF, p-value: 0.01138Park5 <- lm(log(Residuales2) ~ log(stories))
summary(Park5)##
## Call:
## lm(formula = log(Residuales2) ~ log(stories))
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.0417 -0.8627 0.4259 1.4286 4.9716
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.75601 0.08397 223.366 < 2e-16 ***
## log(stories) 1.10527 0.26638 4.149 3.66e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.218 on 878 degrees of freedom
## Multiple R-squared: 0.01923, Adjusted R-squared: 0.01811
## F-statistic: 17.22 on 1 and 878 DF, p-value: 3.661e-05### Prueba de Glesjer
## años
age.x <- (age + 0.001)
Glesjer <- abs(res)
summary(lm(Glesjer ~ age.x, data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ age.x, data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21103 -11826 -4634 6304 145909
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 21541.27 1011.52 21.296 <2e-16 ***
## age.x -56.19 31.53 -1.782 0.0751 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19300 on 878 degrees of freedom
## Multiple R-squared: 0.003604, Adjusted R-squared: 0.002469
## F-statistic: 3.176 on 1 and 878 DF, p-value: 0.07508summary(lm(Glesjer ~ I(1/(age.x)), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(1/(age.x)), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22911 -11974 -4389 6466 147345
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19934.918 672.253 29.654 <2e-16 ***
## I(1/(age.x)) 3.683 2.714 1.357 0.175
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19320 on 878 degrees of freedom
## Multiple R-squared: 0.002093, Adjusted R-squared: 0.0009565
## F-statistic: 1.842 on 1 and 878 DF, p-value: 0.1751summary(lm(Glesjer ~ I(1/sqrt(age.x)), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(1/sqrt(age.x)), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -23077 -12016 -4403 6490 147319
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19891.75 678.15 29.332 <2e-16 ***
## I(1/sqrt(age.x)) 123.09 86.51 1.423 0.155
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19320 on 878 degrees of freedom
## Multiple R-squared: 0.002301, Adjusted R-squared: 0.001164
## F-statistic: 2.025 on 1 and 878 DF, p-value: 0.1551summary(lm(Glesjer ~ sqrt(age.x), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ sqrt(age.x), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22907 -11698 -4411 6293 145001
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23638.5 1456.0 16.236 < 2e-16 ***
## sqrt(age.x) -783.9 293.8 -2.668 0.00776 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19260 on 878 degrees of freedom
## Multiple R-squared: 0.008044, Adjusted R-squared: 0.006914
## F-statistic: 7.12 on 1 and 878 DF, p-value: 0.007764summary(lm(Glesjer ~ I(age.x^2), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(age.x^2), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -20243 -11930 -4537 6710 146884
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20399.2177 778.1990 26.21 <2e-16 ***
## I(age.x^2) -0.2313 0.4131 -0.56 0.576
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19340 on 878 degrees of freedom
## Multiple R-squared: 0.0003568, Adjusted R-squared: -0.0007818
## F-statistic: 0.3134 on 1 and 878 DF, p-value: 0.5758summary(lm(Glesjer ~ I(age.x^-2), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(age.x^-2), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22906 -11974 -4389 6465 147346
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.994e+04 6.722e+02 29.658 <2e-16 ***
## I(age.x^-2) 3.678e-03 2.714e-03 1.355 0.176
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19320 on 878 degrees of freedom
## Multiple R-squared: 0.002088, Adjusted R-squared: 0.0009512
## F-statistic: 1.837 on 1 and 878 DF, p-value: 0.1757## pies cuadrados
summary(lm(Glesjer ~ sqft, data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ sqft, data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -45149 -9764 -2894 7419 113946
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8775.521 1809.443 -4.85 1.46e-06 ***
## sqft 17.951 1.066 16.84 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16810 on 878 degrees of freedom
## Multiple R-squared: 0.2441, Adjusted R-squared: 0.2433
## F-statistic: 283.6 on 1 and 878 DF, p-value: < 2.2e-16summary(lm(Glesjer ~ I(1/(sqft)), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(1/(sqft)), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -31771 -11071 -3165 7534 133372
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 43984 2083 21.11 <2e-16 ***
## I(1/(sqft)) -34858880 2916934 -11.95 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17940 on 878 degrees of freedom
## Multiple R-squared: 0.1399, Adjusted R-squared: 0.1389
## F-statistic: 142.8 on 1 and 878 DF, p-value: < 2.2e-16summary(lm(Glesjer ~ I(1/sqrt(sqft)), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(1/sqrt(sqft)), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -34678 -10887 -3177 7479 129623
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 71308 3937 18.11 <2e-16 ***
## I(1/sqrt(sqft)) -1979307 150612 -13.14 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17680 on 878 degrees of freedom
## Multiple R-squared: 0.1644, Adjusted R-squared: 0.1634
## F-statistic: 172.7 on 1 and 878 DF, p-value: < 2.2e-16summary(lm(Glesjer ~ sqrt(sqft), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ sqrt(sqft), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41540 -10045 -2931 7420 119810
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -36310.28 3659.48 -9.922 <2e-16 ***
## sqrt(sqft) 1424.33 91.15 15.627 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17110 on 878 degrees of freedom
## Multiple R-squared: 0.2176, Adjusted R-squared: 0.2167
## F-statistic: 244.2 on 1 and 878 DF, p-value: < 2.2e-16summary(lm(Glesjer ~ I(sqft^2), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(sqft^2), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -51157 -9414 -2729 6950 112852
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.867e+03 9.368e+02 6.262 5.94e-10 ***
## I(sqft^2) 4.961e-03 2.632e-04 18.849 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16320 on 878 degrees of freedom
## Multiple R-squared: 0.2881, Adjusted R-squared: 0.2873
## F-statistic: 355.3 on 1 and 878 DF, p-value: < 2.2e-16summary(lm(Glesjer ~ I(sqft^-2), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(sqft^-2), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27248 -11271 -3590 6806 138788
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.013e+04 1.194e+03 25.235 <2e-16 ***
## I(sqft^-2) -1.954e+10 2.001e+09 -9.762 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18370 on 878 degrees of freedom
## Multiple R-squared: 0.09792, Adjusted R-squared: 0.09689
## F-statistic: 95.3 on 1 and 878 DF, p-value: < 2.2e-16## camas
summary(lm(Glesjer ~ beds, data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ beds, data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -26743 -11745 -4043 6701 147861
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6386.2 3023.3 2.112 0.0349 *
## beds 4344.8 931.7 4.663 3.6e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19100 on 878 degrees of freedom
## Multiple R-squared: 0.02417, Adjusted R-squared: 0.02306
## F-statistic: 21.75 on 1 and 878 DF, p-value: 3.595e-06summary(lm(Glesjer ~ I(1/(beds)), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(1/(beds)), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22399 -11996 -4070 6806 147176
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 29258 2820 10.374 < 2e-16 ***
## I(1/(beds)) -27459 8285 -3.314 0.000957 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19220 on 878 degrees of freedom
## Multiple R-squared: 0.01236, Adjusted R-squared: 0.01123
## F-statistic: 10.98 on 1 and 878 DF, p-value: 0.0009569summary(lm(Glesjer ~ I(1/sqrt(beds)), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(1/sqrt(beds)), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -23429 -11974 -4024 6935 147322
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 41418 5740 7.216 1.16e-12 ***
## I(1/sqrt(beds)) -37168 9973 -3.727 0.000206 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19190 on 878 degrees of freedom
## Multiple R-squared: 0.01557, Adjusted R-squared: 0.01445
## F-statistic: 13.89 on 1 and 878 DF, p-value: 0.0002063summary(lm(Glesjer ~ sqrt(beds), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ sqrt(beds), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25655 -11837 -4003 6865 147680
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5900 5941 -0.993 0.321
## sqrt(beds) 14723 3337 4.413 1.15e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19130 on 878 degrees of freedom
## Multiple R-squared: 0.0217, Adjusted R-squared: 0.02058
## F-statistic: 19.47 on 1 and 878 DF, p-value: 1.148e-05summary(lm(Glesjer ~ I(beds^2), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(beds^2), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28573 -11586 -4045 6723 148154
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13045.7 1575.3 8.282 4.51e-16 ***
## I(beds^2) 675.8 136.6 4.948 8.99e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19070 on 878 degrees of freedom
## Multiple R-squared: 0.02713, Adjusted R-squared: 0.02602
## F-statistic: 24.48 on 1 and 878 DF, p-value: 8.986e-07summary(lm(Glesjer ~ I(beds^-2), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(beds^-2), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21409 -12081 -4348 6764 147002
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23044 1362 16.913 <2e-16 ***
## I(beds^-2) -24877 10336 -2.407 0.0163 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19280 on 878 degrees of freedom
## Multiple R-squared: 0.006555, Adjusted R-squared: 0.005423
## F-statistic: 5.793 on 1 and 878 DF, p-value: 0.01629## Baños
summary(lm(Glesjer ~ baths, data = Taller_1)) ##
## Call:
## lm(formula = Glesjer ~ baths, data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28588 -11022 -3326 7253 138403
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1217.7 2001.7 0.608 0.543
## baths 9220.3 926.7 9.950 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18330 on 878 degrees of freedom
## Multiple R-squared: 0.1013, Adjusted R-squared: 0.1003
## F-statistic: 99 on 1 and 878 DF, p-value: < 2.2e-16summary(lm(Glesjer ~ I(1/(baths)), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(1/(baths)), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -23931 -11726 -3814 6972 143061
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30416 1719 17.694 < 2e-16 ***
## I(1/(baths)) -18585 2894 -6.423 2.19e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18900 on 878 degrees of freedom
## Multiple R-squared: 0.04488, Adjusted R-squared: 0.04379
## F-statistic: 41.25 on 1 and 878 DF, p-value: 2.188e-10summary(lm(Glesjer ~ I(1/sqrt(baths)), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(1/sqrt(baths)), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24966 -11613 -3847 6973 142025
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 44523 3427 12.992 < 2e-16 ***
## I(1/sqrt(baths)) -33371 4613 -7.234 1.02e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18790 on 878 degrees of freedom
## Multiple R-squared: 0.05624, Adjusted R-squared: 0.05517
## F-statistic: 52.32 on 1 and 878 DF, p-value: 1.025e-12summary(lm(Glesjer ~ sqrt(baths), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ sqrt(baths), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27438 -11377 -3337 7016 139553
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -13417 3756 -3.572 0.000374 ***
## sqrt(baths) 23756 2620 9.065 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18490 on 878 degrees of freedom
## Multiple R-squared: 0.08559, Adjusted R-squared: 0.08455
## F-statistic: 82.18 on 1 and 878 DF, p-value: < 2.2e-16summary(lm(Glesjer ~ I(baths^2), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(baths^2), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -31666 -10720 -3152 6977 137112
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9387.2 1131.4 8.297 4e-16 ***
## I(baths^2) 2309.1 204.3 11.300 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18070 on 878 degrees of freedom
## Multiple R-squared: 0.127, Adjusted R-squared: 0.126
## F-statistic: 127.7 on 1 and 878 DF, p-value: < 2.2e-16summary(lm(Glesjer ~ I(baths^-2), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(baths^-2), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22490 -11933 -3971 6653 144501
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23983.2 978.7 24.504 < 2e-16 ***
## I(baths^-2) -10828.8 2092.6 -5.175 2.83e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19050 on 878 degrees of freedom
## Multiple R-squared: 0.0296, Adjusted R-squared: 0.02849
## F-statistic: 26.78 on 1 and 878 DF, p-value: 2.83e-07## pisos o plantas
summary(lm(Glesjer ~ stories, data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ stories, data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27950 -11526 -3667 6219 139042
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7870 2002 3.931 9.11e-05 ***
## stories 10185 1572 6.477 1.55e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18890 on 878 degrees of freedom
## Multiple R-squared: 0.0456, Adjusted R-squared: 0.04452
## F-statistic: 41.95 on 1 and 878 DF, p-value: 1.554e-10summary(lm(Glesjer ~ I(1/(stories)), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(1/(stories)), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27950 -11526 -3667 6219 139042
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 38425 2891 13.292 < 2e-16 ***
## I(1/(stories)) -20370 3145 -6.477 1.55e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18890 on 878 degrees of freedom
## Multiple R-squared: 0.0456, Adjusted R-squared: 0.04452
## F-statistic: 41.95 on 1 and 878 DF, p-value: 1.554e-10summary(lm(Glesjer ~ I(1/sqrt(stories)), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(1/sqrt(stories)), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27950 -11526 -3667 6219 139042
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 52829 5084 10.392 < 2e-16 ***
## I(1/sqrt(stories)) -34774 5369 -6.477 1.55e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18890 on 878 degrees of freedom
## Multiple R-squared: 0.0456, Adjusted R-squared: 0.04452
## F-statistic: 41.95 on 1 and 878 DF, p-value: 1.554e-10summary(lm(Glesjer ~ sqrt(stories), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ sqrt(stories), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27950 -11526 -3667 6219 139042
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6534 4170 -1.567 0.118
## sqrt(stories) 24589 3796 6.477 1.55e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18890 on 878 degrees of freedom
## Multiple R-squared: 0.0456, Adjusted R-squared: 0.04452
## F-statistic: 41.95 on 1 and 878 DF, p-value: 1.554e-10summary(lm(Glesjer ~ I(stories^2), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(stories^2), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27950 -11526 -3667 6219 139042
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 14659.7 1061.6 13.809 < 2e-16 ***
## I(stories^2) 3395.0 524.2 6.477 1.55e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18890 on 878 degrees of freedom
## Multiple R-squared: 0.0456, Adjusted R-squared: 0.04452
## F-statistic: 41.95 on 1 and 878 DF, p-value: 1.554e-10summary(lm(Glesjer ~ I(stories^-2), data = Taller_1))##
## Call:
## lm(formula = Glesjer ~ I(stories^-2), data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27950 -11526 -3667 6219 139042
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 31635 1882 16.806 < 2e-16 ***
## I(stories^-2) -13580 2097 -6.477 1.55e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18890 on 878 degrees of freedom
## Multiple R-squared: 0.0456, Adjusted R-squared: 0.04452
## F-statistic: 41.95 on 1 and 878 DF, p-value: 1.554e-10punto d
se procede a estimar los a1 y a2 que suponen una estructura de la heteroceasticidad aditiva y/o multiplicativa
Modelo1 <- lm(price ~ sqft + beds + baths + age + stories + vacant, data = Taller_1)
summary(Modelo1)##
## Call:
## lm(formula = price ~ sqft + beds + baths + age + stories + vacant,
## data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -90740 -17215 -1734 13923 167282
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36741.177 5529.365 6.645 5.34e-11 ***
## sqft 96.054 2.979 32.248 < 2e-16 ***
## beds -17786.861 1956.722 -9.090 < 2e-16 ***
## baths -1009.123 2651.334 -0.381 0.7036
## age -331.464 53.565 -6.188 9.36e-10 ***
## stories -5743.812 3206.128 -1.792 0.0736 .
## vacant -9895.778 1938.365 -5.105 4.06e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 28030 on 873 degrees of freedom
## Multiple R-squared: 0.7202, Adjusted R-squared: 0.7183
## F-statistic: 374.5 on 6 and 873 DF, p-value: < 2.2e-16Residuales1 <- residuals(Modelo1)
Resid2 <- Residuales1^2
# Con exponencial
logud1 <- log(Resid2)
var1 <- lm(logud1 ~ sqft + beds + baths + age + stories + vacant, data = Taller_1)
summary(var1)##
## Call:
## lm(formula = logud1 ~ sqft + beds + baths + age + stories + vacant,
## data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.7235 -0.7729 0.3912 1.3590 4.3669
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.2422397 0.4138533 44.079 < 2e-16 ***
## sqft 0.0017948 0.0002229 8.051 2.68e-15 ***
## beds -0.7210164 0.1464537 -4.923 1.02e-06 ***
## baths 0.1671947 0.1984429 0.843 0.400
## age -0.0011555 0.0040092 -0.288 0.773
## stories -0.1151625 0.2399672 -0.480 0.631
## vacant -0.2104465 0.1450797 -1.451 0.147
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.098 on 873 degrees of freedom
## Multiple R-squared: 0.1277, Adjusted R-squared: 0.1217
## F-statistic: 21.29 on 6 and 873 DF, p-value: < 2.2e-16w <- 1/exp(fitted(var1))
MCGF1 <-lm(price ~ sqft + beds + baths + age + stories + vacant, weights = w)
summary(MCGF1)##
## Call:
## lm(formula = price ~ sqft + beds + baths + age + stories + vacant,
## weights = w)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -5.2104 -1.0376 -0.2312 0.9359 7.4328
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 31574.489 4023.337 7.848 1.24e-14 ***
## sqft 69.642 2.705 25.745 < 2e-16 ***
## beds -6791.853 1407.623 -4.825 1.65e-06 ***
## baths -3622.475 1839.187 -1.970 0.0492 *
## age -208.733 37.156 -5.618 2.60e-08 ***
## stories 2963.214 2602.607 1.139 0.2552
## vacant -6300.409 1321.778 -4.767 2.19e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.649 on 873 degrees of freedom
## Multiple R-squared: 0.6406, Adjusted R-squared: 0.6381
## F-statistic: 259.3 on 6 and 873 DF, p-value: < 2.2e-16# Sin exponencial
w <- (fitted(var1))
MCGF2 <-lm(price ~ sqft + beds + baths + age + stories + vacant, weights = w)
summary(MCGF2)##
## Call:
## lm(formula = price ~ sqft + beds + baths + age + stories + vacant,
## weights = w)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -427645 -76170 -6604 63157 774179
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 37113.182 5655.100 6.563 9.05e-11 ***
## sqft 98.234 2.985 32.905 < 2e-16 ***
## beds -18702.390 1996.782 -9.366 < 2e-16 ***
## baths -952.480 2706.901 -0.352 0.7250
## age -346.535 54.841 -6.319 4.19e-10 ***
## stories -6251.973 3252.402 -1.922 0.0549 .
## vacant -10187.413 1989.117 -5.122 3.73e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 125200 on 873 degrees of freedom
## Multiple R-squared: 0.7272, Adjusted R-squared: 0.7254
## F-statistic: 387.9 on 6 and 873 DF, p-value: < 2.2e-16punto e
encontrar estimaciones de MCG
### punto e
M1 <- log(resid(modelo1)^2)
varreg1 <- lm(M1 ~ sqft + beds + baths + age + stories + vacant, data = Taller_1)
summary(varreg1)##
## Call:
## lm(formula = M1 ~ sqft + beds + baths + age + stories + vacant,
## data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.7235 -0.7729 0.3912 1.3590 4.3669
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.2422397 0.4138533 44.079 < 2e-16 ***
## sqft 0.0017948 0.0002229 8.051 2.68e-15 ***
## beds -0.7210164 0.1464537 -4.923 1.02e-06 ***
## baths 0.1671947 0.1984429 0.843 0.400
## age -0.0011555 0.0040092 -0.288 0.773
## stories -0.1151625 0.2399672 -0.480 0.631
## vacant -0.2104465 0.1450797 -1.451 0.147
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.098 on 873 degrees of freedom
## Multiple R-squared: 0.1277, Adjusted R-squared: 0.1217
## F-statistic: 21.29 on 6 and 873 DF, p-value: < 2.2e-16p <- 1/exp(fitted(varreg1))
MCGF <-lm(price ~ sqft + beds + baths + age + stories + vacant, weights = p)
summary(MCGF)##
## Call:
## lm(formula = price ~ sqft + beds + baths + age + stories + vacant,
## weights = p)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -5.2104 -1.0376 -0.2312 0.9359 7.4328
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 31574.489 4023.337 7.848 1.24e-14 ***
## sqft 69.642 2.705 25.745 < 2e-16 ***
## beds -6791.853 1407.623 -4.825 1.65e-06 ***
## baths -3622.475 1839.187 -1.970 0.0492 *
## age -208.733 37.156 -5.618 2.60e-08 ***
## stories 2963.214 2602.607 1.139 0.2552
## vacant -6300.409 1321.778 -4.767 2.19e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.649 on 873 degrees of freedom
## Multiple R-squared: 0.6406, Adjusted R-squared: 0.6381
## F-statistic: 259.3 on 6 and 873 DF, p-value: < 2.2e-16ResiMCGF <- residuals(MCGF)
### Prueba de Breusch-Pagan
library(lmtest)
bptest(MCGF,studentize = FALSE)##
## Breusch-Pagan test
##
## data: MCGF
## BP = 1.2107e+11, df = 6, p-value < 2.2e-16bptest(MCGF)##
## studentized Breusch-Pagan test
##
## data: MCGF
## BP = 1.3162e-07, df = 6, p-value = 1### Errores estandar robustos ###
library(sandwich)
coeftest(Modelo1, vcov. = vcovHC, type = "HC4")##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36741.1769 6785.9475 5.4143 7.956e-08 ***
## sqft 96.0541 6.7059 14.3237 < 2.2e-16 ***
## beds -17786.8611 2977.7770 -5.9732 3.384e-09 ***
## baths -1009.1226 3564.9137 -0.2831 0.7772
## age -331.4641 65.4809 -5.0620 5.061e-07 ***
## stories -5743.8121 4660.1475 -1.2325 0.2181
## vacant -9895.7775 2070.3602 -4.7797 2.059e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modelo1)##
## Call:
## lm(formula = price ~ sqft + beds + baths + age + stories + vacant)
##
## Residuals:
## Min 1Q Median 3Q Max
## -90740 -17215 -1734 13923 167282
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36741.177 5529.365 6.645 5.34e-11 ***
## sqft 96.054 2.979 32.248 < 2e-16 ***
## beds -17786.861 1956.722 -9.090 < 2e-16 ***
## baths -1009.123 2651.334 -0.381 0.7036
## age -331.464 53.565 -6.188 9.36e-10 ***
## stories -5743.812 3206.128 -1.792 0.0736 .
## vacant -9895.778 1938.365 -5.105 4.06e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 28030 on 873 degrees of freedom
## Multiple R-squared: 0.7202, Adjusted R-squared: 0.7183
## F-statistic: 374.5 on 6 and 873 DF, p-value: < 2.2e-16punto f
predecir nuevamente con valores la primera: sqft1: 1400 y age1: 20; para la segunda: sqft2: 1800 y age2: 20
precio.fact = 31574.489+ 69.642*sqft + -208.733*age
ModeloFP<- lm(precio.fact ~ sqft + age, data =Taller_1)
summary(ModeloFP)## Warning in summary.lm(ModeloFP): essentially perfect fit: summary may be
## unreliable##
## Call:
## lm(formula = precio.fact ~ sqft + age, data = Taller_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.146e-11 -8.280e-12 -1.610e-12 5.750e-12 9.245e-10
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.157e+04 5.494e-12 5.747e+15 <2e-16 ***
## sqft 6.964e+01 2.859e-15 2.435e+16 <2e-16 ***
## age -2.087e+02 7.367e-14 -2.833e+15 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.412e-11 on 877 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 3.29e+32 on 2 and 877 DF, p-value: < 2.2e-16tidy(ModeloFP, quick=TRUE)## Warning in summary.lm(x): essentially perfect fit: summary may be unreliable## # A tibble: 3 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 31574. 5.49e-12 5.75e15 0
## 2 sqft 69.6 2.86e-15 2.44e16 0
## 3 age -209. 7.37e-14 -2.83e15 0nuevoFP <- data.frame(sqft=c(1400, 1800),
age=c(20))
predict(object=ModeloFP, newdata=nuevoFP, interval = "prediction")## fit lwr upr
## 1 124898.6 124898.6 124898.6
## 2 152755.4 152755.4 152755.4