Talle 2- Regresion multiple
Karen Andrea Acevedo Landinez c.c 1019109777
2023-03-14
Maria comenzó como agente de bienes raíces en Cali hace 10 años. Después de laborar dos años para una empresa nacional, se traslado a Bogotá y trabajó para otra agencia de bienes raíces. Sus amigos y familiares la convencieron de que con su experiencia y conocimientos del negocio debía abrir su propia agencia. Terminó por adquirir la licencia de intermediario y al poco tiempo fundó su propia compañía, C&A (Casas y Apartamentos) en Cali. Santiago y Lina, dos vendedores de la empresa anterior aceptaron trabajar en la nueva compaña. En la actualidad ocho agentes de bienes raíces colaboran con ella en C&A.
Actualmente las ventas de bienes raíces en Cali se han visto disminuidas de manera significativa en lo corrido del año. Durante este periodo muchas instituciones bancarias de ahorro y vivienda están prestando grandes sumas de dinero para la industria y la construcción comercial y residencial. Cuando el efecto producto de las tensiones políticas y sociales disminuya, se espera que la actividad económica de este sector se reactive.
Hace dos días, Maria recibió una carta solicitando asesoria para la compra de dos viviendas por parte de una compañía internacional que desea ubicar a dos de sus empleados con sus familias en la ciudad. Las solicitudes incluyen las siguientes condiciones:
vivienda 1: casa, área construida de 200 m2, 1 parqueadero, 2 baños, 4 habitaciones, estrato 4 o 5, zona Norte, con un crédito preaprobado de 350 millones.
vivienda 2: apartamento, área construida de 300 m2, 3 parqueaderos, 3 baños, 5 habitaciones, estrato 5 o 6, zona Sur, con un crédito preaprobado de 850 millones.
Ayude a Maria a responder la solicitud, mediante técnicas modelación que usted conoce. Ella requiere le envíe un informe ejecutivo (no mas de dos paginas) donde analice los dos casos y sus recomendaciones. Como soporte del informe debe anexar las estimaciones, validaciones y comparación de modelos requeridos.
#install.packages("devtools") # solo la primera vez
#install.packages("rlang")
#devtools::install_github("dgonxalex80/paqueteMOD", force =TRUE)#install.packages("learnr") # solo una vez
#learnr::run_tutorial("Tutorial201", "paqueteMOD") # carga Tutorial101En primera instancia realizamos la carga de la información e identificamos las variables para el análisis:
library(paqueteMOD)
data("vivienda")
head(vivienda)## Zona piso Estrato precio_millon Area_contruida parqueaderos Banos
## 1 Zona Sur 2 6 880 237 2 5
## 2 Zona Oeste 2 4 1200 800 3 6
## 3 Zona Sur 3 5 250 86 NA 2
## 4 Zona Sur NA 6 1280 346 4 6
## 5 Zona Sur 2 6 1300 600 4 7
## 6 Zona Sur 3 6 513 160 2 4
## Habitaciones Tipo Barrio cordenada_longitud Cordenada_latitud
## 1 4 Casa pance -76.46300 3.43000
## 2 7 Casa miraflores -76.46400 3.42800
## 3 3 Apartamento multicentro -76.46400 3.42900
## 4 5 Apartamento ciudad jardín -76.46400 3.43300
## 5 5 Casa pance -76.46438 3.43463
## 6 4 Casa pance -76.46438 3.43463vivienda$parqueaderos=as.numeric(vivienda$parqueaderos)## Warning: NAs introduced by coercionvivienda$piso=as.numeric(vivienda$piso)## Warning: NAs introduced by coercionDatos de vivienda: - Zona: ubicaciòn de apartamento - piso: numero de plantas - Estrato: estrato socio economico donde se encuentra la vivienda - precio_millon: Precio de la vivienda - Area_construida: Area construida - parqueaderos: numero de parqueaderos - Banos: numero de baños - Habitaciones: numero de habitaciones - Tipo: Si es casa o apartamento - Barrio: Ubicación de la vivienda
Realice un filtro a la base de datos e incluya solo las ofertas de : base1: casas, de la zona norte de la ciudad. Presente los primeros 3 registros de las bases y algunas tablas que comprueben la consulta. (Adicional un mapa con los puntos de las bases. Discutir si todos los puntos se ubican en la zona correspondiente o se presentan valores en otras zonas, por que?).
Clasificamos el conjunto de datos en diferentes bases: - base1: casas, de la zona norte de la ciudad
vivienda_zona_norte <- subset(vivienda, Zona == "Zona Norte" & Tipo == "Casa")
head(vivienda_zona_norte,3)## Zona piso Estrato precio_millon Area_contruida parqueaderos Banos
## 58 Zona Norte NA 5 400 212 NA 2
## 88 Zona Norte NA 3 175 130 NA 3
## 94 Zona Norte 2 4 265 162 1 3
## Habitaciones Tipo Barrio cordenada_longitud
## 58 4 Casa santa mónica residencial -76.47300
## 88 4 Casa brisas de los -76.48200
## 94 4 Casa zona norte -76.48238
## Cordenada_latitud
## 58 3.41800
## 88 3.47800
## 94 3.46786Mapa:
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.0 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.1 ✔ tibble 3.2.0
## ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
## ✔ purrr 1.0.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsrequire(leaflet)## Loading required package: leafletleaflet() %>% addCircleMarkers(lng= vivienda_zona_norte$cordenada_longitud, lat = vivienda_zona_norte$Cordenada_latitud, radius = 0.3, color = "black") %>% addTiles()Podemos observar que en el mapa hay viviendas fuera del Zona Norte de la ciudad y se encuentran marcadas con un punto gris oscuro. Esto se da debido a que hay viviendas en las que la Zona indicada en la base de datos es incorrecta generando que a pesar de ser un barrio de otra zona este clasificado como Zona Norte o por otra parte puede que las codenadas no se capturaron correctamente en el set de datos generando estas posibles inconsistencias. Adicional a esto podemos ver que hay zonas intermedias como NorOeste o NorEste que estan agrupados en un solo grupo lo que genera que el grupo de Zona Norte no este correctamente delimitado y de esta forma se amplia la zona.
- base2: Apartamentos, de la zona Sur de la ciudad
vivienda_zona_sur <- subset(vivienda, Zona == "Zona Sur" & Tipo == "Apartamento")
head(vivienda_zona_sur,3)## # A tibble: 3 × 12
## Zona piso Estrato preci…¹ Area_…² parqu…³ Banos Habit…⁴ Tipo Barrio corde…⁵
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <chr> <dbl>
## 1 Zona… 3 5 250 86 NA 2 3 Apar… multi… -76.5
## 2 Zona… NA 6 1280 346 4 6 5 Apar… ciuda… -76.5
## 3 Zona… 5 5 310 82.5 1 2 3 Apar… valle… -76.5
## # … with 1 more variable: Cordenada_latitud <dbl>, and abbreviated variable
## # names ¹precio_millon, ²Area_contruida, ³parqueaderos, ⁴Habitaciones,
## # ⁵cordenada_longitudMapa:
library(tidyverse)
require(leaflet)
leaflet() %>% addCircleMarkers(lng= vivienda_zona_sur$cordenada_longitud, lat = vivienda_zona_sur$Cordenada_latitud, radius = 0.3, color = "red") %>% addTiles()igualmente que para el caso de la zona norte, en la clasificación para la zona Sur se identifican puntos rojos fuera de la zona correcta por errores en el set de datos en clasificación a la zona o a las cordenadas correctas. Adicional tal como se nombra en la zona norte no tenemos subgrupos como SurOste y Sureste lo que genera que el grupo sea mayor de lo esperado y cubra zonas que no estan correctamente clasificadas.
Realice un análisis exploratorio de datos enfocado en la correlación entre la variable respuesta (precio del apartamento) en función del área construida, estrato, numero de baños, numero de habitaciones y zona donde se ubica la vivienda. Use gráficos interactivos con el paquete plotly e interprete los resultados.
Analsis Exploratorio de las variables:
- En primera instancia podemos observar que en el set de datos hay valores ausentes en las variables como es el caso de los parqueaderos. Dentro de la base se identifican 8 variables cuantitativas:Precio, area construida, parqueaderos, baños, habitaciones, zona, piso, estrato; 5 categoricas y otra que podemos identificar como string.
vivienda_zona_norte$parqueaderos=as.numeric(vivienda_zona_norte$parqueaderos)
Variables_analizar_norte = select(vivienda_zona_norte, precio_millon, Area_contruida, parqueaderos, Estrato)
summary(Variables_analizar_norte)## precio_millon Area_contruida parqueaderos Estrato
## Min. : 89.0 Min. : 30.0 Min. : 1.000 Min. :3.000
## 1st Qu.: 261.2 1st Qu.: 140.0 1st Qu.: 1.000 1st Qu.:3.000
## Median : 390.0 Median : 240.0 Median : 2.000 Median :4.000
## Mean : 445.9 Mean : 264.9 Mean : 2.182 Mean :4.202
## 3rd Qu.: 550.0 3rd Qu.: 336.8 3rd Qu.: 3.000 3rd Qu.:5.000
## Max. :1940.0 Max. :1440.0 Max. :10.000 Max. :6.000
## NA's :287library(ggpubr)
library(ggplot2)
g4=ggplot(vivienda_zona_norte,aes(x=precio_millon))+geom_histogram(bins=30)+theme_bw()
ggarrange(g4, labels = c("D"),ncol = 1, nrow = 1)
Poder identificar que el precio promedio de una casa en el norte de Cali es de 445.9 millones de pesos. y el precio de la vivienda en la zona norte de la ciudad se encuentra entre los 89 a 1’940 millones de pesos.Para el área construida (m2) en la zona norte la ciudad tenemos un promedio de 264.9 m2, tienen en promedio 2 parqueaderos.Y podemos identificar que no hay viviendas de estrato 1 o 2 en el norte de Cali.Con el fin de incorporar la variable estrato socio económico se crean las variables binarias.
vivienda_zona_sur$parqueaderos=as.numeric(vivienda_zona_sur$parqueaderos)
Variables_analizar_sur = select(vivienda_zona_sur, precio_millon, Area_contruida, parqueaderos, Estrato)
summary(Variables_analizar_sur)## precio_millon Area_contruida parqueaderos Estrato
## Min. : 75.0 Min. : 40.00 Min. : 1.000 Min. :3.00
## 1st Qu.: 175.0 1st Qu.: 65.00 1st Qu.: 1.000 1st Qu.:4.00
## Median : 245.0 Median : 85.00 Median : 1.000 Median :5.00
## Mean : 297.3 Mean : 97.47 Mean : 1.415 Mean :4.63
## 3rd Qu.: 335.0 3rd Qu.:110.00 3rd Qu.: 2.000 3rd Qu.:5.00
## Max. :1750.0 Max. :932.00 Max. :10.000 Max. :6.00
## NA's :406g4=ggplot(vivienda_zona_sur,aes(x=precio_millon))+geom_histogram(bins=30)+theme_bw()
ggarrange(g4, labels = c("D"),ncol = 1, nrow = 1)
Poder identificar que el precio promedio de un apartamento en el sur de Cali es de 297.3 millones de pesos. y el precio de la vivienda en la zona sur de la ciudad se encuentra entre los 75 a 1’750 millones de pesos.Para el área construida (m2) en la zona sur la ciudad tenemos un promedio de 97.47 m2, con un promedio de 1 parqueadero.Y podemos identificar que no hay viviendas de estrato 1 o 2 en el sur de Cali.Con el fin de incorporar la variable estrato socio económico se crean las variables binarias.
vivienda$E3<-as.numeric(vivienda$Estrato==3)
vivienda$E4<-as.numeric(vivienda$Estrato==4)
vivienda$E5<-as.numeric(vivienda$Estrato==5)
vivienda$E6<-as.numeric(vivienda$Estrato==6)
summary(vivienda)## Zona piso Estrato precio_millon
## Length:8322 Min. : 1.000 Min. :3.000 Min. : 58.0
## Class :character 1st Qu.: 2.000 1st Qu.:4.000 1st Qu.: 220.0
## Mode :character Median : 3.000 Median :5.000 Median : 330.0
## Mean : 3.771 Mean :4.634 Mean : 433.9
## 3rd Qu.: 5.000 3rd Qu.:5.000 3rd Qu.: 540.0
## Max. :12.000 Max. :6.000 Max. :1999.0
## NA's :2638 NA's :3 NA's :2
## Area_contruida parqueaderos Banos Habitaciones
## Min. : 30.0 Min. : 1.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 80.0 1st Qu.: 1.000 1st Qu.: 2.000 1st Qu.: 3.000
## Median : 123.0 Median : 2.000 Median : 3.000 Median : 3.000
## Mean : 174.9 Mean : 1.835 Mean : 3.111 Mean : 3.605
## 3rd Qu.: 229.0 3rd Qu.: 2.000 3rd Qu.: 4.000 3rd Qu.: 4.000
## Max. :1745.0 Max. :10.000 Max. :10.000 Max. :10.000
## NA's :3 NA's :1605 NA's :3 NA's :3
## Tipo Barrio cordenada_longitud Cordenada_latitud
## Length:8322 Length:8322 Min. :-76.59 Min. :3.333
## Class :character Class :character 1st Qu.:-76.54 1st Qu.:3.381
## Mode :character Mode :character Median :-76.53 Median :3.416
## Mean :-76.53 Mean :3.418
## 3rd Qu.:-76.52 3rd Qu.:3.452
## Max. :-76.46 Max. :3.498
## NA's :3 NA's :3
## E3 E4 E5 E6
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1747 Mean :0.2559 Mean :0.3306 Mean :0.2389
## 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## NA's :3 NA's :3 NA's :3 NA's :3pie(table(vivienda$Zona))
Podemos observar en la grafica que la oferta de viviendas se concentra
en la zona sur, seguida por la zona norte y la zona con mas excasa es la
Zona Centro.
Podemos observar el comportamiento general de las viviendas en la ciudad de cali:
g2=ggplot(vivienda,aes(x=Banos))+geom_bar()+theme_bw()
g3=ggplot(vivienda,aes(x=parqueaderos))+geom_bar()+theme_bw()
g4=ggplot(vivienda,aes(x=Habitaciones))+geom_bar()+theme_bw()
ggarrange(g2, g3, g4, labels = c("C", "D", "E"),ncol = 3, nrow = 1)## Warning: Removed 3 rows containing non-finite values (`stat_count()`).## Warning: Removed 1605 rows containing non-finite values (`stat_count()`).## Warning: Removed 3 rows containing non-finite values (`stat_count()`).
La mayoria de las viviendas cuentas con 1 baño, seguido por aquellas que
tienen entre 2 a 5 baños. También podemos identificar que la mayoria de
las viviendas en la ciudad de Cali tiene 1 parqueadedo, seguido por
algunas que cuentan con 2. Sin embargo, hay un grupo iportante del que
se desconoce si no tienen parqueadero o no se recolecto la información
en el set de datos. Para el caso de las habitaciones podemos ver que el
gruso esta entre 2 a 5 habitaciones en la ciudad.
Podemos posteriormente validar la relación del precio frente a algunas variables para la zona norte y zona sur:
require(ggplot2)
require(ggpubr)
grafico_zona_norte=ggplot(vivienda_zona_norte,aes(y=precio_millon,x=Area_contruida)) + geom_point(colour = "black", size = 2)
grafico_zona_sur=ggplot(vivienda_zona_sur,aes(y=precio_millon,x=Area_contruida)) + geom_point(colour = "black", size = 2)
ggarrange(grafico_zona_norte,grafico_zona_sur, labels = c("Viviendas_Norte", "Viviendas_Sur"),ncol = 2, nrow = 1)
Podemos observar que tanto en la zona sur, como en la zona norte de la
ciudad de Cali al incrementarse el area construida se incrementa el
precio de las viviendas.
Correlaciones:
library(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2cor_norte <-vivienda_zona_norte[,c("precio_millon","Area_contruida","Estrato","Banos","Habitaciones")]
ggpairs(cor_norte, title="GGally_zona_norte ") 
cor_sur <-vivienda_zona_sur[,c("precio_millon","Area_contruida","Estrato","Banos","Habitaciones")]
ggpairs(cor_sur, title="GGally_zona_sur ") 
CORRELACIONES PARA LAS VIVIENDAS DE LA ZONA NORTE Y DE LA ZONA SUR: -
Correlación Precio/Area construida es del 0,73 para la zona norte y 0,75
para zona sur correspondiente a la mas alta de todas las variables
analizadas, y podemos indicar que es una variable importante para el
modelo. - Correlación Precio/Estrato es del 0,61 para la zona norte y
0,67 para zona sur. Estrato seria la segunda variable que puede explicar
el precio de la vivienda. - Correlación Precio/Baños es del 0,52 para la
zona norte y 0,72 para zona sur. Los Baños pueden considerarse menos
relevantes a la hora de definir el precio de la vivienda ya que apenas
sobrepasa el 0.5 para el caso de la zona norte, pero pueden ser
significativos en el precio para las viviendas de la zona sur. -
Correlación Precio/Habitaciones es del 0,31 para la zona norte y 0,33
para zona sur y en ultimo lugrar podemos indicar que el numero de
habitaciones no tendria una correlación significativa con el precio.
- ###Estime un modelo de regresión lineal múltiple con las variables del punto anterior(precio = f(área construida, estrato, numero de cuartos, numero de parqueaderos,numero de baños ) ) e interprete los coeficientes si son estadísticamente significativos. Las interpretaciones deber están contextualizadas y discutir si losresultados son lógicos. Adicionalmente interprete el coeficiente y discuta el ajuste del modelo e implicaciones (que podrían hacer para mejorarlo).
modl_multi_vivienda = lm(precio_millon ~ Area_contruida + Estrato + parqueaderos + Banos + Habitaciones, data = vivienda )
summary(modl_multi_vivienda)##
## Call:
## lm(formula = precio_millon ~ Area_contruida + Estrato + parqueaderos +
## Banos + Habitaciones, data = vivienda)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1412.57 -88.36 -17.55 56.24 1101.38
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -380.7629 14.3638 -26.51 <2e-16 ***
## Area_contruida 0.8510 0.0222 38.33 <2e-16 ***
## Estrato 97.9107 2.8342 34.55 <2e-16 ***
## parqueaderos 74.4922 2.5900 28.76 <2e-16 ***
## Banos 61.0554 2.6271 23.24 <2e-16 ***
## Habitaciones -31.2744 2.2613 -13.83 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 177.2 on 6711 degrees of freedom
## (1605 observations deleted due to missingness)
## Multiple R-squared: 0.7206, Adjusted R-squared: 0.7204
## F-statistic: 3462 on 5 and 6711 DF, p-value: < 2.2e-16Este modelo nos aroja el siguiente resultado
Precio = -380.76 + 0.85 * (Area_construida) + 97.91 * (Estrato) + 74.49 * (parqueaderos) + 61.05 * (Banos) -31.27*(habitaciones) Donde β0 toma el valor de -380.76, β1 toma el valor de 0.85, β2 toma el valor de 97.91, β3 toma el valor de 74.49 ,β4 toma el valor de 61,05 Y β5 toma el valor de -31.27. Por lo que a partir de estos coeficientes podemos decir que cuando el Area, el estrato, parqueaderos, baños y habitaciones son 0.00 el precio sera igual a β0 correspondiente a -501.70 y en el caso que las variables tomen un valor diferente de 0.00: El β1 indica que por cada metro cuadrado el valor de la vivienda se incrementa 0.77 millone, El β2 indica que por cambios en el estrato el valor de la vivienda se incrementa 114.09 millones, El β3 indica que por cada parqueadero el valor de la vivienda se incrementa 76.66 millones, el β4 indica que por cada Baño el valor de la vivienda se incrementa 42.61 millones y el β5 indica que por cada habitación el valor de la vivienda se disminuye 31.27 millones.
El valor p indica si el coeficiente es significativo, para este caso presenta *** mostrando que todas las variables son significativas para el modelo y el r cuadrado muestra que el modelo logra explicar un 72% del precio de las viviendas. Sin embargo, no podriamos indicar que este sea el mejor modelo que explique el precio de las viviendas en ciudad de cali ya que puede haber una doble relación al tener encuenta en el modelo tanto el area construida como las habitaciones. Por lo cual se plantea el sigueinte modelo:
modl2_multi_vivienda = lm(precio_millon ~ Area_contruida + Estrato + parqueaderos + Banos, data = vivienda )
summary(modl2_multi_vivienda)##
## Call:
## lm(formula = precio_millon ~ Area_contruida + Estrato + parqueaderos +
## Banos, data = vivienda)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1215.99 -92.07 -15.21 61.13 1114.90
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -501.70651 11.55529 -43.42 <2e-16 ***
## Area_contruida 0.77321 0.02178 35.50 <2e-16 ***
## Estrato 114.09088 2.61782 43.58 <2e-16 ***
## parqueaderos 76.66904 2.62164 29.25 <2e-16 ***
## Banos 42.61132 2.29529 18.57 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 179.6 on 6712 degrees of freedom
## (1605 observations deleted due to missingness)
## Multiple R-squared: 0.7127, Adjusted R-squared: 0.7125
## F-statistic: 4162 on 4 and 6712 DF, p-value: < 2.2e-16Este modelo nos aroja el siguiente resultado
Precio = -501.70 + 0.77 * (Area_construida) + 114.09 * (Estrato) + 76.66 * (parqueaderos) + 42.61 * (Banos) Donde β0 toma el valor de -501.70, β1 toma el valor de 0.77, β2 toma el valor de 114.09, β3 toma el valor de76.66 ,β4 toma el valor de 76.66. Por lo que a partir de estos coeficientes podemos decir que cuando el Area, el estrato, parqueaderos y baños son 0.00 el precio sera igual a β0 correspondiente a -501.70 y en el caso que las variables tomen un valor diferente de 0.00: El β1 indica que por cada metro cuadrado el valor de la vivienda se incrementa 0.77 millone, El β2 indica que por cambios en el estrato el valor de la vivienda se incrementa 114.09 millones, El β3 indica que por cada parqueadero el valor de la vivienda se incrementa 76.66 millones y el β4 indica que por cada Baño el valor de la vivienda se incrementa 42.61 millones.
El valor p indica si el coeficiente es significativo, para este caso presenta *** mostrando que todas las variables son significativas para el modelo y el r cuadrado muestra que el modelo logra explicar un 71% del precio de las viviendas. Sin embargo, no podriamos indicar que este sea el mejor modelo que explique el precio de las viviendas en ciudad de cali.
summary(modl2_multi_vivienda)$adj.r.squared## [1] 0.712503Para el modelo calculado anteriormente podemos ver que el coeficiente de determinación es una medida utilizada para explicar cuánta variabilidad en el precio de la vivienda puede ser causada por su relación con el area construida, el estrato,los parqueaderos y los baños. Esta correlación, conocida como “bondad de ajuste”, se representa como un valor entre 0,0 y 1,0 que para este caso se enceuntra en 0,71 lo que indica que el valor al ser inferior a 0,90 el ajuste del modelo no seria aceptable.
- ###Realice la validación de supuestos del modelo e interprete los resultados (no es necesario corregir en caso de presentar problemas solo realizar sugerencias de quese podría hacer).
par(mfrow=c(2,2))
plot(modl2_multi_vivienda)
t.test(modl2_multi_vivienda$residuals, mu=0)##
## One Sample t-test
##
## data: modl2_multi_vivienda$residuals
## t = -5.6236e-15, df = 6716, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -4.295628 4.295628
## sample estimates:
## mean of x
## -1.232293e-14Pvalor=1 > α=0.05, se puede indicar que no rechaza Ho:ßo=0 y por tanto el supuesto se cumple.Podriamos ver que los residuales tienen un comportamiento lineal, lo que refleja que la relaciòn entre la variable dependiente (Precio_millon) y las variables independietes del modelo son lineales y que el area construida, el estrato, los parqueaderos y baños son variables explicativas para el modelo.
Para este modelo podemos observar que los puntos del grafico de normalidad se acercan a la línea oblicua del grafico que representa una distribución normal. Por lo cual para este caso podemos indicar que hay una distribución de residuos asimétrica. y podemos concluir que para el caso de los errores no se distibuyen de forma normal, el supuesto no se cumple.
En este caso, se espera que la dispersiòn de la raiz cuadrada de los residuos estandarizados no presente muchas variaciones según los valores esperados de Y. En la gráfica no se identifica una tendencia marcada en los residuos, esto podría indicar que no hay presencia de heterocedasticidad.
lmtest::dwtest(modl2_multi_vivienda)##
## Durbin-Watson test
##
## data: modl2_multi_vivienda
## DW = 1.7447, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0Como Pvalor=2.2e−16 < α=0.05 se rechaza la hipótesis nula,y por lo tanto los errores no son indepentientes, el supuesto de que los errores son independientes unos de otros no se cumple.
Podemos realizar un ajuste al modelo para obtener un resultado mas consistente en relación a los residuos.Por lo tanto para ajustar el modelo se puede hacer una transformación utilizando un logaritmo.como el que se muestra a continuación y analizar nuevamente los supuestos con el fin de identificar si este si los cumple.
- ###Con el modelo identificado debe predecir el precio de la vivienda con las características de la primera solicitud:
- vivienda 1: casa, área construida de 200 m2, 1 parqueadero, 2 baños, 4 habitaciones, estrato 4 o 5, zona Norte, con un crédito preaprobado de 350 millones.
predict(modl_multi_vivienda,list(Estrato=4,Banos=2,Area_contruida=200,parqueaderos=1,Habitaciones=4,Zona = "Zona Norte"))## 1
## 252.586Para la primera predicciòn tomamos en cuenta las caracteristicas indicadas que aplicanm para el estrato 4, y bajo estas podemos indicar que el Precio de una casa en la zona norte de la ciudad de cali de 200 m2, con 1 parqueadero, 2 baños, 4 habitaciones, esta en 252 millones de pesos.
predict(modl2_multi_vivienda,list(Estrato=4,Banos=2,Area_contruida=200,parqueaderos=1,Zona = "Zona Norte"))## 1
## 271.1908Relializando la predicción con el modelo 2, sin tener en cuenta el factor habitaciones podemos ver que el Precio de la vivienda se incrementa en 20 millones aproximadamente.
predict(modl_multi_vivienda,list(Estrato=5,Banos=2,Area_contruida=200,parqueaderos=1,Habitaciones=4,Zona = "Zona Norte"))## 1
## 350.4967Para la primera predicciòn tomamos en cuenta las caracteristicas indicadas que aplicanm para el estrato 5, y bajo estas podemos indicar que el Precio de una casa en la zona norte de la ciudad de cali de 200 m2, con 1 parqueadero, 2 baños, 4 habitaciones, esta en 350 millones de pesos.La cual esta en el limite del crédito preaprobado.
predict(modl2_multi_vivienda,list(Estrato=5,Banos=2,Area_contruida=200,parqueaderos=1,Zona = "Zona Norte"))## 1
## 385.2817Relializando la predicción con el modelo 2, sin tener en cuenta el factor habitaciones podemos ver que el Precio de la vivienda se incrementa en 30 millones aproximadamente.
- vivienda 2: apartamento, área construida de 300 m2, 3 parqueaderos, 3 baños, 5 habitaciones, estrato 5 o 6, zona Sur, con un crédito preaprobado de 850 millones.
predict(modl_multi_vivienda,list(Estrato=5,Banos=3,Area_contruida=300,parqueaderos=3,Habitaciones=5,Zona = "Zona Sur"))## 1
## 614.3625Para la primera predicciòn tomamos en cuenta las caracteristicas indicadas que aplicanm para el estrato 5, y bajo estas podemos indicar que el Precio de una casa en la zona norte de la ciudad de cali de 300 m2, con 3 parqueadero, 3 baños, 5 habitaciones, esta en 614 millones de pesos.
predict(modl2_multi_vivienda,list(Estrato=5,Banos=3,Area_contruida=300,parqueaderos=3,Zona = "Zona Sur"))## 1
## 658.5521Relializando la predicción con el modelo 2, sin tener en cuenta el factor habitaciones podemos ver que el Precio de la vivienda se incrementa en 45 millones aproximadamente
predict(modl_multi_vivienda,list(Estrato=6,Banos=3,Area_contruida=300,parqueaderos=3,Habitaciones=5,Zona = "Zona Sur"))## 1
## 712.2732Para la primera predicciòn tomamos en cuenta las caracteristicas indicadas que aplicanm para el estrato 6, y bajo estas podemos indicar que el Precio de una casa en la zona norte de la ciudad de cali de 300 m2, con 3 parqueadero, 3 baños, 5 habitaciones, esta en 712 millones de pesos.La cual esta por debajo del valor del crèdito preaprobado.
predict(modl2_multi_vivienda,list(Estrato=6,Banos=3,Area_contruida=300,parqueaderos=3,Zona = "Zona Sur"))## 1
## 772.643Relializando la predicción con el modelo 2, sin tener en cuenta el factor habitaciones podemos ver que el Precio de la vivienda se incrementa en 60 millones aproximadamente
vivienda_multi=na.omit(vivienda_zona_norte)
calc_valida=function(i){
modl2_multi_vivienda=lm(precio_millon~Area_contruida+Estrato+parqueaderos+Banos,data=vivienda_multi[-i,])
modl_multi_vivienda=lm(precio_millon~Area_contruida+parqueaderos+Habitaciones+Estrato+Banos,data=vivienda_multi[-i,])
pred0=predict(modl2_multi_vivienda,list(Area_contruida=vivienda_multi$Area_contruida[i],
parqueaderos=vivienda_multi$parqueaderos[i],
Banos=vivienda_multi$Banos[i],
Estrato=vivienda_multi$Estrato[i]))
pred=predict(modl_multi_vivienda,list(Area_contruida=vivienda_multi$Area_contruida[i],
parqueaderos=vivienda_multi$parqueaderos[i],
Banos=vivienda_multi$Banos[i],
Habitaciones=vivienda_multi$Habitaciones[i],
Estrato=vivienda_multi$Estrato[i]))
return(c(pred0,pred))
}
calc_valida(1)## 1 1
## 303.5616 302.8941prediciones=sapply(1:254, calc_valida)
prediciones=t(prediciones)
prediciones## 1 1
## [1,] 303.5616 302.8941
## [2,] 189.9297 192.2797
## [3,] 182.5609 176.0969
## [4,] 166.1619 205.5478
## [5,] 206.9654 211.9152
## [6,] 231.3976 227.3940
## [7,] 189.0684 182.3237
## [8,] 525.7184 528.1615
## [9,] 450.3134 445.2618
## [10,] 624.0248 625.1967
## [11,] 195.7938 197.8745
## [12,] 207.5237 209.0744
## [13,] 323.0740 315.8588
## [14,] 200.9315 187.8238
## [15,] 243.5401 236.1279
## [16,] 250.0441 242.3281
## [17,] 242.0422 243.6801
## [18,] 599.6138 610.3184
## [19,] 1407.4072 1424.7038
## [20,] 223.4604 209.4212
## [21,] 203.5494 199.5254
## [22,] 179.9625 182.6143
## [23,] 251.2488 248.6176
## [24,] 380.5553 395.8879
## [25,] 226.2700 227.1457
## [26,] 421.3556 414.9388
## [27,] 139.6949 134.7326
## [28,] 576.7838 584.5459
## [29,] 451.5287 468.1897
## [30,] 115.3551 117.2045
## [31,] 231.3492 245.7911
## [32,] 166.1071 207.0720
## [33,] 301.1179 293.5447
## [34,] 451.7815 475.5594
## [35,] 484.2453 485.0667
## [36,] 209.4884 231.4482
## [37,] 256.5525 261.8540
## [38,] 173.5612 176.4128
## [39,] 515.2401 537.7701
## [40,] 413.0128 409.4291
## [41,] 409.6689 415.2368
## [42,] 192.4353 180.7103
## [43,] 175.8400 163.4652
## [44,] 675.5879 670.8465
## [45,] 327.4527 321.3157
## [46,] 392.9430 399.2578
## [47,] 192.1398 202.8292
## [48,] 162.2174 165.5161
## [49,] 632.9559 630.3778
## [50,] 371.1728 367.9876
## [51,] 553.1322 568.9500
## [52,] 554.2639 589.6701
## [53,] 397.8523 386.0632
## [54,] 355.9501 363.4306
## [55,] 350.3296 317.3033
## [56,] 382.9622 393.3649
## [57,] 423.5364 439.6621
## [58,] 310.1774 307.1325
## [59,] 500.2008 503.0164
## [60,] 316.5232 316.5247
## [61,] 629.8390 637.5094
## [62,] 350.4484 354.9284
## [63,] 422.6574 412.4892
## [64,] 436.5066 431.2563
## [65,] 680.5637 671.1472
## [66,] 465.9061 460.3198
## [67,] 666.2599 674.2180
## [68,] 411.9534 406.4911
## [69,] 452.3045 456.3157
## [70,] 363.7351 360.0455
## [71,] 458.0648 454.1640
## [72,] 384.2532 387.6914
## [73,] 444.9320 427.4069
## [74,] 545.2195 566.8120
## [75,] 458.0779 459.8243
## [76,] 561.1018 549.1396
## [77,] 478.8451 483.1149
## [78,] 421.1319 411.2744
## [79,] 384.2877 377.3045
## [80,] 498.2777 486.7316
## [81,] 256.1175 262.9762
## [82,] 810.2791 791.8086
## [83,] 507.0405 490.6082
## [84,] 505.5553 507.6609
## [85,] 628.2917 642.0602
## [86,] 391.6717 390.9339
## [87,] 533.2809 537.7519
## [88,] 550.6583 549.0095
## [89,] 467.5833 469.0285
## [90,] 442.0070 444.4187
## [91,] 369.6648 379.8685
## [92,] 480.5822 488.3730
## [93,] 356.1772 350.3190
## [94,] 397.4410 400.3418
## [95,] 600.8721 589.8955
## [96,] 397.4410 400.3418
## [97,] 512.3782 499.6808
## [98,] 374.2798 372.0845
## [99,] 565.1998 609.1513
## [100,] 565.1998 609.1513
## [101,] 479.9424 464.8340
## [102,] 718.9651 728.7239
## [103,] 557.9400 552.3223
## [104,] 443.8234 440.4027
## [105,] 420.2687 410.8302
## [106,] 894.6590 885.5679
## [107,] 697.2624 700.0290
## [108,] 524.1512 535.9072
## [109,] 538.5991 530.4531
## [110,] 537.3966 530.7458
## [111,] 493.2386 492.5623
## [112,] 406.3826 400.3811
## [113,] 524.6876 557.5026
## [114,] 441.4062 444.4960
## [115,] 792.1010 770.7480
## [116,] 728.1384 704.9729
## [117,] 550.3881 540.7710
## [118,] 591.4272 573.3323
## [119,] 571.5134 550.2250
## [120,] 484.4549 478.3506
## [121,] 567.1269 576.9634
## [122,] 727.5237 720.1691
## [123,] 609.7389 616.3574
## [124,] 523.2781 524.7055
## [125,] 734.0235 726.7009
## [126,] 650.3464 647.3668
## [127,] 777.2797 779.4120
## [128,] 712.6279 714.4583
## [129,] 481.7713 493.9640
## [130,] 457.1861 453.2423
## [131,] 442.2535 430.7631
## [132,] 531.5739 515.9862
## [133,] 637.8484 638.4407
## [134,] 440.2504 434.8921
## [135,] 478.7605 474.1275
## [136,] 465.2409 462.1791
## [137,] 651.4771 651.2269
## [138,] 367.0977 356.2943
## [139,] 766.7835 762.8330
## [140,] 673.2123 671.3993
## [141,] 418.1346 411.2512
## [142,] 583.8251 608.8188
## [143,] 467.6983 480.3653
## [144,] 390.8898 388.2319
## [145,] 479.6690 487.3798
## [146,] 547.3005 563.8089
## [147,] 806.8364 798.9988
## [148,] 521.3649 522.7817
## [149,] 634.6401 633.0436
## [150,] 453.3839 438.7429
## [151,] 457.2397 452.1803
## [152,] 692.6950 691.2184
## [153,] 916.6470 896.2501
## [154,] 882.7732 867.3070
## [155,] 719.6462 726.1607
## [156,] 424.3959 440.1288
## [157,] 571.6802 570.3847
## [158,] 567.4065 564.5261
## [159,] 533.9143 532.7939
## [160,] 399.0519 397.1930
## [161,] 580.4747 568.7306
## [162,] 531.4629 532.2296
## [163,] 339.2743 334.0150
## [164,] 753.7026 756.4551
## [165,] 574.2517 559.2923
## [166,] 491.9307 486.5459
## [167,] 286.3573 287.4427
## [168,] 658.5224 646.1417
## [169,] 513.4899 517.6557
## [170,] 573.0150 589.0052
## [171,] 413.3715 414.2845
## [172,] 888.2538 862.7748
## [173,] 440.2722 434.5126
## [174,] 678.7343 678.6910
## [175,] 980.4612 996.6972
## [176,] 577.7029 581.8540
## [177,] 535.0841 541.2460
## [178,] 442.0726 441.6399
## [179,] 545.9885 541.8798
## [180,] 630.4557 637.0536
## [181,] 388.9446 395.5864
## [182,] 448.3381 456.9554
## [183,] 573.4904 578.7677
## [184,] 468.2758 470.8770
## [185,] 399.4908 400.3117
## [186,] 431.4607 436.4257
## [187,] 519.7007 513.5573
## [188,] 390.9078 394.0365
## [189,] 1032.8290 1055.0023
## [190,] 564.2882 553.4627
## [191,] 425.8297 418.7910
## [192,] 362.9400 359.9730
## [193,] 782.4971 801.9156
## [194,] 673.2805 684.9805
## [195,] 574.9469 575.5930
## [196,] 467.5833 488.4243
## [197,] 644.1950 624.8176
## [198,] 667.9145 647.7091
## [199,] 424.2397 414.7404
## [200,] 527.0884 517.5104
## [201,] 320.8605 313.7058
## [202,] 464.7159 477.9687
## [203,] 414.0385 412.4463
## [204,] 557.1423 563.0551
## [205,] 535.2448 541.6095
## [206,] 611.9546 621.4201
## [207,] 483.2590 478.1595
## [208,] 588.6383 578.8482
## [209,] 679.2773 680.4541
## [210,] 532.8399 516.0961
## [211,] 989.1068 993.5169
## [212,] 732.7361 729.6789
## [213,] 472.0160 473.1895
## [214,] 194.9340 197.0100
## [215,] 546.5454 539.2365
## [216,] 641.4849 654.2631
## [217,] 682.4402 664.0007
## [218,] 649.3194 620.2917
## [219,] 377.9929 341.8620
## [220,] 570.4857 553.2249
## [221,] 492.4211 487.2921
## [222,] 456.9530 472.4160
## [223,] 959.6392 948.1096
## [224,] 717.2851 725.2665
## [225,] 484.4974 476.4976
## [226,] 494.0146 501.4395
## [227,] 467.4053 460.5538
## [228,] 451.8676 448.9287
## [229,] 477.9662 472.1545
## [230,] 445.8047 446.8869
## [231,] 165.9324 148.1298
## [232,] 469.6333 465.0892
## [233,] 404.5975 408.3747
## [234,] 498.0860 500.4440
## [235,] 733.4566 723.6745
## [236,] 520.0873 534.9359
## [237,] 1045.1877 1051.2811
## [238,] 933.7373 928.3675
## [239,] 976.6510 992.3828
## [240,] 726.5582 715.7101
## [241,] 509.6681 525.0764
## [242,] 611.5019 604.7727
## [243,] 513.0398 513.2555
## [244,] 529.2103 524.6774
## [245,] 475.9342 465.1143
## [246,] 551.7052 536.0998
## [247,] 634.8216 622.3651
## [248,] 744.3718 774.1082
## [249,] 592.7646 598.0225
## [250,] 431.5177 439.7487
## [251,] 495.0700 494.3426
## [252,] 438.4227 449.7297
## [253,] 316.3684 318.2923
## [254,] 514.0354 519.3719resultados=data.frame(vivienda_multi$precio_millon,prediciones)
names(resultados)=c("precio_real","precio_msimple","precio_mmulti")
resultados## precio_real precio_msimple precio_mmulti
## 1 265 303.5616 302.8941
## 2 125 189.9297 192.2797
## 3 140 182.5609 176.0969
## 4 275 166.1619 205.5478
## 5 180 206.9654 211.9152
## 6 280 231.3976 227.3940
## 7 165 189.0684 182.3237
## 8 550 525.7184 528.1615
## 9 480 450.3134 445.2618
## 10 780 624.0248 625.1967
## 11 180 195.7938 197.8745
## 12 290 207.5237 209.0744
## 13 330 323.0740 315.8588
## 14 200 200.9315 187.8238
## 15 215 243.5401 236.1279
## 16 253 250.0441 242.3281
## 17 223 242.0422 243.6801
## 18 550 599.6138 610.3184
## 19 370 1407.4072 1424.7038
## 20 235 223.4604 209.4212
## 21 175 203.5494 199.5254
## 22 195 179.9625 182.6143
## 23 280 251.2488 248.6176
## 24 380 380.5553 395.8879
## 25 270 226.2700 227.1457
## 26 370 421.3556 414.9388
## 27 165 139.6949 134.7326
## 28 430 576.7838 584.5459
## 29 520 451.5287 468.1897
## 30 120 115.3551 117.2045
## 31 210 231.3492 245.7911
## 32 245 166.1071 207.0720
## 33 270 301.1179 293.5447
## 34 470 451.7815 475.5594
## 35 350 484.2453 485.0667
## 36 300 209.4884 231.4482
## 37 300 256.5525 261.8540
## 38 230 173.5612 176.4128
## 39 560 515.2401 537.7701
## 40 350 413.0128 409.4291
## 41 330 409.6689 415.2368
## 42 215 192.4353 180.7103
## 43 220 175.8400 163.4652
## 44 850 675.5879 670.8465
## 45 280 327.4527 321.3157
## 46 230 392.9430 399.2578
## 47 350 192.1398 202.8292
## 48 200 162.2174 165.5161
## 49 350 632.9559 630.3778
## 50 330 371.1728 367.9876
## 51 540 553.1322 568.9500
## 52 550 554.2639 589.6701
## 53 330 397.8523 386.0632
## 54 365 355.9501 363.4306
## 55 370 350.3296 317.3033
## 56 395 382.9622 393.3649
## 57 320 423.5364 439.6621
## 58 340 310.1774 307.1325
## 59 525 500.2008 503.0164
## 60 253 316.5232 316.5247
## 61 575 629.8390 637.5094
## 62 360 350.4484 354.9284
## 63 570 422.6574 412.4892
## 64 390 436.5066 431.2563
## 65 780 680.5637 671.1472
## 66 445 465.9061 460.3198
## 67 690 666.2599 674.2180
## 68 360 411.9534 406.4911
## 69 520 452.3045 456.3157
## 70 320 363.7351 360.0455
## 71 320 458.0648 454.1640
## 72 320 384.2532 387.6914
## 73 449 444.9320 427.4069
## 74 360 545.2195 566.8120
## 75 485 458.0779 459.8243
## 76 780 561.1018 549.1396
## 77 400 478.8451 483.1149
## 78 480 421.1319 411.2744
## 79 270 384.2877 377.3045
## 80 550 498.2777 486.7316
## 81 275 256.1175 262.9762
## 82 600 810.2791 791.8086
## 83 430 507.0405 490.6082
## 84 430 505.5553 507.6609
## 85 520 628.2917 642.0602
## 86 370 391.6717 390.9339
## 87 550 533.2809 537.7519
## 88 410 550.6583 549.0095
## 89 350 467.5833 469.0285
## 90 340 442.0070 444.4187
## 91 380 369.6648 379.8685
## 92 300 480.5822 488.3730
## 93 320 356.1772 350.3190
## 94 380 397.4410 400.3418
## 95 600 600.8721 589.8955
## 96 380 397.4410 400.3418
## 97 680 512.3782 499.6808
## 98 430 374.2798 372.0845
## 99 480 565.1998 609.1513
## 100 480 565.1998 609.1513
## 101 334 479.9424 464.8340
## 102 690 718.9651 728.7239
## 103 505 557.9400 552.3223
## 104 365 443.8234 440.4027
## 105 340 420.2687 410.8302
## 106 900 894.6590 885.5679
## 107 655 697.2624 700.0290
## 108 830 524.1512 535.9072
## 109 710 538.5991 530.4531
## 110 430 537.3966 530.7458
## 111 420 493.2386 492.5623
## 112 450 406.3826 400.3811
## 113 600 524.6876 557.5026
## 114 550 441.4062 444.4960
## 115 950 792.1010 770.7480
## 116 600 728.1384 704.9729
## 117 990 550.3881 540.7710
## 118 590 591.4272 573.3323
## 119 488 571.5134 550.2250
## 120 450 484.4549 478.3506
## 121 590 567.1269 576.9634
## 122 570 727.5237 720.1691
## 123 530 609.7389 616.3574
## 124 470 523.2781 524.7055
## 125 550 734.0235 726.7009
## 126 440 650.3464 647.3668
## 127 720 777.2797 779.4120
## 128 790 712.6279 714.4583
## 129 440 481.7713 493.9640
## 130 420 457.1861 453.2423
## 131 480 442.2535 430.7631
## 132 500 531.5739 515.9862
## 133 550 637.8484 638.4407
## 134 370 440.2504 434.8921
## 135 320 478.7605 474.1275
## 136 360 465.2409 462.1791
## 137 780 651.4771 651.2269
## 138 350 367.0977 356.2943
## 139 449 766.7835 762.8330
## 140 440 673.2123 671.3993
## 141 400 418.1346 411.2512
## 142 340 583.8251 608.8188
## 143 750 467.6983 480.3653
## 144 395 390.8898 388.2319
## 145 580 479.6690 487.3798
## 146 550 547.3005 563.8089
## 147 950 806.8364 798.9988
## 148 660 521.3649 522.7817
## 149 585 634.6401 633.0436
## 150 530 453.3839 438.7429
## 151 390 457.2397 452.1803
## 152 650 692.6950 691.2184
## 153 1050 916.6470 896.2501
## 154 680 882.7732 867.3070
## 155 730 719.6462 726.1607
## 156 480 424.3959 440.1288
## 157 450 571.6802 570.3847
## 158 1500 567.4065 564.5261
## 159 650 533.9143 532.7939
## 160 490 399.0519 397.1930
## 161 660 580.4747 568.7306
## 162 400 531.4629 532.2296
## 163 330 339.2743 334.0150
## 164 690 753.7026 756.4551
## 165 430 574.2517 559.2923
## 166 610 491.9307 486.5459
## 167 350 286.3573 287.4427
## 168 550 658.5224 646.1417
## 169 370 513.4899 517.6557
## 170 600 573.0150 589.0052
## 171 520 413.3715 414.2845
## 172 750 888.2538 862.7748
## 173 400 440.2722 434.5126
## 174 700 678.7343 678.6910
## 175 1600 980.4612 996.6972
## 176 450 577.7029 581.8540
## 177 480 535.0841 541.2460
## 178 810 442.0726 441.6399
## 179 600 545.9885 541.8798
## 180 535 630.4557 637.0536
## 181 295 388.9446 395.5864
## 182 360 448.3381 456.9554
## 183 350 573.4904 578.7677
## 184 350 468.2758 470.8770
## 185 245 399.4908 400.3117
## 186 335 431.4607 436.4257
## 187 400 519.7007 513.5573
## 188 400 390.9078 394.0365
## 189 1270 1032.8290 1055.0023
## 190 450 564.2882 553.4627
## 191 335 425.8297 418.7910
## 192 485 362.9400 359.9730
## 193 490 782.4971 801.9156
## 194 1200 673.2805 684.9805
## 195 450 574.9469 575.5930
## 196 350 467.5833 488.4243
## 197 950 644.1950 624.8176
## 198 570 667.9145 647.7091
## 199 315 424.2397 414.7404
## 200 625 527.0884 517.5104
## 201 340 320.8605 313.7058
## 202 342 464.7159 477.9687
## 203 435 414.0385 412.4463
## 204 570 557.1423 563.0551
## 205 850 535.2448 541.6095
## 206 500 611.9546 621.4201
## 207 650 483.2590 478.1595
## 208 850 588.6383 578.8482
## 209 430 679.2773 680.4541
## 210 490 532.8399 516.0961
## 211 1300 989.1068 993.5169
## 212 790 732.7361 729.6789
## 213 650 472.0160 473.1895
## 214 220 194.9340 197.0100
## 215 550 546.5454 539.2365
## 216 780 641.4849 654.2631
## 217 600 682.4402 664.0007
## 218 785 649.3194 620.2917
## 219 415 377.9929 341.8620
## 220 690 570.4857 553.2249
## 221 340 492.4211 487.2921
## 222 480 456.9530 472.4160
## 223 800 959.6392 948.1096
## 224 650 717.2851 725.2665
## 225 630 484.4974 476.4976
## 226 630 494.0146 501.4395
## 227 470 467.4053 460.5538
## 228 350 451.8676 448.9287
## 229 404 477.9662 472.1545
## 230 420 445.8047 446.8869
## 231 89 165.9324 148.1298
## 232 600 469.6333 465.0892
## 233 395 404.5975 408.3747
## 234 480 498.0860 500.4440
## 235 1100 733.4566 723.6745
## 236 500 520.0873 534.9359
## 237 850 1045.1877 1051.2811
## 238 950 933.7373 928.3675
## 239 1530 976.6510 992.3828
## 240 700 726.5582 715.7101
## 241 470 509.6681 525.0764
## 242 750 611.5019 604.7727
## 243 750 513.0398 513.2555
## 244 460 529.2103 524.6774
## 245 540 475.9342 465.1143
## 246 530 551.7052 536.0998
## 247 670 634.8216 622.3651
## 248 1080 744.3718 774.1082
## 249 450 592.7646 598.0225
## 250 260 431.5177 439.7487
## 251 380 495.0700 494.3426
## 252 340 438.4227 449.7297
## 253 600 316.3684 318.2923
## 254 420 514.0354 519.3719Podemos construir un dataframe en los resultados que identificamos: el precio leal y los precios obtenidos para los dos modelos con las variables de la zona norte.
##metricas de validación para (numericas)
MAE_simple=mean(abs(resultados$precio_msimple-resultados$precio_real))
MAE_simple## [1] 104.6715MAPE_simple=MAE_simple/mean(resultados$precio_real)*100
MAPE_simple## [1] 20.95262MAE_multi=mean(abs(resultados$precio_mmulti-resultados$precio_real),na.rm = TRUE)
MAE_multi## [1] 105.0124MAPE_multi=MAE_multi/mean(resultados$precio_real)*100
MAPE_multi## [1] 21.02085data.frame(MAE_simple,MAE_multi)## MAE_simple MAE_multi
## 1 104.6715 105.0124data.frame(MAPE_simple,MAPE_multi)## MAPE_simple MAPE_multi
## 1 20.95262 21.02085Para el caso del error de predicción (MAE) en el caso del los dos modelos podemos evidenciar una diferencia muy pequeña entre los dos modelos de alrededor de un millon. Es por esto que en el caso de usar cualquiera de los dos modelos se puede tener un error de predicción de alrededor 105 millones de pesos.
Y para el caso del error procentual de los modelos (MAPE) podemos ver que el modelo simple se equivoca en 20% y el modelo multiple se equivoca en 21%.
vivienda_multi=na.omit(vivienda_zona_sur)
calc_valida=function(i){
modl2_multi_vivienda=lm(precio_millon~Area_contruida+Estrato+parqueaderos+Banos,data=vivienda_multi[-i,])
modl_multi_vivienda=lm(precio_millon~Area_contruida+parqueaderos+Habitaciones+Estrato+Banos,data=vivienda_multi[-i,])
pred0=predict(modl2_multi_vivienda,list(Area_contruida=vivienda_multi$Area_contruida[i],
parqueaderos=vivienda_multi$parqueaderos[i],
Banos=vivienda_multi$Banos[i],
Estrato=vivienda_multi$Estrato[i]))
pred=predict(modl_multi_vivienda,list(Area_contruida=vivienda_multi$Area_contruida[i],
parqueaderos=vivienda_multi$parqueaderos[i],
Banos=vivienda_multi$Banos[i],
Habitaciones=vivienda_multi$Habitaciones[i],
Estrato=vivienda_multi$Estrato[i]))
return(c(pred0,pred))
}
calc_valida(1)## 1 1
## 249.1307 245.3937prediciones=sapply(1:1860, calc_valida)
prediciones=t(prediciones)
prediciones## 1 1
## [1,] 249.13071 245.39366
## [2,] 186.93430 184.43886
## [3,] 594.92434 591.09437
## [4,] 235.69106 231.58585
## [5,] 300.41291 303.33553
## [6,] 537.69628 527.02921
## [7,] 341.98044 337.03444
## [8,] 589.55171 604.29869
## [9,] 186.94897 184.45403
## [10,] 287.43427 289.99687
## [11,] 246.84709 243.04976
## [12,] 163.39692 160.24857
## [13,] 194.00609 191.70710
## [14,] 549.41785 539.06009
## [15,] 510.72066 512.73120
## [16,] 184.58877 182.02828
## [17,] 183.37704 180.78256
## [18,] 162.20483 177.65532
## [19,] 582.11568 586.14087
## [20,] 588.87170 589.25977
## [21,] 226.27202 221.90619
## [22,] 209.31692 207.44340
## [23,] 333.32556 336.34405
## [24,] 166.91034 182.47395
## [25,] 186.96572 184.47137
## [26,] 181.05188 178.39316
## [27,] 569.30343 564.75222
## [28,] 395.61418 389.18264
## [29,] 250.99619 265.24486
## [30,] 232.13513 227.93038
## [31,] 416.22882 400.14743
## [32,] 188.07270 185.60866
## [33,] 458.98572 459.55487
## [34,] 379.51192 380.84415
## [35,] 311.04444 314.26235
## [36,] 224.69176 228.48128
## [37,] 263.67618 249.95091
## [38,] 210.54246 208.70239
## [39,] 309.75684 331.49667
## [40,] 337.25174 350.87893
## [41,] 228.51724 224.20792
## [42,] 256.55956 261.23624
## [43,] 164.55036 161.43342
## [44,] 365.47813 361.18252
## [45,] 396.18106 397.97335
## [46,] 313.48874 298.22102
## [47,] 163.39692 160.24857
## [48,] 125.77804 116.33826
## [49,] 168.10206 165.08410
## [50,] 163.40246 178.90818
## [51,] 320.48016 305.33052
## [52,] 403.11579 405.10247
## [53,] 169.29573 184.95930
## [54,] 177.50436 174.74697
## [55,] 39.22968 49.01031
## [56,] 352.21459 337.14649
## [57,] 416.09736 399.83804
## [58,] 193.99517 191.69587
## [59,] 169.25323 166.26664
## [60,] 251.86254 237.80485
## [61,] 165.79016 162.70907
## [62,] 258.03993 254.55235
## [63,] 234.44426 230.30123
## [64,] 266.17059 262.08034
## [65,] 359.56538 355.10533
## [66,] 179.87112 177.17959
## [67,] 223.88251 219.44865
## [68,] 60.34061 52.01908
## [69,] 236.83930 232.76450
## [70,] 261.48625 257.26558
## [71,] 119.35900 117.95215
## [72,] 122.20073 112.65401
## [73,] 333.23854 317.59035
## [74,] 268.47636 264.45031
## [75,] 177.50953 174.75235
## [76,] 224.94701 257.65023
## [77,] 314.74555 327.71388
## [78,] 116.31290 125.26445
## [79,] 323.79409 321.30762
## [80,] 177.50333 174.74589
## [81,] 262.75038 259.39333
## [82,] 74.47871 66.55218
## [83,] 399.60628 382.90869
## [84,] 222.75170 218.28901
## [85,] 295.86530 298.66180
## [86,] 294.65131 292.17833
## [87,] 175.11666 190.83611
## [88,] 196.38333 194.15035
## [89,] 275.53222 272.52860
## [90,] 444.53436 439.46163
## [91,] 191.67230 189.30854
## [92,] 242.36393 246.64437
## [93,] 228.61959 224.31837
## [94,] 103.28018 111.86055
## [95,] 246.22977 242.41381
## [96,] 181.07252 197.03714
## [97,] 163.41907 160.27188
## [98,] 157.52731 172.89578
## [99,] 234.45745 248.95868
## [100,] 242.21453 265.07725
## [101,] 165.75863 162.67594
## [102,] 165.74232 162.65880
## [103,] 163.39692 178.89565
## [104,] 225.08441 220.68515
## [105,] 223.91083 219.47927
## [106,] 184.61474 182.05520
## [107,] 254.38067 249.96184
## [108,] 241.55052 237.60619
## [109,] 179.85565 177.16349
## [110,] 178.66764 175.94234
## [111,] 234.46536 230.32392
## [112,] 163.34153 160.19029
## [113,] 172.75973 169.86999
## [114,] 163.33045 178.74529
## [115,] 235.63859 231.52945
## [116,] 109.85687 108.18715
## [117,] 182.23983 179.61421
## [118,] 235.65564 250.20704
## [119,] 163.41021 160.26255
## [120,] 241.53335 256.25189
## [121,] 241.58405 237.64208
## [122,] 234.47063 230.32960
## [123,] 227.39482 241.71298
## [124,] 234.46404 248.97140
## [125,] 175.13222 190.87353
## [126,] 239.24671 235.24090
## [127,] 169.22666 184.79743
## [128,] 181.04155 196.96152
## [129,] 388.94541 390.53929
## [130,] 158.68126 155.40195
## [131,] 173.97204 171.11660
## [132,] 162.23281 177.71811
## [133,] 228.57865 224.27419
## [134,] 163.36369 160.21360
## [135,] 234.47063 248.98411
## [136,] 228.58411 242.94358
## [137,] 234.47722 230.33669
## [138,] 406.63347 408.71790
## [139,] 233.28954 229.11563
## [140,] 175.12703 190.86106
## [141,] 186.92383 184.42803
## [142,] 164.56682 161.45073
## [143,] 169.24791 184.84723
## [144,] 157.50971 154.19806
## [145,] 172.82243 169.93560
## [146,] 166.86398 182.36670
## [147,] 178.99227 186.71772
## [148,] 238.01382 233.97140
## [149,] 275.71143 272.71383
## [150,] 133.07855 113.00005
## [151,] 242.16117 246.43148
## [152,] 319.20764 322.65067
## [153,] 407.37773 409.48271
## [154,] 198.76125 196.59421
## [155,] 299.23160 302.12143
## [156,] 275.77940 278.01702
## [157,] 299.21579 283.44492
## [158,] 228.58548 224.28156
## [159,] 186.96572 184.47137
## [160,] 250.97980 247.29685
## [161,] 222.75456 218.29211
## [162,] 261.46840 276.60756
## [163,] 192.82578 190.49400
## [164,] 240.35007 255.00989
## [165,] 302.40180 299.32232
## [166,] 403.11579 405.10247
## [167,] 262.66777 259.30679
## [168,] 403.24566 405.23595
## [169,] 406.62130 408.70547
## [170,] 386.56765 388.09595
## [171,] 163.40689 160.25906
## [172,] 163.41354 178.93324
## [173,] 163.40024 160.25206
## [174,] 159.87703 156.63137
## [175,] 266.24379 262.98295
## [176,] 222.77174 237.03674
## [177,] 163.41354 178.93324
## [178,] 158.72528 174.14876
## [179,] 163.41354 178.93324
## [180,] 386.56765 388.09595
## [181,] 149.28199 164.43039
## [182,] 161.07244 176.54831
## [183,] 151.61773 166.80795
## [184,] 163.41354 160.26605
## [185,] 151.42265 166.40515
## [186,] 300.39720 303.31933
## [187,] 163.41575 178.93825
## [188,] 194.01701 191.71833
## [189,] 172.84020 169.95419
## [190,] 163.40800 160.26022
## [191,] 228.64689 224.34783
## [192,] 251.00573 247.32436
## [193,] 270.84311 266.88297
## [194,] 163.41132 217.20095
## [195,] 281.61629 278.78250
## [196,] 172.80153 169.91373
## [197,] 265.23975 242.66975
## [198,] 155.14799 170.42741
## [199,] 156.34670 171.68081
## [200,] 116.29677 106.58439
## [201,] 157.52731 154.21662
## [202,] 194.02447 209.69790
## [203,] 166.93945 182.54129
## [204,] 166.93945 182.54129
## [205,] 163.41354 160.26605
## [206,] 190.49707 188.10070
## [207,] 292.17641 294.87047
## [208,] 163.38584 178.87059
## [209,] 169.76281 177.24644
## [210,] 240.95735 245.19385
## [211,] 295.76834 298.56211
## [212,] 246.21690 242.40009
## [213,] 248.57895 244.82789
## [214,] 188.13587 185.67394
## [215,] 386.62176 388.15053
## [216,] 184.60955 182.04982
## [217,] 246.28123 242.46866
## [218,] 343.72982 347.03870
## [219,] 290.96174 293.62220
## [220,] 301.60202 304.55768
## [221,] 157.51558 154.20424
## [222,] 292.12665 294.81944
## [223,] 406.62130 408.70547
## [224,] 186.95001 184.45511
## [225,] 299.22369 302.11328
## [226,] 406.62130 408.70547
## [227,] 394.96370 396.72269
## [228,] 295.76834 298.56211
## [229,] 169.30317 166.31902
## [230,] 170.48709 167.53590
## [231,] 158.70790 174.11076
## [232,] 153.99152 169.26374
## [233,] 312.13567 309.32319
## [234,] 92.04651 108.50453
## [235,] 191.66800 189.30411
## [236,] 169.30104 166.31679
## [237,] 158.71138 174.11836
## [238,] 336.13505 331.02814
## [239,] 336.13505 331.02814
## [240,] 169.24260 184.83478
## [241,] 252.17390 248.52454
## [242,] 175.15815 172.33577
## [243,] 197.59189 195.39238
## [244,] 363.66026 354.95509
## [245,] 183.45991 199.53114
## [246,] 299.18417 302.07254
## [247,] 268.61085 264.58857
## [248,] 246.26193 242.44809
## [249,] 383.16132 366.05961
## [250,] 299.16836 283.35408
## [251,] 299.25531 302.14587
## [252,] 299.17626 302.06440
## [253,] 177.54051 174.78467
## [254,] 90.98049 107.40767
## [255,] 306.30401 309.39007
## [256,] 163.40800 160.26022
## [257,] 169.31698 166.33351
## [258,] 250.86314 247.17308
## [259,] 201.04095 198.93760
## [260,] 281.48067 300.39066
## [261,] 227.39069 223.05277
## [262,] 225.09142 220.69273
## [263,] 299.23160 283.47520
## [264,] 166.96102 182.59117
## [265,] 158.68821 174.06770
## [266,] 252.18691 248.53832
## [267,] 258.00655 254.51720
## [268,] 177.55084 174.79544
## [269,] 114.65887 113.12083
## [270,] 184.57838 182.01751
## [271,] 320.41470 341.95258
## [272,] 186.95525 184.46053
## [273,] 258.01990 254.53126
## [274,] 169.29573 184.95930
## [275,] 161.06339 157.85086
## [276,] 299.21579 302.10514
## [277,] 187.07994 184.58834
## [278,] 185.74333 183.21471
## [279,] 172.81198 169.92467
## [280,] 199.82677 197.68983
## [281,] 165.77494 162.69308
## [282,] 254.47721 250.89006
## [283,] 163.41354 160.26605
## [284,] 175.19446 172.37371
## [285,] 156.34670 171.68081
## [286,] 202.33103 205.49924
## [287,] 258.01323 254.52423
## [288,] 359.59053 355.13164
## [289,] 178.66970 175.94449
## [290,] 403.11579 405.10247
## [291,] 249.23324 253.69909
## [292,] 165.74776 162.66451
## [293,] 239.75334 225.19121
## [294,] 186.91440 184.41827
## [295,] 254.47721 250.89006
## [296,] 165.77820 162.69650
## [297,] 163.41354 160.26605
## [298,] 185.79964 183.27302
## [299,] 252.18041 248.53143
## [300,] 234.03574 238.08354
## [301,] 181.05704 178.39853
## [302,] 104.46261 113.07613
## [303,] 177.53018 174.77390
## [304,] 168.10634 165.08859
## [305,] 234.48382 230.34378
## [306,] 216.35871 219.91652
## [307,] 240.40177 236.42690
## [308,] 179.87628 177.18496
## [309,] 205.10708 218.88171
## [310,] 162.22498 159.04426
## [311,] 263.37097 268.22804
## [312,] 263.37097 268.22804
## [313,] 228.61959 224.31837
## [314,] 361.90521 357.50984
## [315,] 253.36812 249.75232
## [316,] 357.36357 352.84545
## [317,] 357.41379 352.89805
## [318,] 311.07476 314.29387
## [319,] 235.63203 250.16128
## [320,] 186.91440 184.41827
## [321,] 234.47722 248.99683
## [322,] 179.88660 177.19570
## [323,] 249.25445 253.72146
## [324,] 299.23950 302.12958
## [325,] 239.81770 244.02353
## [326,] 178.66455 175.93912
## [327,] 163.40246 160.25439
## [328,] 257.99988 254.51017
## [329,] 157.50150 154.18940
## [330,] 205.80842 203.83715
## [331,] 110.29399 119.05778
## [332,] 163.42461 178.95830
## [333,] 171.64683 187.36492
## [334,] 246.25550 261.08679
## [335,] 163.40246 160.25439
## [336,] 157.53904 172.92120
## [337,] 158.71369 174.12343
## [338,] 163.39692 160.24857
## [339,] 162.22162 177.69300
## [340,] 225.14891 220.75485
## [341,] 190.45444 188.05673
## [342,] 163.40246 178.90818
## [343,] 169.25323 184.85969
## [344,] 175.13222 172.30868
## [345,] 110.36276 119.14006
## [346,] 228.63597 224.33605
## [347,] 157.51910 172.87798
## [348,] 163.36369 178.82047
## [349,] 169.23729 184.82233
## [350,] 175.16334 190.94839
## [351,] 163.40246 160.25439
## [352,] 315.71074 319.05748
## [353,] 223.91791 219.48692
## [354,] 240.38884 236.41305
## [355,] 175.14778 172.32494
## [356,] 163.41354 178.93324
## [357,] 163.39692 160.24857
## [358,] 204.60637 202.60192
## [359,] 234.46404 248.97140
## [360,] 220.30321 234.41363
## [361,] 175.18927 172.36829
## [362,] 110.32837 119.09892
## [363,] 163.40246 178.90818
## [364,] 241.55955 237.61586
## [365,] 299.24741 302.13773
## [366,] 299.21579 302.10514
## [367,] 157.53904 154.22899
## [368,] 177.55084 174.79544
## [369,] 161.02039 157.80557
## [370,] 205.73459 203.76196
## [371,] 175.17060 172.34878
## [372,] 163.41354 178.93324
## [373,] 163.40578 160.25789
## [374,] 175.17371 172.35203
## [375,] 270.84311 266.88297
## [376,] 184.56799 182.00673
## [377,] 186.92907 184.43344
## [378,] 299.23950 320.86165
## [379,] 299.26322 302.15402
## [380,] 299.25373 302.14424
## [381,] 201.11204 199.01026
## [382,] 157.51558 154.20424
## [383,] 163.41354 160.26605
## [384,] 181.03329 178.37384
## [385,] 175.10110 172.27617
## [386,] 172.83288 169.94654
## [387,] 172.81721 169.93013
## [388,] 356.10569 351.55112
## [389,] 299.19998 302.08884
## [390,] 246.89024 251.29166
## [391,] 131.62950 141.00482
## [392,] 163.40246 160.25439
## [393,] 306.25804 309.34243
## [394,] 192.82578 190.49400
## [395,] 165.77276 162.69079
## [396,] 235.80260 249.65497
## [397,] 228.57592 242.92821
## [398,] 173.99806 171.14381
## [399,] 184.56799 182.00673
## [400,] 318.53880 312.94530
## [401,] 161.06339 157.85086
## [402,] 240.37592 236.39921
## [403,] 465.79019 456.16722
## [404,] 169.26916 166.28336
## [405,] 174.01159 171.15795
## [406,] 178.71098 175.98750
## [407,] 234.46404 248.97140
## [408,] 163.39138 160.24274
## [409,] 163.39360 160.24507
## [410,] 235.62547 250.14857
## [411,] 178.72130 175.99825
## [412,] 260.40878 256.98714
## [413,] 262.83464 240.15547
## [414,] 375.84653 380.04942
## [415,] 177.56117 174.80621
## [416,] 177.54258 193.42139
## [417,] 116.31981 106.61291
## [418,] 183.39257 180.79869
## [419,] 186.90812 184.41177
## [420,] 181.05188 178.39316
## [421,] 225.10545 239.41685
## [422,] 186.90812 184.41177
## [423,] 624.22188 600.97391
## [424,] 259.16047 255.70257
## [425,] 469.25186 451.28510
## [426,] 655.29952 649.33253
## [427,] 457.65772 439.52157
## [428,] 668.26506 666.50794
## [429,] 469.25186 451.28510
## [430,] 191.64008 189.27535
## [431,] 169.29254 184.95183
## [432,] 156.31698 152.97183
## [433,] 156.31698 152.97183
## [434,] 156.33481 171.65529
## [435,] 169.29254 184.95183
## [436,] 404.31016 425.09813
## [437,] 238.01382 233.97140
## [438,] 110.44299 119.23605
## [439,] 169.27448 166.28893
## [440,] 62.88165 54.64476
## [441,] 155.14799 170.42741
## [442,] 156.29915 171.57874
## [443,] 227.42510 241.76949
## [444,] 230.41124 234.35739
## [445,] 400.79305 402.71489
## [446,] 406.71868 408.80488
## [447,] 490.93523 491.56438
## [448,] 171.65208 168.73293
## [449,] 178.65939 175.93374
## [450,] 328.40301 331.28699
## [451,] 328.40301 331.28699
## [452,] 400.81885 402.74111
## [453,] 245.07442 241.22731
## [454,] 478.60256 469.30379
## [455,] 162.23841 159.05840
## [456,] 110.45216 119.24702
## [457,] 165.76950 181.35105
## [458,] 168.12025 165.10319
## [459,] 159.83926 156.59158
## [460,] 177.53845 174.78251
## [461,] 156.34670 171.68081
## [462,] 349.95877 353.43974
## [463,] 353.74067 349.12035
## [464,] 468.24680 481.19404
## [465,] 400.79305 402.71489
## [466,] 355.04847 346.09790
## [467,] 246.24263 242.42752
## [468,] 178.69034 175.96599
## [469,] 164.19201 161.06642
## [470,] 117.00223 115.52975
## [471,] 163.39692 160.24857
## [472,] 181.07252 178.41463
## [473,] 260.39388 256.97149
## [474,] 177.53845 174.78251
## [475,] 191.65082 189.28641
## [476,] 155.14799 170.42741
## [477,] 186.94478 184.44970
## [478,] 175.15815 172.33577
## [479,] 299.22369 302.11328
## [480,] 276.89549 273.93076
## [481,] 182.19848 198.11844
## [482,] 299.19207 302.08069
## [483,] 184.57319 182.01212
## [484,] 158.71948 155.44225
## [485,] 250.96684 247.28310
## [486,] 361.89260 357.49666
## [487,] 296.94107 299.76744
## [488,] 185.74333 183.21471
## [489,] 258.01323 254.52423
## [490,] 248.54154 244.78812
## [491,] 175.15296 190.92344
## [492,] 182.21192 179.58521
## [493,] 282.48133 278.84571
## [494,] 259.24784 255.79446
## [495,] 392.57686 394.26994
## [496,] 163.39692 160.24857
## [497,] 179.86597 177.17423
## [498,] 228.57592 242.92821
## [499,] 289.72736 343.38999
## [500,] 257.99988 254.51017
## [501,] 194.00609 191.70710
## [502,] 303.94133 325.66704
## [503,] 169.31698 166.33351
## [504,] 258.06663 254.58046
## [505,] 249.27989 272.31991
## [506,] 246.25550 242.44123
## [507,] 299.22369 302.11328
## [508,] 299.20788 302.09699
## [509,] 233.34259 229.17273
## [510,] 246.24392 242.42889
## [511,] 206.67337 209.96367
## [512,] 157.50736 172.85256
## [513,] 286.29643 288.82721
## [514,] 246.26193 242.44809
## [515,] 173.99286 189.75809
## [516,] 169.29573 166.31122
## [517,] 163.41354 160.26605
## [518,] 62.76537 54.51665
## [519,] 338.61550 333.58110
## [520,] 221.21244 224.90563
## [521,] 299.18259 302.07091
## [522,] 246.25550 242.44123
## [523,] 175.17994 172.35853
## [524,] 175.18512 172.36395
## [525,] 358.40799 353.91621
## [526,] 397.25233 399.07588
## [527,] 228.61959 243.01020
## [528,] 184.56280 182.00135
## [529,] 258.09332 254.60858
## [530,] 236.79360 232.71541
## [531,] 172.84856 169.96294
## [532,] 299.22369 320.81877
## [533,] 228.58548 224.28156
## [534,] 309.88594 331.86223
## [535,] 151.62403 166.82094
## [536,] 267.29295 263.23393
## [537,] 228.54454 242.86928
## [538,] 241.08571 245.32852
## [539,] 168.09885 165.08073
## [540,] 305.21806 308.27469
## [541,] 184.58357 182.02289
## [542,] 234.45745 230.31541
## [543,] 234.45745 230.31541
## [544,] 299.28693 302.17847
## [545,] 382.12292 383.52230
## [546,] 198.72712 196.55926
## [547,] 258.04660 254.55938
## [548,] 243.88692 240.00652
## [549,] 239.82199 244.02803
## [550,] 186.93221 203.00600
## [551,] 298.16169 301.02207
## [552,] 184.56280 182.00135
## [553,] 197.55814 195.35778
## [554,] 184.57007 182.00889
## [555,] 175.18927 172.36829
## [556,] 169.25323 166.26664
## [557,] 337.99516 335.90232
## [558,] 288.73528 291.33338
## [559,] 176.33385 173.54407
## [560,] 176.34937 173.56027
## [561,] 301.54737 304.50125
## [562,] 184.56280 182.00135
## [563,] 186.92907 184.43344
## [564,] 184.56799 182.00673
## [565,] 232.15515 227.95195
## [566,] 301.56298 304.51737
## [567,] 195.16433 192.89753
## [568,] 275.71922 272.72188
## [569,] 175.14778 172.32494
## [570,] 249.83491 246.12139
## [571,] 192.87990 190.54971
## [572,] 289.83093 292.45984
## [573,] 225.09843 220.70030
## [574,] 315.67898 300.32385
## [575,] 236.82624 251.40202
## [576,] 298.15373 301.01388
## [577,] 184.56799 182.00673
## [578,] 252.25194 248.60724
## [579,] 173.99806 171.14381
## [580,] 310.99896 314.21506
## [581,] 243.89335 240.01339
## [582,] 236.35672 259.11463
## [583,] 268.50999 264.48487
## [584,] 236.85235 232.77852
## [585,] 236.85235 232.77852
## [586,] 186.92488 184.42911
## [587,] 240.35653 236.37844
## [588,] 240.34361 236.36459
## [589,] 295.72794 298.52058
## [590,] 323.86747 326.62332
## [591,] 406.63347 408.71790
## [592,] 222.80179 218.34317
## [593,] 239.84988 244.05726
## [594,] 249.75994 246.04175
## [595,] 62.72661 54.47394
## [596,] 92.18958 90.02726
## [597,] 228.03437 231.91457
## [598,] 249.79872 246.08295
## [599,] 268.45955 264.43302
## [600,] 175.14778 172.32494
## [601,] 195.17535 192.90885
## [602,] 189.30589 186.87639
## [603,] 172.78063 169.89186
## [604,] 230.37792 234.32270
## [605,] 424.42442 427.00305
## [606,] 465.81809 456.20169
## [607,] 188.11692 185.65435
## [608,] 177.50953 193.34130
## [609,] 188.10429 185.64130
## [610,] 158.63260 155.35066
## [611,] 175.13222 172.30868
## [612,] 222.74455 236.98731
## [613,] 163.39138 178.88312
## [614,] 186.91650 184.42044
## [615,] 188.12008 185.65762
## [616,] 239.86275 244.07075
## [617,] 260.43586 257.01559
## [618,] 394.91946 378.12389
## [619,] 253.34853 249.73158
## [620,] 251.02517 247.34498
## [621,] 311.02928 314.24658
## [622,] 258.07330 273.25619
## [623,] 257.97318 254.48206
## [624,] 241.53762 237.59239
## [625,] 236.87847 232.80657
## [626,] 184.57838 182.01751
## [627,] 201.08989 198.98763
## [628,] 677.52830 694.60084
## [629,] 182.23260 179.60669
## [630,] 195.15551 192.88848
## [631,] 190.46510 188.06772
## [632,] 177.51159 174.75451
## [633,] 164.55036 161.43342
## [634,] 176.32350 173.53327
## [635,] 181.02297 196.91616
## [636,] 243.91265 240.03400
## [637,] 391.37266 374.46420
## [638,] 188.12008 185.65762
## [639,] 400.80595 402.72800
## [640,] 265.06243 260.94141
## [641,] 293.32470 296.05067
## [642,] 258.00655 254.51720
## [643,] 163.42461 160.27770
## [644,] 390.25888 391.88687
## [645,] 184.59396 182.03366
## [646,] 177.51469 174.75774
## [647,] 177.51469 174.75774
## [648,] 178.69550 175.97137
## [649,] 53.28553 44.76804
## [650,] 63.89051 55.66928
## [651,] 106.37350 104.60556
## [652,] 227.37005 241.66675
## [653,] 222.61576 236.75318
## [654,] 201.04678 198.94356
## [655,] 350.38216 345.67289
## [656,] 399.58668 401.47534
## [657,] 220.24468 234.30872
## [658,] 230.90044 226.65863
## [659,] 606.74693 603.24770
## [660,] 257.99988 254.51017
## [661,] 246.21047 242.39324
## [662,] 211.58996 209.78072
## [663,] 312.11977 315.36620
## [664,] 463.61557 464.31570
## [665,] 62.71111 54.45686
## [666,] 222.60145 218.12654
## [667,] 63.92940 55.71209
## [668,] 60.38684 52.07012
## [669,] 163.37144 160.22176
## [670,] 308.60575 311.75510
## [671,] 169.27448 166.28893
## [672,] 325.23702 310.25061
## [673,] 234.44426 230.30123
## [674,] 163.39692 160.24857
## [675,] 169.27979 166.29450
## [676,] 169.27979 166.29450
## [677,] 163.37809 160.22875
## [678,] 164.14797 161.02011
## [679,] 240.32422 236.34382
## [680,] 62.72661 54.47394
## [681,] 175.13740 172.31410
## [682,] 62.77312 54.52519
## [683,] 292.29250 313.92475
## [684,] 343.18818 338.27651
## [685,] 406.79172 408.87944
## [686,] 169.27979 166.29450
## [687,] 551.68589 554.84062
## [688,] 150.44329 165.60597
## [689,] 62.72661 54.47394
## [690,] 119.85494 110.24565
## [691,] 59.21488 50.86595
## [692,] 232.13513 227.93038
## [693,] 243.88048 239.99965
## [694,] 232.14848 227.94476
## [695,] 243.89978 240.02026
## [696,] 243.91908 240.04087
## [697,] 353.87878 349.26531
## [698,] 550.05703 553.15890
## [699,] 316.96624 301.74082
## [700,] 396.15381 379.45923
## [701,] 362.14872 363.82015
## [702,] 577.63979 573.32171
## [703,] 315.67898 300.32385
## [704,] 253.35506 249.73849
## [705,] 246.16544 242.34524
## [706,] 351.38832 346.70285
## [707,] 338.43391 333.38910
## [708,] 440.20447 440.24922
## [709,] 308.60575 311.75510
## [710,] 306.80046 301.68791
## [711,] 217.94788 231.99619
## [712,] 311.41377 306.42877
## [713,] 168.14700 165.13127
## [714,] 242.69038 257.39722
## [715,] 336.02156 345.22711
## [716,] 237.99041 233.94628
## [717,] 177.50953 174.75235
## [718,] 232.09510 227.88725
## [719,] 306.80046 301.68791
## [720,] 256.12642 247.36089
## [721,] 74.51913 66.59624
## [722,] 489.33606 490.75582
## [723,] 357.36357 352.84545
## [724,] 262.67466 259.31400
## [725,] 281.24608 286.60763
## [726,] 334.75769 338.63793
## [727,] 359.12119 362.85713
## [728,] 316.84515 320.22262
## [729,] 191.58102 189.21450
## [730,] 322.13685 317.45054
## [731,] 318.58299 313.79792
## [732,] 362.14152 363.81291
## [733,] 208.04209 206.13421
## [734,] 309.14854 304.10121
## [735,] 346.70934 341.89495
## [736,] 310.22932 305.21130
## [737,] 406.68216 408.76760
## [738,] 341.95481 337.00738
## [739,] 243.34839 239.45128
## [740,] 262.74350 259.38612
## [741,] 406.68216 390.18500
## [742,] 377.83388 379.94203
## [743,] 362.21355 363.88526
## [744,] 319.51732 314.75727
## [745,] 586.19351 590.32009
## [746,] 780.56747 793.15681
## [747,] 529.62967 532.16581
## [748,] 251.59723 237.39441
## [749,] 182.24293 198.22715
## [750,] 313.79980 337.60890
## [751,] 319.24737 343.18227
## [752,] 387.21133 399.27557
## [753,] 554.04442 557.26493
## [754,] 304.99960 308.04852
## [755,] 332.86913 327.66328
## [756,] 181.07768 178.41999
## [757,] 323.40540 318.75454
## [758,] 338.55207 334.32170
## [759,] 226.21647 240.50290
## [760,] 234.46404 230.32251
## [761,] 539.99073 604.59291
## [762,] 319.76758 315.01544
## [763,] 269.77803 266.61536
## [764,] 489.68931 491.11102
## [765,] 267.43147 264.20376
## [766,] 172.82452 169.93779
## [767,] 163.40246 160.25439
## [768,] 336.02156 345.22711
## [769,] 189.30589 186.87639
## [770,] 189.30589 186.87639
## [771,] 161.02378 157.80915
## [772,] 229.69202 225.41514
## [773,] 232.06840 227.85850
## [774,] 466.04839 466.81416
## [775,] 492.17526 484.59315
## [776,] 369.17118 371.03918
## [777,] 298.07414 300.93191
## [778,] 542.32144 550.43415
## [779,] 191.67767 189.31407
## [780,] 240.28545 236.30228
## [781,] 240.28545 236.30228
## [782,] 365.63051 361.34135
## [783,] 454.51416 436.58112
## [784,] 281.73341 278.90289
## [785,] 177.47854 174.72004
## [786,] 308.98267 303.92939
## [787,] 466.08310 448.31651
## [788,] 226.20953 221.83868
## [789,] 538.78416 546.79980
## [790,] 267.40284 264.17392
## [791,] 269.96100 266.80560
## [792,] 191.62398 189.25875
## [793,] 444.41346 428.94181
## [794,] 477.64266 478.73556
## [795,] 535.28282 524.53466
## [796,] 643.96509 659.92818
## [797,] 234.45745 230.31541
## [798,] 166.92543 163.87486
## [799,] 517.46381 527.89391
## [800,] 479.99838 470.78325
## [801,] 349.49202 356.76408
## [802,] 604.32461 619.34338
## [803,] 169.32760 166.34465
## [804,] 55.51159 65.71352
## [805,] 565.82355 574.56966
## [806,] 593.68599 589.82197
## [807,] 738.13295 734.48774
## [808,] 727.45970 723.51737
## [809,] 548.45160 538.11942
## [810,] 175.13740 172.31410
## [811,] 122.14936 112.59098
## [812,] 622.28436 627.43124
## [813,] 606.74693 603.24770
## [814,] 335.92551 312.01336
## [815,] 586.25685 590.38474
## [816,] 172.82243 169.93560
## [817,] 537.57722 545.55617
## [818,] 496.29875 479.03132
## [819,] 524.52049 526.91995
## [820,] 234.51019 230.37215
## [821,] 133.12390 132.11005
## [822,] 243.91265 240.03400
## [823,] 253.27018 249.64865
## [824,] 223.83294 219.39508
## [825,] 281.56610 278.73091
## [826,] 175.12184 190.84858
## [827,] 406.69433 408.78003
## [828,] 294.44476 291.14098
## [829,] 571.29001 574.99599
## [830,] 550.70770 543.40036
## [831,] 225.09843 220.70030
## [832,] 299.23160 302.12143
## [833,] 188.12008 185.65762
## [834,] 477.60985 478.70264
## [835,] 606.26301 621.22781
## [836,] 563.37009 572.03238
## [837,] 606.26301 621.22781
## [838,] 601.99926 598.36750
## [839,] 606.74693 603.24770
## [840,] 463.74478 464.44507
## [841,] 606.79532 603.29680
## [842,] 595.22632 610.07962
## [843,] 60.39839 52.08288
## [844,] 60.39839 52.08288
## [845,] 252.06335 248.40738
## [846,] 222.76601 218.30449
## [847,] 127.41977 144.78872
## [848,] 553.73188 562.09807
## [849,] 470.70565 490.38507
## [850,] 761.54168 758.59631
## [851,] 65.15181 56.97176
## [852,] 184.58357 182.02289
## [853,] 122.21941 112.67693
## [854,] 178.66970 231.68860
## [855,] 115.12147 124.03782
## [856,] 503.84692 487.14021
## [857,] 573.92547 582.18208
## [858,] 74.57976 66.66232
## [859,] 489.05365 493.42733
## [860,] 475.16761 476.19470
## [861,] 510.71267 502.34402
## [862,] 268.61085 264.58857
## [863,] 175.22039 172.40080
## [864,] 475.13452 476.16151
## [865,] 572.06244 581.04171
## [866,] 475.34411 476.37169
## [867,] 527.28067 516.37128
## [868,] 336.09600 331.79770
## [869,] 405.01655 398.84581
## [870,] 306.51532 290.27870
## [871,] 513.39504 502.15573
## [872,] 227.36316 223.02305
## [873,] 530.84873 520.04700
## [874,] 146.27620 150.87144
## [875,] 181.07252 178.41463
## [876,] 299.21579 283.44492
## [877,] 129.33723 119.99989
## [878,] 245.89921 231.64197
## [879,] 412.66591 396.45141
## [880,] 344.76551 348.90711
## [881,] 448.67583 430.60917
## [882,] 535.35522 543.29034
## [883,] 336.54071 360.83325
## [884,] 537.48197 545.44600
## [885,] 268.59036 265.39457
## [886,] 115.85929 114.35415
## [887,] 394.87799 396.63586
## [888,] 245.03584 241.18615
## [889,] 593.00598 589.11755
## [890,] 109.90763 108.23816
## [891,] 259.42379 284.43636
## [892,] 490.77569 476.72264
## [893,] 677.35489 690.81683
## [894,] 168.09885 165.08073
## [895,] 246.20404 242.38638
## [896,] 322.58256 317.90826
## [897,] 548.47438 538.14845
## [898,] 260.40200 256.98003
## [899,] 501.24187 502.98979
## [900,] 529.07648 526.38487
## [901,] 598.27550 608.03437
## [902,] 421.87201 424.37868
## [903,] 526.97460 534.66456
## [904,] 457.70674 458.24305
## [905,] 399.09687 411.50958
## [906,] 461.20435 461.83891
## [907,] 416.55044 410.69530
## [908,] 412.52856 415.60774
## [909,] 489.57156 490.99262
## [910,] 491.79655 511.92205
## [911,] 412.66591 396.45141
## [912,] 232.09510 227.88725
## [913,] 238.01382 233.97140
## [914,] 548.38329 556.68720
## [915,] 320.84775 316.12529
## [916,] 519.04040 526.54279
## [917,] 230.15620 225.89364
## [918,] 239.22079 253.89629
## [919,] 365.51549 362.03591
## [920,] 406.79172 408.87944
## [921,] 341.87792 355.59817
## [922,] 246.17187 242.35210
## [923,] 316.84817 320.22579
## [924,] 230.90044 226.65863
## [925,] 253.26365 249.64174
## [926,] 477.75203 478.84527
## [927,] 399.09687 411.50958
## [928,] 407.29553 419.92911
## [929,] 542.55414 532.05770
## [930,] 500.10325 483.14345
## [931,] 248.57895 244.82789
## [932,] 246.21690 242.40009
## [933,] 462.61145 463.27901
## [934,] 540.24950 548.34362
## [935,] 175.19965 172.37912
## [936,] 240.35007 255.00989
## [937,] 376.32351 386.68733
## [938,] 311.09750 295.73527
## [939,] 234.45745 230.31541
## [940,] 115.84915 114.34397
## [941,] 336.21362 331.11129
## [942,] 163.33045 160.17863
## [943,] 537.76772 564.60221
## [944,] 341.85230 336.89915
## [945,] 326.44203 330.08922
## [946,] 412.65426 414.90537
## [947,] 241.44219 256.04942
## [948,] 241.49635 256.15644
## [949,] 241.48604 256.13606
## [950,] 413.85047 416.13485
## [951,] 480.58857 471.38989
## [952,] 329.43674 324.95308
## [953,] 477.75203 478.84527
## [954,] 299.28693 302.17847
## [955,] 282.41646 278.77930
## [956,] 228.60004 237.71792
## [957,] 672.03092 646.16823
## [958,] 250.93703 247.25147
## [959,] 429.03814 413.09420
## [960,] 436.14451 420.43344
## [961,] 544.88244 544.02070
## [962,] 519.01313 526.51226
## [963,] 172.81198 169.92467
## [964,] 306.51532 308.78258
## [965,] 257.97986 254.48909
## [966,] 480.04127 489.49350
## [967,] 473.53696 474.50037
## [968,] 408.80494 404.26597
## [969,] 325.20613 310.19337
## [970,] 363.23936 358.88354
## [971,] 475.36396 476.39160
## [972,] 534.26993 523.53500
## [973,] 258.00655 254.51720
## [974,] 611.25360 607.88348
## [975,] 246.22977 261.03544
## [976,] 632.07160 620.20054
## [977,] 318.81870 314.73706
## [978,] 615.59372 625.77262
## [979,] 254.48377 250.89699
## [980,] 536.44180 544.39523
## [981,] 575.19456 589.50623
## [982,] 474.20633 475.20127
## [983,] 503.54784 494.97040
## [984,] 495.24961 486.43797
## [985,] 253.25059 249.62792
## [986,] 248.56605 244.81418
## [987,] 246.10755 242.28353
## [988,] 595.07998 612.96157
## [989,] 310.10493 323.74927
## [990,] 547.82392 550.87435
## [991,] 191.65082 189.28641
## [992,] 166.94484 163.89524
## [993,] 163.38584 178.87059
## [994,] 305.10729 308.16001
## [995,] 901.32759 903.57206
## [996,] 316.88299 301.58288
## [997,] 117.47896 126.46059
## [998,] 372.52223 368.42177
## [999,] 253.25712 249.63483
## [1000,] 382.84643 379.83353
## [1001,] 115.74099 114.23539
## [1002,] 618.51418 615.34455
## [1003,] 553.67957 546.41204
## [1004,] 613.28817 604.73378
## [1005,] 447.78055 418.78616
## [1006,] 515.55413 504.32972
## [1007,] 390.61973 393.08069
## [1008,] 609.52894 606.10174
## [1009,] 463.62966 464.32981
## [1010,] 261.33535 260.90264
## [1011,] 412.66591 414.91732
## [1012,] 124.56746 115.08807
## [1013,] 316.95111 301.71211
## [1014,] 216.34556 214.66801
## [1015,] 198.76694 196.60004
## [1016,] 569.61941 565.07484
## [1017,] 253.27018 249.64865
## [1018,] 578.34102 586.65586
## [1019,] 606.98888 622.15603
## [1020,] 189.29530 186.86546
## [1021,] 189.29530 186.86546
## [1022,] 197.51314 195.31166
## [1023,] 222.66584 218.19617
## [1024,] 197.51314 195.31166
## [1025,] 211.70965 209.90213
## [1026,] 510.23939 506.99550
## [1027,] 189.55581 216.12131
## [1028,] 163.40246 160.25439
## [1029,] 534.21381 536.87933
## [1030,] 393.71154 395.43684
## [1031,] 632.31591 639.17749
## [1032,] 258.03993 254.55235
## [1033,] 553.68105 551.67533
## [1034,] 245.71443 250.08340
## [1035,] 390.23240 391.86011
## [1036,] 390.23534 391.86309
## [1037,] 376.34408 367.98925
## [1038,] 421.42135 415.70414
## [1039,] 330.90825 333.86014
## [1040,] 253.25712 249.63483
## [1041,] 283.99686 267.89384
## [1042,] 520.09975 508.96287
## [1043,] 409.09315 411.24527
## [1044,] 192.82037 190.48843
## [1045,] 800.85361 789.71495
## [1046,] 235.30794 234.15495
## [1047,] 220.99747 206.08532
## [1048,] 258.01323 273.13589
## [1049,] 171.59957 168.67794
## [1050,] 247.39794 243.61401
## [1051,] 192.82795 190.49623
## [1052,] 258.06663 254.58046
## [1053,] 296.99719 299.82519
## [1054,] 282.88680 279.26079
## [1055,] 159.81408 156.56504
## [1056,] 186.93430 184.43886
## [1057,] 237.99431 233.95047
## [1058,] 327.89827 336.88461
## [1059,] 339.74523 353.49506
## [1060,] 298.17761 301.03847
## [1061,] 295.73602 279.91935
## [1062,] 388.67896 379.80486
## [1063,] 154.00252 169.28691
## [1064,] 154.00619 169.29463
## [1065,] 189.39060 186.96386
## [1066,] 50.75894 79.17198
## [1067,] 322.01074 330.83188
## [1068,] 474.25067 475.24572
## [1069,] 189.39060 186.96386
## [1070,] 570.24566 572.48541
## [1071,] 457.67962 471.66195
## [1072,] 499.08328 500.76721
## [1073,] 530.24354 528.43393
## [1074,] 345.31334 348.66446
## [1075,] 345.31334 348.66446
## [1076,] 177.51986 193.36633
## [1077,] 427.92238 430.59796
## [1078,] 408.41312 421.06699
## [1079,] 400.76081 402.68211
## [1080,] 248.55960 244.80732
## [1081,] 424.95381 419.33452
## [1082,] 197.49289 195.29090
## [1083,] 397.23890 399.06226
## [1084,] 182.21709 198.16395
## [1085,] 400.80595 384.16761
## [1086,] 228.57865 242.93333
## [1087,] 278.70294 283.98604
## [1088,] 178.75226 176.03050
## [1089,] 209.41350 207.54151
## [1090,] 290.95261 288.37842
## [1091,] 490.47357 491.92191
## [1092,] 233.14632 247.49389
## [1093,] 421.92815 424.43666
## [1094,] 421.92815 424.43666
## [1095,] 305.16883 308.22372
## [1096,] 136.43308 127.29504
## [1097,] 123.41104 132.56402
## [1098,] 388.81140 385.16309
## [1099,] 346.78532 341.97499
## [1100,] 493.35358 494.87452
## [1101,] 253.27671 249.65556
## [1102,] 293.58191 306.76730
## [1103,] 890.40001 895.52604
## [1104,] 417.24019 439.03349
## [1105,] 417.24019 420.45065
## [1106,] 299.61476 312.99651
## [1107,] 163.39138 178.88312
## [1108,] 458.96143 459.53056
## [1109,] 486.78370 499.40388
## [1110,] 536.24588 538.97193
## [1111,] 313.90715 308.99238
## [1112,] 654.58862 637.47427
## [1113,] 113.43478 111.86373
## [1114,] 559.82404 549.70824
## [1115,] 553.91169 543.62541
## [1116,] 299.40448 281.41678
## [1117,] 434.64917 438.33635
## [1118,] 617.91472 605.64368
## [1119,] 334.66004 319.91984
## [1120,] 429.05840 413.14108
## [1121,] 363.39101 359.04184
## [1122,] 451.45047 436.12836
## [1123,] 165.76080 162.67822
## [1124,] 239.88206 244.09099
## [1125,] 338.31485 323.75805
## [1126,] 447.86904 451.09717
## [1127,] 577.63979 573.32171
## [1128,] 539.92015 547.96120
## [1129,] 627.32781 634.04391
## [1130,] 426.50101 429.13772
## [1131,] 246.19760 242.37952
## [1132,] 558.52959 551.40625
## [1133,] 500.10325 501.81873
## [1134,] 661.47566 669.13420
## [1135,] 299.21438 277.39694
## [1136,] 252.19992 267.24261
## [1137,] 236.91241 232.84304
## [1138,] 259.89128 245.94118
## [1139,] 205.75920 203.78702
## [1140,] 293.62679 271.41827
## [1141,] 242.69939 257.41508
## [1142,] 394.87799 396.63586
## [1143,] 409.12657 411.27945
## [1144,] 451.45047 436.12836
## [1145,] 553.21093 533.18807
## [1146,] 346.70118 340.45226
## [1147,] 394.20862 378.20999
## [1148,] 356.20108 351.65111
## [1149,] 172.80676 169.91920
## [1150,] 446.96831 436.82296
## [1151,] 320.55626 324.03984
## [1152,] 240.27252 236.28843
## [1153,] 345.42553 340.57276
## [1154,] 222.18526 220.67108
## [1155,] 348.15373 356.89786
## [1156,] 297.76611 292.40705
## [1157,] 941.05430 964.96289
## [1158,] 584.50849 593.73996
## [1159,] 457.51765 461.01870
## [1160,] 341.87792 336.92621
## [1161,] 254.46409 250.87619
## [1162,] 276.82914 273.86227
## [1163,] 1139.34771 1148.60022
## [1164,] 417.38895 410.14770
## [1165,] 257.97986 254.48909
## [1166,] 177.53018 174.77390
## [1167,] 165.78038 162.69879
## [1168,] 161.08828 157.87707
## [1169,] 171.66783 168.74942
## [1170,] 173.97725 171.12204
## [1171,] 359.64084 355.18427
## [1172,] 316.95111 301.71211
## [1173,] 445.66481 454.10957
## [1174,] 305.19190 308.24761
## [1175,] 392.40300 394.09405
## [1176,] 261.50799 258.11512
## [1177,] 558.49183 566.99384
## [1178,] 442.87441 463.94301
## [1179,] 232.17517 227.97351
## [1180,] 411.58703 404.19104
## [1181,] 989.16035 969.46846
## [1182,] 136.42062 127.28014
## [1183,] 322.75119 326.29261
## [1184,] 459.64609 458.77462
## [1185,] 399.60366 420.27785
## [1186,] 513.87575 539.62588
## [1187,] 329.13943 324.64753
## [1188,] 683.29943 681.92200
## [1189,] 230.92463 245.33316
## [1190,] 229.74618 225.47355
## [1191,] 245.14516 241.30279
## [1192,] 175.07516 172.24908
## [1193,] 392.51700 394.20939
## [1194,] 254.47721 250.89006
## [1195,] 382.97410 403.00161
## [1196,] 308.74278 311.89734
## [1197,] 319.74672 314.99392
## [1198,] 401.37441 395.09998
## [1199,] 530.55031 519.66621
## [1200,] 299.23160 302.12143
## [1201,] 683.89618 666.75648
## [1202,] 406.71634 400.57885
## [1203,] 406.71634 400.57885
## [1204,] 492.78165 502.54293
## [1205,] 465.71604 450.87385
## [1206,] 451.48354 454.81371
## [1207,] 451.45047 454.77901
## [1208,] 345.31334 348.66446
## [1209,] 304.07713 301.03866
## [1210,] 432.71590 422.14574
## [1211,] 617.71489 624.16222
## [1212,] 533.95398 541.82327
## [1213,] 193.28363 201.41764
## [1214,] 390.09508 383.51976
## [1215,] 617.65179 624.09620
## [1216,] 583.91264 616.34568
## [1217,] 544.61066 566.00792
## [1218,] 449.64901 463.20486
## [1219,] 168.05499 165.03469
## [1220,] 259.16047 255.70257
## [1221,] 246.26836 242.45494
## [1222,] 220.00240 218.42432
## [1223,] 192.89073 190.56085
## [1224,] 554.36233 565.89850
## [1225,] 305.06114 308.11223
## [1226,] 255.75043 252.20127
## [1227,] 304.01087 288.44285
## [1228,] 537.72010 545.72143
## [1229,] 475.37720 476.40487
## [1230,] 963.02934 972.46918
## [1231,] 413.61534 416.72600
## [1232,] 320.42689 305.23033
## [1233,] 358.33261 353.83729
## [1234,] 575.23895 589.56020
## [1235,] 687.66151 690.81852
## [1236,] 347.53968 350.95337
## [1237,] 263.62168 268.49462
## [1238,] 301.67229 286.05698
## [1239,] 442.56415 442.67446
## [1240,] 484.95533 486.24574
## [1241,] 234.87878 249.41003
## [1242,] 238.02032 233.97838
## [1243,] 475.47648 476.50443
## [1244,] 287.47743 271.42540
## [1245,] 404.30892 406.32858
## [1246,] 862.68308 852.71042
## [1247,] 613.56360 623.74007
## [1248,] 589.64999 599.10187
## [1249,] 235.65170 231.54355
## [1250,] 493.05360 494.57265
## [1251,] 523.76370 531.39891
## [1252,] 403.22275 386.72651
## [1253,] 300.46004 303.38415
## [1254,] 324.05172 326.81022
## [1255,] 531.70888 539.53048
## [1256,] 312.30750 315.56155
## [1257,] 293.42660 296.15526
## [1258,] 293.41509 296.14345
## [1259,] 385.67068 381.93541
## [1260,] 252.18691 248.53832
## [1261,] 351.53921 346.86144
## [1262,] 404.42086 406.44267
## [1263,] 294.41242 291.10801
## [1264,] 611.51257 605.85541
## [1265,] 398.55129 401.23877
## [1266,] 495.22453 496.80785
## [1267,] 174.01368 171.16013
## [1268,] 318.37828 316.55950
## [1269,] 461.12749 451.38469
## [1270,] 647.37745 639.69580
## [1271,] 769.51208 776.44897
## [1272,] 406.76128 427.80660
## [1273,] 281.61629 278.78250
## [1274,] 279.21928 262.93091
## [1275,] 249.50638 245.77890
## [1276,] 163.39692 178.89565
## [1277,] 391.48123 393.14249
## [1278,] 354.57648 359.00215
## [1279,] 471.71323 475.61059
## [1280,] 531.75822 520.91496
## [1281,] 611.03991 602.43695
## [1282,] 359.27613 354.80275
## [1283,] 293.43153 296.16032
## [1284,] 508.53724 510.48393
## [1285,] 485.05852 486.34940
## [1286,] 424.31239 408.22695
## [1287,] 518.64661 510.44283
## [1288,] 255.63833 252.08292
## [1289,] 229.82064 225.55386
## [1290,] 560.68504 574.73284
## [1291,] 515.49782 504.25857
## [1292,] 477.67547 478.76847
## [1293,] 996.87797 1015.63434
## [1294,] 538.80782 528.15483
## [1295,] 665.16745 659.47855
## [1296,] 185.74333 183.21471
## [1297,] 164.55584 180.06084
## [1298,] 202.04711 199.13596
## [1299,] 263.94525 260.62164
## [1300,] 394.87799 396.63586
## [1301,] 752.90607 749.68187
## [1302,] 238.07885 234.04119
## [1303,] 640.37040 647.44937
## [1304,] 690.28120 689.08775
## [1305,] 406.69433 408.78003
## [1306,] 281.51591 278.67931
## [1307,] 334.99534 329.85799
## [1308,] 262.70908 259.35006
## [1309,] 186.97934 184.48545
## [1310,] 630.48570 627.64752
## [1311,] 533.64688 536.30370
## [1312,] 577.66222 568.08152
## [1313,] 601.86174 611.52244
## [1314,] 262.70908 259.35006
## [1315,] 537.69628 527.02921
## [1316,] 440.24763 440.29238
## [1317,] 417.95531 412.14312
## [1318,] 299.56877 312.93905
## [1319,] 680.80747 688.95986
## [1320,] 477.59892 478.69167
## [1321,] 363.43261 365.13734
## [1322,] 181.10865 197.12536
## [1323,] 238.05284 234.01327
## [1324,] 239.97861 244.19219
## [1325,] 306.35304 309.44088
## [1326,] 518.71404 510.52207
## [1327,] 304.01860 288.45769
## [1328,] 238.06584 234.02723
## [1329,] 924.30918 940.87362
## [1330,] 225.77087 210.90985
## [1331,] 295.76834 298.56211
## [1332,] 62.66847 54.40989
## [1333,] 455.23599 463.95495
## [1334,] 242.41729 246.70040
## [1335,] 357.21191 360.89475
## [1336,] 471.86491 472.79437
## [1337,] 396.07208 379.27815
## [1338,] 726.71498 721.87108
## [1339,] 403.24177 395.60092
## [1340,] 495.18157 496.76459
## [1341,] 418.38520 402.09527
## [1342,] 656.44805 676.71127
## [1343,] 184.57838 182.01751
## [1344,] 326.68618 316.93447
## [1345,] 322.89669 345.30573
## [1346,] 263.96609 260.64345
## [1347,] 573.44903 554.69673
## [1348,] 463.69779 464.39802
## [1349,] 237.71180 241.86413
## [1350,] 169.25323 166.26664
## [1351,] 606.98888 622.15603
## [1352,] 406.69433 408.78003
## [1353,] 378.47051 361.25519
## [1354,] 216.51259 214.83715
## [1355,] 342.08809 337.14808
## [1356,] 722.17673 718.09250
## [1357,] 571.76293 567.27999
## [1358,] 557.85138 547.77140
## [1359,] 293.40688 277.55050
## [1360,] 306.34691 290.82361
## [1361,] 200.98268 198.87805
## [1362,] 189.87311 187.45957
## [1363,] 595.38188 586.30319
## [1364,] 477.83952 478.93304
## [1365,] 765.95841 781.97005
## [1366,] 515.40344 517.54476
## [1367,] 287.58964 271.63566
## [1368,] 181.03123 178.37169
## [1369,] 488.52849 495.90874
## [1370,] 342.92231 346.20686
## [1371,] 192.86367 171.79636
## [1372,] 571.76293 567.27999
## [1373,] 322.93498 326.48517
## [1374,] 344.48489 339.61237
## [1375,] 294.57131 278.73474
## [1376,] 311.86267 290.13934
## [1377,] 377.46695 379.56492
## [1378,] 471.82010 472.74946
## [1379,] 347.59268 333.17628
## [1380,] 203.44799 219.99336
## [1381,] 520.92115 518.01848
## [1382,] 253.28324 249.66247
## [1383,] 306.99614 310.10169
## [1384,] 177.54051 174.78467
## [1385,] 425.58289 409.65195
## [1386,] 894.39831 895.42367
## [1387,] 305.16114 289.59914
## [1388,] 311.06718 295.67720
## [1389,] 430.25627 432.99646
## [1390,] 239.26616 235.26175
## [1391,] 434.99214 419.28299
## [1392,] 191.71525 189.35279
## [1393,] 281.65812 278.82550
## [1394,] 246.24906 242.43437
## [1395,] 236.81579 232.73925
## [1396,] 175.22247 172.40297
## [1397,] 423.68061 421.01169
## [1398,] 388.93915 385.29432
## [1399,] 103.93776 120.71040
## [1400,] 343.29035 357.14373
## [1401,] 463.59677 445.66063
## [1402,] 412.48070 396.01719
## [1403,] 1175.37175 1166.40598
## [1404,] 165.68252 162.59595
## [1405,] 269.88049 266.72189
## [1406,] 620.04842 630.31076
## [1407,] 196.42786 194.19604
## [1408,] 451.60650 441.57729
## [1409,] 235.73041 250.35195
## [1410,] 168.09350 165.07512
## [1411,] 183.38739 180.79331
## [1412,] 609.48154 618.76214
## [1413,] 184.59396 182.03366
## [1414,] 263.56718 249.78651
## [1415,] 376.34408 367.98925
## [1416,] 310.75745 313.15154
## [1417,] 293.74574 291.24521
## [1418,] 282.70839 279.07816
## [1419,] 430.26755 433.00818
## [1420,] 298.05026 300.90732
## [1421,] 816.78687 814.64898
## [1422,] 269.69323 265.70106
## [1423,] 781.15816 734.38073
## [1424,] 232.20053 228.00083
## [1425,] 237.91344 215.36750
## [1426,] 323.83676 326.59217
## [1427,] 471.84251 472.77191
## [1428,] 489.33133 493.71842
## [1429,] 447.26755 437.18858
## [1430,] 321.77761 325.29600
## [1431,] 405.93720 408.00080
## [1432,] 198.76125 196.59421
## [1433,] 584.50849 593.73996
## [1434,] 595.38188 586.30319
## [1435,] 575.27623 565.62294
## [1436,] 184.56799 182.00673
## [1437,] 302.77550 305.76371
## [1438,] 248.54025 244.78675
## [1439,] 184.57319 182.01212
## [1440,] 302.76153 305.74926
## [1441,] 1673.12068 1725.81782
## [1442,] 184.56799 200.56851
## [1443,] 259.21839 254.93478
## [1444,] 184.59396 182.03366
## [1445,] 306.25804 309.34243
## [1446,] 233.16102 228.98936
## [1447,] 436.04223 447.22880
## [1448,] 253.99798 253.36855
## [1449,] 333.81112 328.64070
## [1450,] 198.69868 196.53014
## [1451,] 532.84326 540.69058
## [1452,] 381.45123 362.49069
## [1453,] 695.06103 708.83424
## [1454,] 495.20800 486.38719
## [1455,] 376.77929 381.00586
## [1456,] 347.59268 351.82654
## [1457,] 683.12799 670.53035
## [1458,] 420.99477 423.47839
## [1459,] 293.74378 310.13871
## [1460,] 344.65817 329.37578
## [1461,] 166.93622 163.88618
## [1462,] 794.55979 805.52559
## [1463,] 542.10038 550.17648
## [1464,] 251.05109 247.37249
## [1465,] 670.88592 676.53404
## [1466,] 265.07028 261.77693
## [1467,] 247.99814 252.42833
## [1468,] 261.10543 265.90287
## [1469,] 223.53320 208.67395
## [1470,] 394.91771 399.65600
## [1471,] 289.87570 287.27090
## [1472,] 522.37114 511.27696
## [1473,] 621.91154 609.81701
## [1474,] 477.52790 463.00181
## [1475,] 404.45818 388.06875
## [1476,] 359.67856 355.22373
## [1477,] 400.85754 402.78045
## [1478,] 597.71681 610.59809
## [1479,] 364.56309 364.02042
## [1480,] 189.26353 167.94565
## [1481,] 536.41784 544.36756
## [1482,] 453.94893 457.34996
## [1483,] 273.37248 270.31015
## [1484,] 70.51174 99.12232
## [1485,] 447.89889 459.42785
## [1486,] 251.73519 256.27443
## [1487,] 251.07054 228.89856
## [1488,] 463.84678 457.43845
## [1489,] 315.75763 319.10639
## [1490,] 432.66954 416.94314
## [1491,] 255.22809 241.17471
## [1492,] 349.88165 335.48505
## [1493,] 319.39944 332.47569
## [1494,] 315.75205 313.03878
## [1495,] 241.26272 240.27351
## [1496,] 471.62816 478.50561
## [1497,] 553.33944 548.33680
## [1498,] 389.37192 373.19390
## [1499,] 178.69550 175.97137
## [1500,] 446.65739 437.22045
## [1501,] 336.20053 331.09743
## [1502,] 153.99397 150.58523
## [1503,] 399.39515 404.25505
## [1504,] 222.32328 217.84974
## [1505,] 430.31268 414.52558
## [1506,] 445.05812 437.75682
## [1507,] 480.77318 471.49589
## [1508,] 430.27319 433.01404
## [1509,] 448.05185 437.91869
## [1510,] 249.51952 235.40569
## [1511,] 523.37048 512.26047
## [1512,] 222.57999 218.10333
## [1513,] 430.27319 414.43452
## [1514,] 489.22139 488.35802
## [1515,] 238.51958 237.46372
## [1516,] 722.12289 736.60513
## [1517,] 496.38482 498.00072
## [1518,] 690.95939 685.99548
## [1519,] 690.59967 685.62714
## [1520,] 733.40746 739.31543
## [1521,] 501.19837 502.94593
## [1522,] 434.10072 428.73214
## [1523,] 424.44726 418.80675
## [1524,] 495.18157 496.76459
## [1525,] 654.64331 652.46616
## [1526,] 953.46793 994.99979
## [1527,] 916.19229 930.82669
## [1528,] 837.93854 837.24782
## [1529,] 597.37284 606.94623
## [1530,] 794.07838 805.00447
## [1531,] 334.99271 329.85520
## [1532,] 473.87379 474.86787
## [1533,] 239.25968 235.25480
## [1534,] 306.33466 309.42182
## [1535,] 543.65845 541.39398
## [1536,] 421.25503 415.51278
## [1537,] 739.81120 745.90635
## [1538,] 252.13488 248.48319
## [1539,] 194.04976 191.75201
## [1540,] 507.38369 504.06820
## [1541,] 507.38369 504.06820
## [1542,] 311.10508 295.74978
## [1543,] 424.49165 408.64684
## [1544,] 346.79798 341.98833
## [1545,] 324.41482 318.98431
## [1546,] 574.13586 569.71933
## [1547,] 414.20628 403.19226
## [1548,] 311.21121 314.43574
## [1549,] 150.97532 150.45407
## [1550,] 281.75851 278.92869
## [1551,] 253.30283 249.68321
## [1552,] 484.12986 474.90907
## [1553,] 438.51856 441.48843
## [1554,] 424.25637 408.09573
## [1555,] 363.27727 358.92312
## [1556,] 267.54600 264.32313
## [1557,] 211.54016 196.24053
## [1558,] 835.76448 849.98732
## [1559,] 239.98933 225.56094
## [1560,] 262.81234 259.45824
## [1561,] 172.79631 169.90826
## [1562,] 336.12195 331.01428
## [1563,] 481.97620 458.27792
## [1564,] 320.52582 305.41639
## [1565,] 315.87410 300.69490
## [1566,] 323.02840 308.10805
## [1567,] 613.62706 628.86080
## [1568,] 320.54104 324.02392
## [1569,] 672.21255 679.42398
## [1570,] 208.14351 206.23733
## [1571,] 719.80168 734.22931
## [1572,] 722.28442 718.20212
## [1573,] 638.07184 635.45838
## [1574,] 699.58942 694.87187
## [1575,] 320.52582 305.41639
## [1576,] 346.42887 350.63078
## [1577,] 328.79023 313.91237
## [1578,] 554.04442 557.26493
## [1579,] 256.95839 272.17327
## [1580,] 251.03165 247.35186
## [1581,] 404.48928 388.14011
## [1582,] 444.25992 446.55401
## [1583,] 463.76827 464.46859
## [1584,] 439.11198 439.12395
## [1585,] 304.09086 298.90179
## [1586,] 183.43401 180.84169
## [1587,] 183.43401 180.84169
## [1588,] 175.17890 172.35745
## [1589,] 306.42659 290.97666
## [1590,] 306.42659 290.97666
## [1591,] 110.35359 119.12908
## [1592,] 210.49012 208.64926
## [1593,] 363.28991 358.93631
## [1594,] 279.27048 276.37167
## [1595,] 320.44211 323.92040
## [1596,] 287.66690 285.00015
## [1597,] 465.99053 466.75621
## [1598,] 294.84098 292.37138
## [1599,] 404.45196 406.47436
## [1600,] 278.37166 309.98975
## [1601,] 722.25211 736.76435
## [1602,] 394.98858 396.74789
## [1603,] 228.29300 232.18331
## [1604,] 442.42364 442.53396
## [1605,] 630.50917 627.67123
## [1606,] 210.52283 208.68246
## [1607,] 322.92732 307.91926
## [1608,] 287.66690 285.00015
## [1609,] 105.90871 135.67480
## [1610,] 273.16754 270.09783
## [1611,] 577.23812 607.77631
## [1612,] 404.48306 388.12584
## [1613,] 365.47813 361.18252
## [1614,] 411.48019 413.69860
## [1615,] 222.40995 226.13659
## [1616,] 133.49717 132.48396
## [1617,] 191.72062 189.35832
## [1618,] 271.08288 267.95780
## [1619,] 108.80865 125.78649
## [1620,] 346.15826 350.34475
## [1621,] 466.19882 448.52558
## [1622,] 366.57030 370.51527
## [1623,] 472.69462 492.06808
## [1624,] 541.91423 531.24032
## [1625,] 161.08036 157.86873
## [1626,] 103.93776 120.71040
## [1627,] 485.20901 486.50056
## [1628,] 411.47432 413.69259
## [1629,] 541.15017 549.23180
## [1630,] 540.03777 548.09778
## [1631,] 176.40110 173.61427
## [1632,] 104.05706 102.22370
## [1633,] 99.44238 97.47836
## [1634,] 729.22466 720.49849
## [1635,] 203.40612 219.89524
## [1636,] 299.23160 302.12143
## [1637,] 824.39203 843.15441
## [1638,] 528.13302 535.85239
## [1639,] 575.24450 570.85959
## [1640,] 92.25994 90.09816
## [1641,] 257.67766 243.73819
## [1642,] 652.48110 665.23269
## [1643,] 569.27470 564.72290
## [1644,] 572.94945 587.22102
## [1645,] 568.14491 582.26981
## [1646,] 316.99652 320.38065
## [1647,] 363.40364 359.05503
## [1648,] 155.17691 170.48890
## [1649,] 234.22820 219.71259
## [1650,] 369.17984 364.98898
## [1651,] 568.31852 582.47838
## [1652,] 222.67014 218.20081
## [1653,] 166.86398 182.36670
## [1654,] 241.00014 245.23874
## [1655,] 228.57183 242.92052
## [1656,] 228.55818 242.89490
## [1657,] 234.45085 230.30832
## [1658,] 483.49939 493.07423
## [1659,] 181.05188 178.39316
## [1660,] 227.40445 241.73096
## [1661,] 217.54909 215.06714
## [1662,] 424.20035 426.77125
## [1663,] 271.98899 268.88636
## [1664,] 175.13222 190.87353
## [1665,] 227.39757 241.71812
## [1666,] 226.20258 240.47715
## [1667,] 227.42510 241.76949
## [1668,] 227.41409 241.74894
## [1669,] 370.33737 366.17824
## [1670,] 453.94893 457.34996
## [1671,] 591.17883 600.52413
## [1672,] 239.21431 235.20616
## [1673,] 173.92521 189.59607
## [1674,] 113.59360 112.02323
## [1675,] 119.39288 117.98614
## [1676,] 239.16895 253.79455
## [1677,] 260.49138 275.79898
## [1678,] 475.27045 460.75262
## [1679,] 239.21561 235.20755
## [1680,] 695.72551 709.43031
## [1681,] 241.14990 245.39585
## [1682,] 596.61899 601.03968
## [1683,] 226.87446 225.49125
## [1684,] 240.10733 244.32712
## [1685,] 536.46577 544.42290
## [1686,] 54.44250 64.62943
## [1687,] 109.89071 108.22116
## [1688,] 256.32103 270.54404
## [1689,] 454.64505 434.37600
## [1690,] 243.93194 240.05461
## [1691,] 86.35041 78.75992
## [1692,] 260.41555 256.99425
## [1693,] 108.74090 107.03866
## [1694,] 252.21292 248.56589
## [1695,] 324.13991 309.19220
## [1696,] 553.06664 542.83764
## [1697,] 203.56164 201.52714
## [1698,] 236.87063 232.79816
## [1699,] 269.92441 266.76755
## [1700,] 501.32501 489.67877
## [1701,] 749.15520 763.79993
## [1702,] 109.83995 108.17015
## [1703,] 173.92521 189.59607
## [1704,] 389.08745 390.68274
## [1705,] 334.50776 318.93704
## [1706,] 134.42823 133.44743
## [1707,] 101.72379 118.50149
## [1708,] 104.05706 102.22370
## [1709,] 329.93276 332.85531
## [1710,] 258.08265 254.59733
## [1711,] 290.00001 274.15958
## [1712,] 62.68398 54.42697
## [1713,] 216.84995 250.01399
## [1714,] 156.30510 171.59149
## [1715,] 175.13740 172.31410
## [1716,] 301.59421 304.54962
## [1717,] 164.55036 180.04833
## [1718,] 288.59244 285.12575
## [1719,] 292.40767 280.78625
## [1720,] 529.83183 545.80134
## [1721,] 293.42331 296.15189
## [1722,] 261.53529 258.14376
## [1723,] 239.25968 235.25480
## [1724,] 177.55084 174.79544
## [1725,] 272.71138 277.82408
## [1726,] 217.48965 215.84450
## [1727,] 414.87642 417.18948
## [1728,] 370.05427 384.50086
## [1729,] 163.43015 160.28353
## [1730,] 269.89513 266.73711
## [1731,] 181.14478 178.48977
## [1732,] 100.50574 98.57380
## [1733,] 240.10733 244.32712
## [1734,] 240.01079 225.59455
## [1735,] 180.51933 167.32025
## [1736,] 106.37350 123.24842
## [1737,] 306.36431 298.99522
## [1738,] 235.26147 220.69570
## [1739,] 161.47797 187.52336
## [1740,] 163.81059 189.89185
## [1741,] 491.47645 467.98041
## [1742,] 161.10865 157.89852
## [1743,] 405.65307 407.70875
## [1744,] 166.96641 163.91789
## [1745,] 221.24064 243.85167
## [1746,] 199.91886 197.78404
## [1747,] 202.27958 200.21028
## [1748,] 183.47545 180.88469
## [1749,] 245.08729 259.89699
## [1750,] 258.00067 253.68304
## [1751,] 186.91336 202.95981
## [1752,] 538.66682 552.76161
## [1753,] 334.99271 348.59419
## [1754,] 697.93415 694.60553
## [1755,] 497.41559 499.06311
## [1756,] 92.27049 108.77968
## [1757,] 184.59396 182.03366
## [1758,] 104.09115 102.25798
## [1759,] 678.27791 684.14815
## [1760,] 177.60972 156.31717
## [1761,] 126.55840 154.58027
## [1762,] 224.71472 228.50507
## [1763,] 265.01810 260.89579
## [1764,] 300.86445 294.77756
## [1765,] 181.08801 178.43073
## [1766,] 158.70442 155.42637
## [1767,] 322.96561 307.99077
## [1768,] 172.83288 169.94654
## [1769,] 284.04150 267.97666
## [1770,] 181.08801 178.43073
## [1771,] 224.70324 228.49318
## [1772,] 178.67486 194.51883
## [1773,] 276.97131 274.00904
## [1774,] 184.59396 182.03366
## [1775,] 320.55626 305.47364
## [1776,] 169.27448 147.54816
## [1777,] 253.25712 249.63483
## [1778,] 253.52341 267.89376
## [1779,] 184.59396 182.03366
## [1780,] 340.60470 344.64648
## [1781,] 578.39438 581.46370
## [1782,] 203.48986 201.45392
## [1783,] 617.18843 620.73948
## [1784,] 105.35984 103.55999
## [1785,] 181.08801 178.43073
## [1786,] 136.96914 136.05425
## [1787,] 224.66881 209.81819
## [1788,] 177.54568 174.79005
## [1789,] 385.71394 377.61258
## [1790,] 240.01079 225.59455
## [1791,] 385.62202 368.70157
## [1792,] 181.14478 178.48977
## [1793,] 228.61959 224.31837
## [1794,] 267.15839 272.12982
## [1795,] 267.15839 272.12982
## [1796,] 165.76950 162.68736
## [1797,] 222.45041 202.36669
## [1798,] 361.78380 347.04043
## [1799,] 168.16626 165.15148
## [1800,] 228.52407 224.21528
## [1801,] 51.00534 61.11013
## [1802,] 330.34733 325.08303
## [1803,] 174.03137 171.17863
## [1804,] 244.82354 230.59181
## [1805,] 448.10611 456.63004
## [1806,] 478.28021 479.40401
## [1807,] 225.92495 224.51057
## [1808,] 102.94164 119.77051
## [1809,] 181.09833 178.44146
## [1810,] 107.25198 124.01087
## [1811,] 661.94085 626.11985
## [1812,] 153.99397 169.26889
## [1813,] 116.30829 106.59865
## [1814,] 265.02833 260.90632
## [1815,] 217.68388 216.04084
## [1816,] 240.40823 236.43382
## [1817,] 228.59912 224.29628
## [1818,] 312.36351 297.11284
## [1819,] 166.96102 163.91223
## [1820,] 278.09522 261.81864
## [1821,] 216.76953 230.78621
## [1822,] 619.96800 629.51749
## [1823,] 169.27448 166.28893
## [1824,] 318.27195 321.69320
## [1825,] 368.04684 369.05286
## [1826,] 264.02861 260.70886
## [1827,] 192.85284 190.52186
## [1828,] 177.50436 174.74697
## [1829,] 453.88091 462.55169
## [1830,] 361.97080 357.57835
## [1831,] 619.94545 601.40042
## [1832,] 669.40706 665.29509
## [1833,] 365.83368 361.55313
## [1834,] 232.97441 218.38352
## [1835,] 324.17834 327.76449
## [1836,] 324.17988 309.26658
## [1837,] 181.10349 178.44683
## [1838,] 254.47065 250.88312
## [1839,] 244.79165 249.14124
## [1840,] 244.79165 230.54200
## [1841,] 242.43864 246.72281
## [1842,] 60.39839 52.08288
## [1843,] 175.22039 172.40080
## [1844,] 234.44426 248.93324
## [1845,] 376.27615 377.51172
## [1846,] 376.27615 377.51172
## [1847,] 453.91167 443.93695
## [1848,] 179.86597 177.17423
## [1849,] 294.34775 272.27048
## [1850,] 179.85049 177.15812
## [1851,] 287.52059 308.92812
## [1852,] 360.77309 356.34709
## [1853,] 103.98889 102.15514
## [1854,] 198.73850 196.57091
## [1855,] 124.16083 122.88545
## [1856,] 460.00704 468.88619
## [1857,] 514.28781 524.72155
## [1858,] 243.97697 240.10271
## [1859,] 227.45951 241.83370
## [1860,] 483.97393 485.23238resultados=data.frame(vivienda_multi$precio_millon,prediciones)
names(resultados)=c("precio_real","precio_msimple","precio_mmulti")
resultados## precio_real precio_msimple precio_mmulti
## 1 310 249.13071 245.39366
## 2 240 186.93430 184.43886
## 3 690 594.92434 591.09437
## 4 200 235.69106 231.58585
## 5 290 300.41291 303.33553
## 6 550 537.69628 527.02921
## 7 300 341.98044 337.03444
## 8 580 589.55171 604.29869
## 9 226 186.94897 184.45403
## 10 280 287.43427 289.99687
## 11 240 246.84709 243.04976
## 12 165 163.39692 160.24857
## 13 250 194.00609 191.70710
## 14 595 549.41785 539.06009
## 15 510 510.72066 512.73120
## 16 225 184.58877 182.02828
## 17 255 183.37704 180.78256
## 18 175 162.20483 177.65532
## 19 1200 582.11568 586.14087
## 20 550 588.87170 589.25977
## 21 180 226.27202 221.90619
## 22 275 209.31692 207.44340
## 23 290 333.32556 336.34405
## 24 192 166.91034 182.47395
## 25 210 186.96572 184.47137
## 26 220 181.05188 178.39316
## 27 595 569.30343 564.75222
## 28 315 395.61418 389.18264
## 29 185 250.99619 265.24486
## 30 210 232.13513 227.93038
## 31 270 416.22882 400.14743
## 32 280 188.07270 185.60866
## 33 390 458.98572 459.55487
## 34 370 379.51192 380.84415
## 35 290 311.04444 314.26235
## 36 190 224.69176 228.48128
## 37 200 263.67618 249.95091
## 38 240 210.54246 208.70239
## 39 360 309.75684 331.49667
## 40 300 337.25174 350.87893
## 41 265 228.51724 224.20792
## 42 210 256.55956 261.23624
## 43 190 164.55036 161.43342
## 44 360 365.47813 361.18252
## 45 270 396.18106 397.97335
## 46 236 313.48874 298.22102
## 47 165 163.39692 160.24857
## 48 125 125.77804 116.33826
## 49 182 168.10206 165.08410
## 50 160 163.40246 178.90818
## 51 300 320.48016 305.33052
## 52 380 403.11579 405.10247
## 53 170 169.29573 184.95930
## 54 225 177.50436 174.74697
## 55 78 39.22968 49.01031
## 56 300 352.21459 337.14649
## 57 385 416.09736 399.83804
## 58 260 193.99517 191.69587
## 59 210 169.25323 166.26664
## 60 195 251.86254 237.80485
## 61 136 165.79016 162.70907
## 62 270 258.03993 254.55235
## 63 250 234.44426 230.30123
## 64 242 266.17059 262.08034
## 65 360 359.56538 355.10533
## 66 220 179.87112 177.17959
## 67 200 223.88251 219.44865
## 68 130 60.34061 52.01908
## 69 225 236.83930 232.76450
## 70 228 261.48625 257.26558
## 71 150 119.35900 117.95215
## 72 138 122.20073 112.65401
## 73 320 333.23854 317.59035
## 74 260 268.47636 264.45031
## 75 220 177.50953 174.75235
## 76 283 224.94701 257.65023
## 77 314 314.74555 327.71388
## 78 128 116.31290 125.26445
## 79 350 323.79409 321.30762
## 80 226 177.50333 174.74589
## 81 280 262.75038 259.39333
## 82 145 74.47871 66.55218
## 83 355 399.60628 382.90869
## 84 165 222.75170 218.28901
## 85 180 295.86530 298.66180
## 86 280 294.65131 292.17833
## 87 250 175.11666 190.83611
## 88 235 196.38333 194.15035
## 89 415 275.53222 272.52860
## 90 240 444.53436 439.46163
## 91 225 191.67230 189.30854
## 92 215 242.36393 246.64437
## 93 190 228.61959 224.31837
## 94 140 103.28018 111.86055
## 95 270 246.22977 242.41381
## 96 200 181.07252 197.03714
## 97 145 163.41907 160.27188
## 98 135 157.52731 172.89578
## 99 240 234.45745 248.95868
## 100 285 242.21453 265.07725
## 101 165 165.75863 162.67594
## 102 180 165.74232 162.65880
## 103 165 163.39692 178.89565
## 104 185 225.08441 220.68515
## 105 180 223.91083 219.47927
## 106 200 184.61474 182.05520
## 107 230 254.38067 249.96184
## 108 235 241.55052 237.60619
## 109 235 179.85565 177.16349
## 110 242 178.66764 175.94234
## 111 234 234.46536 230.32392
## 112 215 163.34153 160.19029
## 113 245 172.75973 169.86999
## 114 225 163.33045 178.74529
## 115 240 235.63859 231.52945
## 116 160 109.85687 108.18715
## 117 213 182.23983 179.61421
## 118 227 235.65564 250.20704
## 119 153 163.41021 160.26255
## 120 230 241.53335 256.25189
## 121 209 241.58405 237.64208
## 122 230 234.47063 230.32960
## 123 222 227.39482 241.71298
## 124 235 234.46404 248.97140
## 125 235 175.13222 190.87353
## 126 190 239.24671 235.24090
## 127 235 169.22666 184.79743
## 128 230 181.04155 196.96152
## 129 380 388.94541 390.53929
## 130 158 158.68126 155.40195
## 131 215 173.97204 171.11660
## 132 150 162.23281 177.71811
## 133 220 228.57865 224.27419
## 134 195 163.36369 160.21360
## 135 230 234.47063 248.98411
## 136 216 228.58411 242.94358
## 137 225 234.47722 230.33669
## 138 400 406.63347 408.71790
## 139 230 233.28954 229.11563
## 140 240 175.12703 190.86106
## 141 250 186.92383 184.42803
## 142 175 164.56682 161.45073
## 143 215 169.24791 184.84723
## 144 150 157.50971 154.19806
## 145 185 172.82243 169.93560
## 146 235 166.86398 182.36670
## 147 225 178.99227 186.71772
## 148 230 238.01382 233.97140
## 149 300 275.71143 272.71383
## 150 288 133.07855 113.00005
## 151 310 242.16117 246.43148
## 152 360 319.20764 322.65067
## 153 390 407.37773 409.48271
## 154 220 198.76125 196.59421
## 155 290 299.23160 302.12143
## 156 197 275.77940 278.01702
## 157 300 299.21579 283.44492
## 158 215 228.58548 224.28156
## 159 210 186.96572 184.47137
## 160 250 250.97980 247.29685
## 161 163 222.75456 218.29211
## 162 354 261.46840 276.60756
## 163 250 192.82578 190.49400
## 164 250 240.35007 255.00989
## 165 380 302.40180 299.32232
## 166 380 403.11579 405.10247
## 167 340 262.66777 259.30679
## 168 380 403.24566 405.23595
## 169 410 406.62130 408.70547
## 170 390 386.56765 388.09595
## 171 156 163.40689 160.25906
## 172 150 163.41354 178.93324
## 173 162 163.40024 160.25206
## 174 145 159.87703 156.63137
## 175 315 266.24379 262.98295
## 176 151 222.77174 237.03674
## 177 150 163.41354 178.93324
## 178 120 158.72528 174.14876
## 179 150 163.41354 178.93324
## 180 390 386.56765 388.09595
## 181 120 149.28199 164.43039
## 182 132 161.07244 176.54831
## 183 140 151.61773 166.80795
## 184 150 163.41354 160.26605
## 185 295 151.42265 166.40515
## 186 300 300.39720 303.31933
## 187 148 163.41575 178.93825
## 188 240 194.01701 191.71833
## 189 168 172.84020 169.95419
## 190 155 163.40800 160.26022
## 191 170 228.64689 224.34783
## 192 230 251.00573 247.32436
## 193 260 270.84311 266.88297
## 194 152 163.41132 217.20095
## 195 300 281.61629 278.78250
## 196 205 172.80153 169.91373
## 197 168 265.23975 242.66975
## 198 150 155.14799 170.42741
## 199 135 156.34670 171.68081
## 200 135 116.29677 106.58439
## 201 135 157.52731 154.21662
## 202 150 194.02447 209.69790
## 203 165 166.93945 182.54129
## 204 165 166.93945 182.54129
## 205 150 163.41354 160.26605
## 206 220 190.49707 188.10070
## 207 270 292.17641 294.87047
## 208 175 163.38584 178.87059
## 209 155 169.76281 177.24644
## 210 320 240.95735 245.19385
## 211 240 295.76834 298.56211
## 212 280 246.21690 242.40009
## 213 280 248.57895 244.82789
## 214 220 188.13587 185.67394
## 215 355 386.62176 388.15053
## 216 205 184.60955 182.04982
## 217 230 246.28123 242.46866
## 218 375 343.72982 347.03870
## 219 290 290.96174 293.62220
## 220 285 301.60202 304.55768
## 221 145 157.51558 154.20424
## 222 300 292.12665 294.81944
## 223 410 406.62130 408.70547
## 224 225 186.95001 184.45511
## 225 295 299.22369 302.11328
## 226 410 406.62130 408.70547
## 227 298 394.96370 396.72269
## 228 240 295.76834 298.56211
## 229 163 169.30317 166.31902
## 230 160 170.48709 167.53590
## 231 135 158.70790 174.11076
## 232 130 153.99152 169.26374
## 233 299 312.13567 309.32319
## 234 140 92.04651 108.50453
## 235 229 191.66800 189.30411
## 236 165 169.30104 166.31679
## 237 132 158.71138 174.11836
## 238 275 336.13505 331.02814
## 239 275 336.13505 331.02814
## 240 220 169.24260 184.83478
## 241 240 252.17390 248.52454
## 242 210 175.15815 172.33577
## 243 210 197.59189 195.39238
## 244 224 363.66026 354.95509
## 245 175 183.45991 199.53114
## 246 320 299.18417 302.07254
## 247 220 268.61085 264.58857
## 248 245 246.26193 242.44809
## 249 305 383.16132 366.05961
## 250 330 299.16836 283.35408
## 251 275 299.25531 302.14587
## 252 325 299.17626 302.06440
## 253 190 177.54051 174.78467
## 254 140 90.98049 107.40767
## 255 300 306.30401 309.39007
## 256 155 163.40800 160.26022
## 257 150 169.31698 166.33351
## 258 340 250.86314 247.17308
## 259 290 201.04095 198.93760
## 260 250 281.48067 300.39066
## 261 225 227.39069 223.05277
## 262 180 225.09142 220.69273
## 263 290 299.23160 283.47520
## 264 145 166.96102 182.59117
## 265 152 158.68821 174.06770
## 266 230 252.18691 248.53832
## 267 295 258.00655 254.51720
## 268 180 177.55084 174.79544
## 269 140 114.65887 113.12083
## 270 235 184.57838 182.01751
## 271 260 320.41470 341.95258
## 272 220 186.95525 184.46053
## 273 285 258.01990 254.53126
## 274 170 169.29573 184.95930
## 275 140 161.06339 157.85086
## 276 300 299.21579 302.10514
## 277 270 187.07994 184.58834
## 278 250 185.74333 183.21471
## 279 195 172.81198 169.92467
## 280 320 199.82677 197.68983
## 281 150 165.77494 162.69308
## 282 285 254.47721 250.89006
## 283 150 163.41354 160.26605
## 284 175 175.19446 172.37371
## 285 135 156.34670 171.68081
## 286 155 202.33103 205.49924
## 287 290 258.01323 254.52423
## 288 350 359.59053 355.13164
## 289 240 178.66970 175.94449
## 290 380 403.11579 405.10247
## 291 320 249.23324 253.69909
## 292 175 165.74776 162.66451
## 293 330 239.75334 225.19121
## 294 259 186.91440 184.41827
## 295 285 254.47721 250.89006
## 296 147 165.77820 162.69650
## 297 150 163.41354 160.26605
## 298 196 185.79964 183.27302
## 299 235 252.18041 248.53143
## 300 240 234.03574 238.08354
## 301 215 181.05704 178.39853
## 302 140 104.46261 113.07613
## 303 200 177.53018 174.77390
## 304 178 168.10634 165.08859
## 305 220 234.48382 230.34378
## 306 215 216.35871 219.91652
## 307 210 240.40177 236.42690
## 308 215 179.87628 177.18496
## 309 130 205.10708 218.88171
## 310 157 162.22498 159.04426
## 311 340 263.37097 268.22804
## 312 340 263.37097 268.22804
## 313 190 228.61959 224.31837
## 314 370 361.90521 357.50984
## 315 230 253.36812 249.75232
## 316 295 357.36357 352.84545
## 317 275 357.41379 352.89805
## 318 270 311.07476 314.29387
## 319 245 235.63203 250.16128
## 320 259 186.91440 184.41827
## 321 225 234.47722 248.99683
## 322 205 179.88660 177.19570
## 323 310 249.25445 253.72146
## 324 285 299.23950 302.12958
## 325 300 239.81770 244.02353
## 326 245 178.66455 175.93912
## 327 160 163.40246 160.25439
## 328 300 257.99988 254.51017
## 329 157 157.50150 154.18940
## 330 250 205.80842 203.83715
## 331 175 110.29399 119.05778
## 332 140 163.42461 178.95830
## 333 180 171.64683 187.36492
## 334 250 246.25550 261.08679
## 335 160 163.40246 160.25439
## 336 125 157.53904 172.92120
## 337 130 158.71369 174.12343
## 338 165 163.39692 160.24857
## 339 160 162.22162 177.69300
## 340 139 225.14891 220.75485
## 341 260 190.45444 188.05673
## 342 160 163.40246 178.90818
## 343 210 169.25323 184.85969
## 344 235 175.13222 172.30868
## 345 145 110.36276 119.14006
## 346 178 228.63597 224.33605
## 347 142 157.51910 172.87798
## 348 195 163.36369 178.82047
## 349 225 169.23729 184.82233
## 350 205 175.16334 190.94839
## 351 160 163.40246 160.25439
## 352 329 315.71074 319.05748
## 353 175 223.91791 219.48692
## 354 220 240.38884 236.41305
## 355 220 175.14778 172.32494
## 356 150 163.41354 178.93324
## 357 165 163.39692 160.24857
## 358 268 204.60637 202.60192
## 359 235 234.46404 248.97140
## 360 225 220.30321 234.41363
## 361 180 175.18927 172.36829
## 362 160 110.32837 119.09892
## 363 160 163.40246 178.90818
## 364 228 241.55955 237.61586
## 365 280 299.24741 302.13773
## 366 300 299.21579 302.10514
## 367 125 157.53904 154.22899
## 368 180 177.55084 174.79544
## 369 178 161.02039 157.80557
## 370 310 205.73459 203.76196
## 371 198 175.17060 172.34878
## 372 150 163.41354 178.93324
## 373 157 163.40578 160.25789
## 374 195 175.17371 172.35203
## 375 260 270.84311 266.88297
## 376 245 184.56799 182.00673
## 377 245 186.92907 184.43344
## 378 285 299.23950 320.86165
## 379 270 299.26322 302.15402
## 380 276 299.25373 302.14424
## 381 229 201.11204 199.01026
## 382 145 157.51558 154.20424
## 383 150 163.41354 160.26605
## 384 238 181.03329 178.37384
## 385 265 175.10110 172.27617
## 386 175 172.83288 169.94654
## 387 190 172.81721 169.93013
## 388 325 356.10569 351.55112
## 389 310 299.19998 302.08884
## 390 310 246.89024 251.29166
## 391 150 131.62950 141.00482
## 392 160 163.40246 160.25439
## 393 330 306.25804 309.34243
## 394 250 192.82578 190.49400
## 395 152 165.77276 162.69079
## 396 142 235.80260 249.65497
## 397 222 228.57592 242.92821
## 398 190 173.99806 171.14381
## 399 245 184.56799 182.00673
## 400 230 318.53880 312.94530
## 401 140 161.06339 157.85086
## 402 230 240.37592 236.39921
## 403 332 465.79019 456.16722
## 404 195 169.26916 166.28336
## 405 177 174.01159 171.15795
## 406 200 178.71098 175.98750
## 407 235 234.46404 248.97140
## 408 170 163.39138 160.24274
## 409 168 163.39360 160.24507
## 410 250 235.62547 250.14857
## 411 190 178.72130 175.99825
## 412 265 260.40878 256.98714
## 413 180 262.83464 240.15547
## 414 310 375.84653 380.04942
## 415 170 177.56117 174.80621
## 416 188 177.54258 193.42139
## 417 125 116.31981 106.61291
## 418 240 183.39257 180.79869
## 419 265 186.90812 184.41177
## 420 220 181.05188 178.39316
## 421 170 225.10545 239.41685
## 422 265 186.90812 184.41177
## 423 350 624.22188 600.97391
## 424 315 259.16047 255.70257
## 425 550 469.25186 451.28510
## 426 700 655.29952 649.33253
## 427 450 457.65772 439.52157
## 428 950 668.26506 666.50794
## 429 550 469.25186 451.28510
## 430 255 191.64008 189.27535
## 431 173 169.29254 184.95183
## 432 160 156.31698 152.97183
## 433 160 156.31698 152.97183
## 434 145 156.33481 171.65529
## 435 173 169.29254 184.95183
## 436 369 404.31016 425.09813
## 437 230 238.01382 233.97140
## 438 110 110.44299 119.23605
## 439 190 169.27448 166.28893
## 440 85 62.88165 54.64476
## 441 150 155.14799 170.42741
## 442 175 156.29915 171.57874
## 443 200 227.42510 241.76949
## 444 275 230.41124 234.35739
## 445 350 400.79305 402.71489
## 446 330 406.71868 408.80488
## 447 415 490.93523 491.56438
## 448 175 171.65208 168.73293
## 449 250 178.65939 175.93374
## 450 355 328.40301 331.28699
## 451 355 328.40301 331.28699
## 452 330 400.81885 402.74111
## 453 250 245.07442 241.22731
## 454 410 478.60256 469.30379
## 455 145 162.23841 159.05840
## 456 106 110.45216 119.24702
## 457 155 165.76950 181.35105
## 458 165 168.12025 165.10319
## 459 178 159.83926 156.59158
## 460 192 177.53845 174.78251
## 461 135 156.34670 171.68081
## 462 260 349.95877 353.43974
## 463 325 353.74067 349.12035
## 464 390 468.24680 481.19404
## 465 350 400.79305 402.71489
## 466 236 355.04847 346.09790
## 467 260 246.24263 242.42752
## 468 220 178.69034 175.96599
## 469 140 164.19201 161.06642
## 470 147 117.00223 115.52975
## 471 165 163.39692 160.24857
## 472 200 181.07252 178.41463
## 473 276 260.39388 256.97149
## 474 192 177.53845 174.78251
## 475 245 191.65082 189.28641
## 476 150 155.14799 170.42741
## 477 230 186.94478 184.44970
## 478 210 175.15815 172.33577
## 479 295 299.22369 302.11328
## 480 298 276.89549 273.93076
## 481 253 182.19848 198.11844
## 482 315 299.19207 302.08069
## 483 240 184.57319 182.01212
## 484 125 158.71948 155.44225
## 485 260 250.96684 247.28310
## 486 375 361.89260 357.49666
## 487 245 296.94107 299.76744
## 488 250 185.74333 183.21471
## 489 290 258.01323 254.52423
## 490 309 248.54154 244.78812
## 491 215 175.15296 190.92344
## 492 240 182.21192 179.58521
## 493 320 282.48133 278.84571
## 494 250 259.24784 255.79446
## 495 318 392.57686 394.26994
## 496 165 163.39692 160.24857
## 497 225 179.86597 177.17423
## 498 222 228.57592 242.92821
## 499 275 289.72736 343.38999
## 500 300 257.99988 254.51017
## 501 250 194.00609 191.70710
## 502 300 303.94133 325.66704
## 503 150 169.31698 166.33351
## 504 250 258.06663 254.58046
## 505 298 249.27989 272.31991
## 506 250 246.25550 242.44123
## 507 295 299.22369 302.11328
## 508 305 299.20788 302.09699
## 509 190 233.34259 229.17273
## 510 259 246.24392 242.42889
## 511 300 206.67337 209.96367
## 512 152 157.50736 172.85256
## 513 255 286.29643 288.82721
## 514 245 246.26193 242.44809
## 515 195 173.99286 189.75809
## 516 170 169.29573 166.31122
## 517 150 163.41354 160.26605
## 518 115 62.76537 54.51665
## 519 230 338.61550 333.58110
## 520 162 221.21244 224.90563
## 521 321 299.18259 302.07091
## 522 250 246.25550 242.44123
## 523 189 175.17994 172.35853
## 524 184 175.18512 172.36395
## 525 350 358.40799 353.91621
## 526 350 397.25233 399.07588
## 527 190 228.61959 243.01020
## 528 250 184.56280 182.00135
## 529 230 258.09332 254.60858
## 530 260 236.79360 232.71541
## 531 160 172.84856 169.96294
## 532 295 299.22369 320.81877
## 533 215 228.58548 224.28156
## 534 275 309.88594 331.86223
## 535 135 151.62403 166.82094
## 536 260 267.29295 263.23393
## 537 245 228.54454 242.86928
## 538 260 241.08571 245.32852
## 539 185 168.09885 165.08073
## 540 238 305.21806 308.27469
## 541 230 184.58357 182.02289
## 542 240 234.45745 230.31541
## 543 240 234.45745 230.31541
## 544 255 299.28693 302.17847
## 545 220 382.12292 383.52230
## 546 250 198.72712 196.55926
## 547 265 258.04660 254.55938
## 548 255 243.88692 240.00652
## 549 298 239.82199 244.02803
## 550 242 186.93221 203.00600
## 551 220 298.16169 301.02207
## 552 250 184.56280 182.00135
## 553 240 197.55814 195.35778
## 554 243 184.57007 182.00889
## 555 180 175.18927 172.36829
## 556 210 169.25323 166.26664
## 557 350 337.99516 335.90232
## 558 210 288.73528 291.33338
## 559 215 176.33385 173.54407
## 560 200 176.34937 173.56027
## 561 320 301.54737 304.50125
## 562 250 184.56280 182.00135
## 563 245 186.92907 184.43344
## 564 245 184.56799 182.00673
## 565 195 232.15515 227.95195
## 566 310 301.56298 304.51737
## 567 270 195.16433 192.89753
## 568 295 275.71922 272.72188
## 569 220 175.14778 172.32494
## 570 222 249.83491 246.12139
## 571 200 192.87990 190.54971
## 572 260 289.83093 292.45984
## 573 175 225.09843 220.70030
## 574 350 315.67898 300.32385
## 575 235 236.82624 251.40202
## 576 225 298.15373 301.01388
## 577 245 184.56799 182.00673
## 578 180 252.25194 248.60724
## 579 190 173.99806 171.14381
## 580 320 310.99896 314.21506
## 581 250 243.89335 240.01339
## 582 260 236.35672 259.11463
## 583 250 268.50999 264.48487
## 584 215 236.85235 232.77852
## 585 215 236.85235 232.77852
## 586 249 186.92488 184.42911
## 587 245 240.35653 236.37844
## 588 255 240.34361 236.36459
## 589 265 295.72794 298.52058
## 590 290 323.86747 326.62332
## 591 400 406.63347 408.71790
## 592 130 222.80179 218.34317
## 593 285 239.84988 244.05726
## 594 280 249.75994 246.04175
## 595 125 62.72661 54.47394
## 596 133 92.18958 90.02726
## 597 280 228.03437 231.91457
## 598 250 249.79872 246.08295
## 599 265 268.45955 264.43302
## 600 220 175.14778 172.32494
## 601 260 195.17535 192.90885
## 602 230 189.30589 186.87639
## 603 225 172.78063 169.89186
## 604 290 230.37792 234.32270
## 605 330 424.42442 427.00305
## 606 320 465.81809 456.20169
## 607 238 188.11692 185.65435
## 608 220 177.50953 193.34130
## 609 250 188.10429 185.64130
## 610 200 158.63260 155.35066
## 611 235 175.13222 172.30868
## 612 170 222.74455 236.98731
## 613 170 163.39138 178.88312
## 614 257 186.91650 184.42044
## 615 235 188.12008 185.65762
## 616 279 239.86275 244.07075
## 617 245 260.43586 257.01559
## 618 330 394.91946 378.12389
## 619 245 253.34853 249.73158
## 620 215 251.02517 247.34498
## 621 300 311.02928 314.24658
## 622 245 258.07330 273.25619
## 623 320 257.97318 254.48206
## 624 245 241.53762 237.59239
## 625 195 236.87847 232.80657
## 626 235 184.57838 182.01751
## 627 248 201.08989 198.98763
## 628 760 677.52830 694.60084
## 629 220 182.23260 179.60669
## 630 278 195.15551 192.88848
## 631 250 190.46510 188.06772
## 632 218 177.51159 174.75451
## 633 190 164.55036 161.43342
## 634 225 176.32350 173.53327
## 635 248 181.02297 196.91616
## 636 235 243.91265 240.03400
## 637 335 391.37266 374.46420
## 638 235 188.12008 185.65762
## 639 340 400.80595 402.72800
## 640 220 265.06243 260.94141
## 641 290 293.32470 296.05067
## 642 295 258.00655 254.51720
## 643 140 163.42461 160.27770
## 644 290 390.25888 391.88687
## 645 220 184.59396 182.03366
## 646 215 177.51469 174.75774
## 647 215 177.51469 174.75774
## 648 215 178.69550 175.97137
## 649 118 53.28553 44.76804
## 650 130 63.89051 55.66928
## 651 140 106.37350 104.60556
## 652 240 227.37005 241.66675
## 653 260 222.61576 236.75318
## 654 285 201.04678 198.94356
## 655 250 350.38216 345.67289
## 656 370 399.58668 401.47534
## 657 265 220.24468 234.30872
## 658 250 230.90044 226.65863
## 659 700 606.74693 603.24770
## 660 300 257.99988 254.51017
## 661 285 246.21047 242.39324
## 662 340 211.58996 209.78072
## 663 360 312.11977 315.36620
## 664 430 463.61557 464.31570
## 665 129 62.71111 54.45686
## 666 270 222.60145 218.12654
## 667 120 63.92940 55.71209
## 668 118 60.38684 52.07012
## 669 188 163.37144 160.22176
## 670 340 308.60575 311.75510
## 671 190 169.27448 166.28893
## 672 280 325.23702 310.25061
## 673 250 234.44426 230.30123
## 674 165 163.39692 160.24857
## 675 185 169.27979 166.29450
## 676 185 169.27979 166.29450
## 677 182 163.37809 160.22875
## 678 180 164.14797 161.02011
## 679 270 240.32422 236.34382
## 680 125 62.72661 54.47394
## 681 230 175.13740 172.31410
## 682 113 62.77312 54.52519
## 683 200 292.29250 313.92475
## 684 290 343.18818 338.27651
## 685 270 406.79172 408.87944
## 686 185 169.27979 166.29450
## 687 650 551.68589 554.84062
## 688 135 150.44329 165.60597
## 689 125 62.72661 54.47394
## 690 130 119.85494 110.24565
## 691 115 59.21488 50.86595
## 692 210 232.13513 227.93038
## 693 260 243.88048 239.99965
## 694 200 232.14848 227.94476
## 695 245 243.89978 240.02026
## 696 230 243.91908 240.04087
## 697 270 353.87878 349.26531
## 698 419 550.05703 553.15890
## 699 280 316.96624 301.74082
## 700 290 396.15381 379.45923
## 701 328 362.14872 363.82015
## 702 590 577.63979 573.32171
## 703 350 315.67898 300.32385
## 704 240 253.35506 249.73849
## 705 320 246.16544 242.34524
## 706 320 351.38832 346.70285
## 707 300 338.43391 333.38910
## 708 350 440.20447 440.24922
## 709 340 308.60575 311.75510
## 710 285 306.80046 301.68791
## 711 220 217.94788 231.99619
## 712 315 311.41377 306.42877
## 713 140 168.14700 165.13127
## 714 267 242.69038 257.39722
## 715 260 336.02156 345.22711
## 716 248 237.99041 233.94628
## 717 220 177.50953 174.75235
## 718 240 232.09510 227.88725
## 719 285 306.80046 301.68791
## 720 152 256.12642 247.36089
## 721 135 74.51913 66.59624
## 722 560 489.33606 490.75582
## 723 295 357.36357 352.84545
## 724 335 262.67466 259.31400
## 725 275 281.24608 286.60763
## 726 240 334.75769 338.63793
## 727 370 359.12119 362.85713
## 728 360 316.84515 320.22262
## 729 310 191.58102 189.21450
## 730 300 322.13685 317.45054
## 731 300 318.58299 313.79792
## 732 330 362.14152 363.81291
## 733 350 208.04209 206.13421
## 734 290 309.14854 304.10121
## 735 300 346.70934 341.89495
## 736 315 310.22932 305.21130
## 737 360 406.68216 408.76760
## 738 310 341.95481 337.00738
## 739 288 243.34839 239.45128
## 740 285 262.74350 259.38612
## 741 360 406.68216 390.18500
## 742 347 377.83388 379.94203
## 743 310 362.21355 363.88526
## 744 360 319.51732 314.75727
## 745 833 586.19351 590.32009
## 746 699 780.56747 793.15681
## 747 515 529.62967 532.16581
## 748 320 251.59723 237.39441
## 749 210 182.24293 198.22715
## 750 245 313.79980 337.60890
## 751 260 319.24737 343.18227
## 752 340 387.21133 399.27557
## 753 650 554.04442 557.26493
## 754 380 304.99960 308.04852
## 755 370 332.86913 327.66328
## 756 195 181.07768 178.41999
## 757 280 323.40540 318.75454
## 758 340 338.55207 334.32170
## 759 220 226.21647 240.50290
## 760 235 234.46404 230.32251
## 761 580 539.99073 604.59291
## 762 300 319.76758 315.01544
## 763 320 269.77803 266.61536
## 764 395 489.68931 491.11102
## 765 310 267.43147 264.20376
## 766 183 172.82452 169.93779
## 767 160 163.40246 160.25439
## 768 260 336.02156 345.22711
## 769 230 189.30589 186.87639
## 770 230 189.30589 186.87639
## 771 175 161.02378 157.80915
## 772 270 229.69202 225.41514
## 773 260 232.06840 227.85850
## 774 400 466.04839 466.81416
## 775 250 492.17526 484.59315
## 776 350 369.17118 371.03918
## 777 275 298.07414 300.93191
## 778 595 542.32144 550.43415
## 779 220 191.67767 189.31407
## 780 300 240.28545 236.30228
## 781 300 240.28545 236.30228
## 782 300 365.63051 361.34135
## 783 290 454.51416 436.58112
## 784 230 281.73341 278.90289
## 785 250 177.47854 174.72004
## 786 330 308.98267 303.92939
## 787 385 466.08310 448.31651
## 788 225 226.20953 221.83868
## 789 590 538.78416 546.79980
## 790 330 267.40284 264.17392
## 791 195 269.96100 266.80560
## 792 270 191.62398 189.25875
## 793 410 444.41346 428.94181
## 794 500 477.64266 478.73556
## 795 570 535.28282 524.53466
## 796 850 643.96509 659.92818
## 797 240 234.45745 230.31541
## 798 178 166.92543 163.87486
## 799 480 517.46381 527.89391
## 800 310 479.99838 470.78325
## 801 380 349.49202 356.76408
## 802 710 604.32461 619.34338
## 803 140 169.32760 166.34465
## 804 155 55.51159 65.71352
## 805 660 565.82355 574.56966
## 806 700 593.68599 589.82197
## 807 750 738.13295 734.48774
## 808 750 727.45970 723.51737
## 809 500 548.45160 538.11942
## 810 230 175.13740 172.31410
## 811 160 122.14936 112.59098
## 812 852 622.28436 627.43124
## 813 700 606.74693 603.24770
## 814 355 335.92551 312.01336
## 815 820 586.25685 590.38474
## 816 185 172.82243 169.93560
## 817 600 537.57722 545.55617
## 818 620 496.29875 479.03132
## 819 667 524.52049 526.91995
## 820 200 234.51019 230.37215
## 821 275 133.12390 132.11005
## 822 235 243.91265 240.03400
## 823 305 253.27018 249.64865
## 824 235 223.83294 219.39508
## 825 330 281.56610 278.73091
## 826 245 175.12184 190.84858
## 827 350 406.69433 408.78003
## 828 280 294.44476 291.14098
## 829 760 571.29001 574.99599
## 830 450 550.70770 543.40036
## 831 175 225.09843 220.70030
## 832 290 299.23160 302.12143
## 833 235 188.12008 185.65762
## 834 515 477.60985 478.70264
## 835 800 606.26301 621.22781
## 836 700 563.37009 572.03238
## 837 800 606.26301 621.22781
## 838 700 601.99926 598.36750
## 839 700 606.74693 603.24770
## 840 375 463.74478 464.44507
## 841 690 606.79532 603.29680
## 842 630 595.22632 610.07962
## 843 115 60.39839 52.08288
## 844 115 60.39839 52.08288
## 845 325 252.06335 248.40738
## 846 155 222.76601 218.30449
## 847 215 127.41977 144.78872
## 848 780 553.73188 562.09807
## 849 430 470.70565 490.38507
## 850 1240 761.54168 758.59631
## 851 110 65.15181 56.97176
## 852 230 184.58357 182.02289
## 853 130 122.21941 112.67693
## 854 240 178.66970 231.68860
## 855 132 115.12147 124.03782
## 856 410 503.84692 487.14021
## 857 387 573.92547 582.18208
## 858 120 74.57976 66.66232
## 859 550 489.05365 493.42733
## 860 550 475.16761 476.19470
## 861 320 510.71267 502.34402
## 862 220 268.61085 264.58857
## 863 150 175.22039 172.40080
## 864 565 475.13452 476.16151
## 865 515 572.06244 581.04171
## 866 470 475.34411 476.37169
## 867 460 527.28067 516.37128
## 868 360 336.09600 331.79770
## 869 330 405.01655 398.84581
## 870 180 306.51532 290.27870
## 871 360 513.39504 502.15573
## 872 245 227.36316 223.02305
## 873 450 530.84873 520.04700
## 874 180 146.27620 150.87144
## 875 200 181.07252 178.41463
## 876 300 299.21579 283.44492
## 877 120 129.33723 119.99989
## 878 220 245.89921 231.64197
## 879 290 412.66591 396.45141
## 880 600 344.76551 348.90711
## 881 270 448.67583 430.60917
## 882 540 535.35522 543.29034
## 883 320 336.54071 360.83325
## 884 640 537.48197 545.44600
## 885 325 268.59036 265.39457
## 886 135 115.85929 114.35415
## 887 360 394.87799 396.63586
## 888 280 245.03584 241.18615
## 889 600 593.00598 589.11755
## 890 145 109.90763 108.23816
## 891 260 259.42379 284.43636
## 892 320 490.77569 476.72264
## 893 600 677.35489 690.81683
## 894 185 168.09885 165.08073
## 895 290 246.20404 242.38638
## 896 335 322.58256 317.90826
## 897 490 548.47438 538.14845
## 898 270 260.40200 256.98003
## 899 520 501.24187 502.98979
## 900 760 529.07648 526.38487
## 901 450 598.27550 608.03437
## 902 500 421.87201 424.37868
## 903 580 526.97460 534.66456
## 904 430 457.70674 458.24305
## 905 330 399.09687 411.50958
## 906 450 461.20435 461.83891
## 907 400 416.55044 410.69530
## 908 470 412.52856 415.60774
## 909 450 489.57156 490.99262
## 910 515 491.79655 511.92205
## 911 290 412.66591 396.45141
## 912 240 232.09510 227.88725
## 913 230 238.01382 233.97140
## 914 530 548.38329 556.68720
## 915 325 320.84775 316.12529
## 916 450 519.04040 526.54279
## 917 250 230.15620 225.89364
## 918 210 239.22079 253.89629
## 919 400 365.51549 362.03591
## 920 270 406.79172 408.87944
## 921 340 341.87792 355.59817
## 922 315 246.17187 242.35210
## 923 358 316.84817 320.22579
## 924 250 230.90044 226.65863
## 925 310 253.26365 249.64174
## 926 450 477.75203 478.84527
## 927 330 399.09687 411.50958
## 928 350 407.29553 419.92911
## 929 495 542.55414 532.05770
## 930 500 500.10325 483.14345
## 931 280 248.57895 244.82789
## 932 280 246.21690 242.40009
## 933 355 462.61145 463.27901
## 934 470 540.24950 548.34362
## 935 170 175.19965 172.37912
## 936 250 240.35007 255.00989
## 937 240 376.32351 386.68733
## 938 255 311.09750 295.73527
## 939 240 234.45745 230.31541
## 940 138 115.84915 114.34397
## 941 245 336.21362 331.11129
## 942 225 163.33045 160.17863
## 943 520 537.76772 564.60221
## 944 350 341.85230 336.89915
## 945 265 326.44203 330.08922
## 946 300 412.65426 414.90537
## 947 319 241.44219 256.04942
## 948 277 241.49635 256.15644
## 949 285 241.48604 256.13606
## 950 286 413.85047 416.13485
## 951 310 480.58857 471.38989
## 952 255 329.43674 324.95308
## 953 450 477.75203 478.84527
## 954 255 299.28693 302.17847
## 955 340 282.41646 278.77930
## 956 250 228.60004 237.71792
## 957 700 672.03092 646.16823
## 958 283 250.93703 247.25147
## 959 428 429.03814 413.09420
## 960 410 436.14451 420.43344
## 961 390 544.88244 544.02070
## 962 460 519.01313 526.51226
## 963 195 172.81198 169.92467
## 964 180 306.51532 308.78258
## 965 315 257.97986 254.48909
## 966 290 480.04127 489.49350
## 967 220 473.53696 474.50037
## 968 370 408.80494 404.26597
## 969 300 325.20613 310.19337
## 970 310 363.23936 358.88354
## 971 461 475.36396 476.39160
## 972 500 534.26993 523.53500
## 973 295 258.00655 254.51720
## 974 750 611.25360 607.88348
## 975 270 246.22977 261.03544
## 976 650 632.07160 620.20054
## 977 295 318.81870 314.73706
## 978 610 615.59372 625.77262
## 979 280 254.48377 250.89699
## 980 580 536.44180 544.39523
## 981 603 575.19456 589.50623
## 982 450 474.20633 475.20127
## 983 350 503.54784 494.97040
## 984 360 495.24961 486.43797
## 985 320 253.25059 249.62792
## 986 290 248.56605 244.81418
## 987 365 246.10755 242.28353
## 988 600 595.07998 612.96157
## 989 345 310.10493 323.74927
## 990 754 547.82392 550.87435
## 991 245 191.65082 189.28641
## 992 160 166.94484 163.89524
## 993 175 163.38584 178.87059
## 994 310 305.10729 308.16001
## 995 690 901.32759 903.57206
## 996 335 316.88299 301.58288
## 997 135 117.47896 126.46059
## 998 380 372.52223 368.42177
## 999 315 253.25712 249.63483
## 1000 268 382.84643 379.83353
## 1001 170 115.74099 114.23539
## 1002 720 618.51418 615.34455
## 1003 640 553.67957 546.41204
## 1004 590 613.28817 604.73378
## 1005 450 447.78055 418.78616
## 1006 430 515.55413 504.32972
## 1007 310 390.61973 393.08069
## 1008 615 609.52894 606.10174
## 1009 424 463.62966 464.32981
## 1010 250 261.33535 260.90264
## 1011 290 412.66591 414.91732
## 1012 137 124.56746 115.08807
## 1013 290 316.95111 301.71211
## 1014 310 216.34556 214.66801
## 1015 215 198.76694 196.60004
## 1016 540 569.61941 565.07484
## 1017 305 253.27018 249.64865
## 1018 660 578.34102 586.65586
## 1019 650 606.98888 622.15603
## 1020 240 189.29530 186.86546
## 1021 240 189.29530 186.86546
## 1022 280 197.51314 195.31166
## 1023 225 222.66584 218.19617
## 1024 280 197.51314 195.31166
## 1025 250 211.70965 209.90213
## 1026 600 510.23939 506.99550
## 1027 250 189.55581 216.12131
## 1028 160 163.40246 160.25439
## 1029 570 534.21381 536.87933
## 1030 350 393.71154 395.43684
## 1031 600 632.31591 639.17749
## 1032 270 258.03993 254.55235
## 1033 580 553.68105 551.67533
## 1034 307 245.71443 250.08340
## 1035 308 390.23240 391.86011
## 1036 306 390.23534 391.86309
## 1037 235 376.34408 367.98925
## 1038 370 421.42135 415.70414
## 1039 308 330.90825 333.86014
## 1040 315 253.25712 249.63483
## 1041 220 283.99686 267.89384
## 1042 495 520.09975 508.96287
## 1043 318 409.09315 411.24527
## 1044 255 192.82037 190.48843
## 1045 1100 800.85361 789.71495
## 1046 258 235.30794 234.15495
## 1047 163 220.99747 206.08532
## 1048 290 258.01323 273.13589
## 1049 225 171.59957 168.67794
## 1050 280 247.39794 243.61401
## 1051 248 192.82795 190.49623
## 1052 250 258.06663 254.58046
## 1053 210 296.99719 299.82519
## 1054 195 282.88680 279.26079
## 1055 200 159.81408 156.56504
## 1056 240 186.93430 184.43886
## 1057 245 237.99431 233.95047
## 1058 229 327.89827 336.88461
## 1059 250 339.74523 353.49506
## 1060 210 298.17761 301.03847
## 1061 260 295.73602 279.91935
## 1062 356 388.67896 379.80486
## 1063 121 154.00252 169.28691
## 1064 118 154.00619 169.29463
## 1065 150 189.39060 186.96386
## 1066 160 50.75894 79.17198
## 1067 225 322.01074 330.83188
## 1068 430 474.25067 475.24572
## 1069 150 189.39060 186.96386
## 1070 480 570.24566 572.48541
## 1071 475 457.67962 471.66195
## 1072 425 499.08328 500.76721
## 1073 680 530.24354 528.43393
## 1074 230 345.31334 348.66446
## 1075 230 345.31334 348.66446
## 1076 210 177.51986 193.36633
## 1077 370 427.92238 430.59796
## 1078 365 408.41312 421.06699
## 1079 375 400.76081 402.68211
## 1080 295 248.55960 244.80732
## 1081 375 424.95381 419.33452
## 1082 298 197.49289 195.29090
## 1083 360 397.23890 399.06226
## 1084 235 182.21709 198.16395
## 1085 340 400.80595 384.16761
## 1086 220 228.57865 242.93333
## 1087 350 278.70294 283.98604
## 1088 160 178.75226 176.03050
## 1089 200 209.41350 207.54151
## 1090 360 290.95261 288.37842
## 1091 498 490.47357 491.92191
## 1092 338 233.14632 247.49389
## 1093 450 421.92815 424.43666
## 1094 450 421.92815 424.43666
## 1095 270 305.16883 308.22372
## 1096 120 136.43308 127.29504
## 1097 126 123.41104 132.56402
## 1098 475 388.81140 385.16309
## 1099 270 346.78532 341.97499
## 1100 340 493.35358 494.87452
## 1101 300 253.27671 249.65556
## 1102 330 293.58191 306.76730
## 1103 950 890.40001 895.52604
## 1104 475 417.24019 439.03349
## 1105 475 417.24019 420.45065
## 1106 304 299.61476 312.99651
## 1107 170 163.39138 178.88312
## 1108 400 458.96143 459.53056
## 1109 420 486.78370 499.40388
## 1110 690 536.24588 538.97193
## 1111 285 313.90715 308.99238
## 1112 350 654.58862 637.47427
## 1113 152 113.43478 111.86373
## 1114 700 559.82404 549.70824
## 1115 700 553.91169 543.62541
## 1116 230 299.40448 281.41678
## 1117 280 434.64917 438.33635
## 1118 635 617.91472 605.64368
## 1119 300 334.66004 319.91984
## 1120 410 429.05840 413.14108
## 1121 250 363.39101 359.04184
## 1122 450 451.45047 436.12836
## 1123 163 165.76080 162.67822
## 1124 270 239.88206 244.09099
## 1125 235 338.31485 323.75805
## 1126 480 447.86904 451.09717
## 1127 590 577.63979 573.32171
## 1128 610 539.92015 547.96120
## 1129 650 627.32781 634.04391
## 1130 300 426.50101 429.13772
## 1131 295 246.19760 242.37952
## 1132 600 558.52959 551.40625
## 1133 500 500.10325 501.81873
## 1134 700 661.47566 669.13420
## 1135 269 299.21438 277.39694
## 1136 220 252.19992 267.24261
## 1137 169 236.91241 232.84304
## 1138 310 259.89128 245.94118
## 1139 290 205.75920 203.78702
## 1140 350 293.62679 271.41827
## 1141 260 242.69939 257.41508
## 1142 360 394.87799 396.63586
## 1143 290 409.12657 411.27945
## 1144 450 451.45047 436.12836
## 1145 231 553.21093 533.18807
## 1146 222 346.70118 340.45226
## 1147 300 394.20862 378.20999
## 1148 287 356.20108 351.65111
## 1149 200 172.80676 169.91920
## 1150 315 446.96831 436.82296
## 1151 250 320.55626 324.03984
## 1152 310 240.27252 236.28843
## 1153 340 345.42553 340.57276
## 1154 345 222.18526 220.67108
## 1155 205 348.15373 356.89786
## 1156 180 297.76611 292.40705
## 1157 1600 941.05430 964.96289
## 1158 750 584.50849 593.73996
## 1159 337 457.51765 461.01870
## 1160 340 341.87792 336.92621
## 1161 295 254.46409 250.87619
## 1162 340 276.82914 273.86227
## 1163 1350 1139.34771 1148.60022
## 1164 340 417.38895 410.14770
## 1165 315 257.97986 254.48909
## 1166 200 177.53018 174.77390
## 1167 145 165.78038 162.69879
## 1168 118 161.08828 157.87707
## 1169 160 171.66783 168.74942
## 1170 210 173.97725 171.12204
## 1171 330 359.64084 355.18427
## 1172 290 316.95111 301.71211
## 1173 360 445.66481 454.10957
## 1174 255 305.19190 308.24761
## 1175 440 392.40300 394.09405
## 1176 325 261.50799 258.11512
## 1177 767 558.49183 566.99384
## 1178 704 442.87441 463.94301
## 1179 180 232.17517 227.97351
## 1180 310 411.58703 404.19104
## 1181 1150 989.16035 969.46846
## 1182 125 136.42062 127.28014
## 1183 360 322.75119 326.29261
## 1184 300 459.64609 458.77462
## 1185 357 399.60366 420.27785
## 1186 605 513.87575 539.62588
## 1187 325 329.13943 324.64753
## 1188 660 683.29943 681.92200
## 1189 232 230.92463 245.33316
## 1190 230 229.74618 225.47355
## 1191 195 245.14516 241.30279
## 1192 290 175.07516 172.24908
## 1193 360 392.51700 394.20939
## 1194 285 254.47721 250.89006
## 1195 420 382.97410 403.00161
## 1196 250 308.74278 311.89734
## 1197 305 319.74672 314.99392
## 1198 350 401.37441 395.09998
## 1199 570 530.55031 519.66621
## 1200 290 299.23160 302.12143
## 1201 650 683.89618 666.75648
## 1202 480 406.71634 400.57885
## 1203 480 406.71634 400.57885
## 1204 410 492.78165 502.54293
## 1205 395 465.71604 450.87385
## 1206 425 451.48354 454.81371
## 1207 450 451.45047 454.77901
## 1208 230 345.31334 348.66446
## 1209 230 304.07713 301.03866
## 1210 350 432.71590 422.14574
## 1211 673 617.71489 624.16222
## 1212 630 533.95398 541.82327
## 1213 199 193.28363 201.41764
## 1214 230 390.09508 383.51976
## 1215 685 617.65179 624.09620
## 1216 750 583.91264 616.34568
## 1217 650 544.61066 566.00792
## 1218 673 449.64901 463.20486
## 1219 226 168.05499 165.03469
## 1220 315 259.16047 255.70257
## 1221 240 246.26836 242.45494
## 1222 230 220.00240 218.42432
## 1223 190 192.89073 190.56085
## 1224 420 554.36233 565.89850
## 1225 340 305.06114 308.11223
## 1226 215 255.75043 252.20127
## 1227 255 304.01087 288.44285
## 1228 540 537.72010 545.72143
## 1229 455 475.37720 476.40487
## 1230 980 963.02934 972.46918
## 1231 495 413.61534 416.72600
## 1232 335 320.42689 305.23033
## 1233 380 358.33261 353.83729
## 1234 595 575.23895 589.56020
## 1235 695 687.66151 690.81852
## 1236 280 347.53968 350.95337
## 1237 225 263.62168 268.49462
## 1238 240 301.67229 286.05698
## 1239 350 442.56415 442.67446
## 1240 398 484.95533 486.24574
## 1241 225 234.87878 249.41003
## 1242 225 238.02032 233.97838
## 1243 410 475.47648 476.50443
## 1244 255 287.47743 271.42540
## 1245 370 404.30892 406.32858
## 1246 1150 862.68308 852.71042
## 1247 500 613.56360 623.74007
## 1248 580 589.64999 599.10187
## 1249 230 235.65170 231.54355
## 1250 480 493.05360 494.57265
## 1251 450 523.76370 531.39891
## 1252 295 403.22275 386.72651
## 1253 260 300.46004 303.38415
## 1254 230 324.05172 326.81022
## 1255 580 531.70888 539.53048
## 1256 236 312.30750 315.56155
## 1257 228 293.42660 296.15526
## 1258 235 293.41509 296.14345
## 1259 330 385.67068 381.93541
## 1260 230 252.18691 248.53832
## 1261 260 351.53921 346.86144
## 1262 280 404.42086 406.44267
## 1263 290 294.41242 291.10801
## 1264 650 611.51257 605.85541
## 1265 410 398.55129 401.23877
## 1266 570 495.22453 496.80785
## 1267 175 174.01368 171.16013
## 1268 260 318.37828 316.55950
## 1269 309 461.12749 451.38469
## 1270 920 647.37745 639.69580
## 1271 930 769.51208 776.44897
## 1272 295 406.76128 427.80660
## 1273 300 281.61629 278.78250
## 1274 250 279.21928 262.93091
## 1275 330 249.50638 245.77890
## 1276 165 163.39692 178.89565
## 1277 260 391.48123 393.14249
## 1278 395 354.57648 359.00215
## 1279 350 471.71323 475.61059
## 1280 560 531.75822 520.91496
## 1281 550 611.03991 602.43695
## 1282 475 359.27613 354.80275
## 1283 225 293.43153 296.16032
## 1284 429 508.53724 510.48393
## 1285 350 485.05852 486.34940
## 1286 430 424.31239 408.22695
## 1287 480 518.64661 510.44283
## 1288 300 255.63833 252.08292
## 1289 175 229.82064 225.55386
## 1290 450 560.68504 574.73284
## 1291 450 515.49782 504.25857
## 1292 485 477.67547 478.76847
## 1293 980 996.87797 1015.63434
## 1294 580 538.80782 528.15483
## 1295 650 665.16745 659.47855
## 1296 250 185.74333 183.21471
## 1297 185 164.55584 180.06084
## 1298 210 202.04711 199.13596
## 1299 270 263.94525 260.62164
## 1300 360 394.87799 396.63586
## 1301 870 752.90607 749.68187
## 1302 180 238.07885 234.04119
## 1303 650 640.37040 647.44937
## 1304 600 690.28120 689.08775
## 1305 350 406.69433 408.78003
## 1306 360 281.51591 278.67931
## 1307 259 334.99534 329.85799
## 1308 310 262.70908 259.35006
## 1309 197 186.97934 184.48545
## 1310 695 630.48570 627.64752
## 1311 780 533.64688 536.30370
## 1312 650 577.66222 568.08152
## 1313 870 601.86174 611.52244
## 1314 310 262.70908 259.35006
## 1315 550 537.69628 527.02921
## 1316 335 440.24763 440.29238
## 1317 350 417.95531 412.14312
## 1318 315 299.56877 312.93905
## 1319 880 680.80747 688.95986
## 1320 520 477.59892 478.69167
## 1321 300 363.43261 365.13734
## 1322 165 181.10865 197.12536
## 1323 200 238.05284 234.01327
## 1324 225 239.97861 244.19219
## 1325 268 306.35304 309.44088
## 1326 450 518.71404 510.52207
## 1327 250 304.01860 288.45769
## 1328 190 238.06584 234.02723
## 1329 950 924.30918 940.87362
## 1330 235 225.77087 210.90985
## 1331 240 295.76834 298.56211
## 1332 140 62.66847 54.40989
## 1333 350 455.23599 463.95495
## 1334 190 242.41729 246.70040
## 1335 385 357.21191 360.89475
## 1336 440 471.86491 472.79437
## 1337 350 396.07208 379.27815
## 1338 690 726.71498 721.87108
## 1339 371 403.24177 395.60092
## 1340 590 495.18157 496.76459
## 1341 450 418.38520 402.09527
## 1342 350 656.44805 676.71127
## 1343 235 184.57838 182.01751
## 1344 235 326.68618 316.93447
## 1345 265 322.89669 345.30573
## 1346 255 263.96609 260.64345
## 1347 550 573.44903 554.69673
## 1348 395 463.69779 464.39802
## 1349 180 237.71180 241.86413
## 1350 210 169.25323 166.26664
## 1351 650 606.98888 622.15603
## 1352 350 406.69433 408.78003
## 1353 290 378.47051 361.25519
## 1354 201 216.51259 214.83715
## 1355 258 342.08809 337.14808
## 1356 850 722.17673 718.09250
## 1357 580 571.76293 567.27999
## 1358 525 557.85138 547.77140
## 1359 240 293.40688 277.55050
## 1360 272 306.34691 290.82361
## 1361 340 200.98268 198.87805
## 1362 185 189.87311 187.45957
## 1363 650 595.38188 586.30319
## 1364 410 477.83952 478.93304
## 1365 650 765.95841 781.97005
## 1366 530 515.40344 517.54476
## 1367 190 287.58964 271.63566
## 1368 240 181.03123 178.37169
## 1369 380 488.52849 495.90874
## 1370 240 342.92231 346.20686
## 1371 215 192.86367 171.79636
## 1372 580 571.76293 567.27999
## 1373 240 322.93498 326.48517
## 1374 245 344.48489 339.61237
## 1375 250 294.57131 278.73474
## 1376 380 311.86267 290.13934
## 1377 347 377.46695 379.56492
## 1378 460 471.82010 472.74946
## 1379 340 347.59268 333.17628
## 1380 250 203.44799 219.99336
## 1381 700 520.92115 518.01848
## 1382 295 253.28324 249.66247
## 1383 280 306.99614 310.10169
## 1384 190 177.54051 174.78467
## 1385 350 425.58289 409.65195
## 1386 1750 894.39831 895.42367
## 1387 275 305.16114 289.59914
## 1388 275 311.06718 295.67720
## 1389 395 430.25627 432.99646
## 1390 175 239.26616 235.26175
## 1391 385 434.99214 419.28299
## 1392 185 191.71525 189.35279
## 1393 275 281.65812 278.82550
## 1394 255 246.24906 242.43437
## 1395 243 236.81579 232.73925
## 1396 148 175.22247 172.40297
## 1397 620 423.68061 421.01169
## 1398 430 388.93915 385.29432
## 1399 160 103.93776 120.71040
## 1400 250 343.29035 357.14373
## 1401 438 463.59677 445.66063
## 1402 449 412.48070 396.01719
## 1403 1150 1175.37175 1166.40598
## 1404 235 165.68252 162.59595
## 1405 250 269.88049 266.72189
## 1406 695 620.04842 630.31076
## 1407 195 196.42786 194.19604
## 1408 344 451.60650 441.57729
## 1409 170 235.73041 250.35195
## 1410 190 168.09350 165.07512
## 1411 245 183.38739 180.79331
## 1412 380 609.48154 618.76214
## 1413 220 184.59396 182.03366
## 1414 250 263.56718 249.78651
## 1415 235 376.34408 367.98925
## 1416 320 310.75745 313.15154
## 1417 139 293.74574 291.24521
## 1418 250 282.70839 279.07816
## 1419 385 430.26755 433.00818
## 1420 290 298.05026 300.90732
## 1421 1250 816.78687 814.64898
## 1422 250 269.69323 265.70106
## 1423 1500 781.15816 734.38073
## 1424 161 232.20053 228.00083
## 1425 171 237.91344 215.36750
## 1426 300 323.83676 326.59217
## 1427 450 471.84251 472.77191
## 1428 430 489.33133 493.71842
## 1429 206 447.26755 437.18858
## 1430 224 321.77761 325.29600
## 1431 236 405.93720 408.00080
## 1432 220 198.76125 196.59421
## 1433 750 584.50849 593.73996
## 1434 650 595.38188 586.30319
## 1435 660 575.27623 565.62294
## 1436 245 184.56799 182.00673
## 1437 290 302.77550 305.76371
## 1438 310 248.54025 244.78675
## 1439 240 184.57319 182.01212
## 1440 299 302.76153 305.74926
## 1441 299 1673.12068 1725.81782
## 1442 245 184.56799 200.56851
## 1443 200 259.21839 254.93478
## 1444 220 184.59396 182.03366
## 1445 330 306.25804 309.34243
## 1446 140 233.16102 228.98936
## 1447 360 436.04223 447.22880
## 1448 340 253.99798 253.36855
## 1449 260 333.81112 328.64070
## 1450 275 198.69868 196.53014
## 1451 600 532.84326 540.69058
## 1452 450 381.45123 362.49069
## 1453 810 695.06103 708.83424
## 1454 380 495.20800 486.38719
## 1455 400 376.77929 381.00586
## 1456 340 347.59268 351.82654
## 1457 350 683.12799 670.53035
## 1458 230 420.99477 423.47839
## 1459 140 293.74378 310.13871
## 1460 296 344.65817 329.37578
## 1461 168 166.93622 163.88618
## 1462 1700 794.55979 805.52559
## 1463 690 542.10038 550.17648
## 1464 195 251.05109 247.37249
## 1465 350 670.88592 676.53404
## 1466 310 265.07028 261.77693
## 1467 345 247.99814 252.42833
## 1468 295 261.10543 265.90287
## 1469 180 223.53320 208.67395
## 1470 270 394.91771 399.65600
## 1471 305 289.87570 287.27090
## 1472 530 522.37114 511.27696
## 1473 550 621.91154 609.81701
## 1474 410 477.52790 463.00181
## 1475 250 404.45818 388.06875
## 1476 315 359.67856 355.22373
## 1477 300 400.85754 402.78045
## 1478 340 597.71681 610.59809
## 1479 300 364.56309 364.02042
## 1480 270 189.26353 167.94565
## 1481 590 536.41784 544.36756
## 1482 350 453.94893 457.34996
## 1483 285 273.37248 270.31015
## 1484 250 70.51174 99.12232
## 1485 360 447.89889 459.42785
## 1486 255 251.73519 256.27443
## 1487 180 251.07054 228.89856
## 1488 240 463.84678 457.43845
## 1489 298 315.75763 319.10639
## 1490 350 432.66954 416.94314
## 1491 280 255.22809 241.17471
## 1492 380 349.88165 335.48505
## 1493 341 319.39944 332.47569
## 1494 280 315.75205 313.03878
## 1495 235 241.26272 240.27351
## 1496 591 471.62816 478.50561
## 1497 490 553.33944 548.33680
## 1498 328 389.37192 373.19390
## 1499 215 178.69550 175.97137
## 1500 480 446.65739 437.22045
## 1501 250 336.20053 331.09743
## 1502 128 153.99397 150.58523
## 1503 355 399.39515 404.25505
## 1504 151 222.32328 217.84974
## 1505 345 430.31268 414.52558
## 1506 400 445.05812 437.75682
## 1507 500 480.77318 471.49589
## 1508 380 430.27319 433.01404
## 1509 350 448.05185 437.91869
## 1510 185 249.51952 235.40569
## 1511 600 523.37048 512.26047
## 1512 285 222.57999 218.10333
## 1513 380 430.27319 414.43452
## 1514 355 489.22139 488.35802
## 1515 420 238.51958 237.46372
## 1516 860 722.12289 736.60513
## 1517 580 496.38482 498.00072
## 1518 700 690.95939 685.99548
## 1519 760 690.59967 685.62714
## 1520 660 733.40746 739.31543
## 1521 540 501.19837 502.94593
## 1522 450 434.10072 428.73214
## 1523 490 424.44726 418.80675
## 1524 590 495.18157 496.76459
## 1525 600 654.64331 652.46616
## 1526 170 953.46793 994.99979
## 1527 1561 916.19229 930.82669
## 1528 1600 837.93854 837.24782
## 1529 790 597.37284 606.94623
## 1530 1750 794.07838 805.00447
## 1531 260 334.99271 329.85520
## 1532 600 473.87379 474.86787
## 1533 180 239.25968 235.25480
## 1534 280 306.33466 309.42182
## 1535 832 543.65845 541.39398
## 1536 677 421.25503 415.51278
## 1537 720 739.81120 745.90635
## 1538 270 252.13488 248.48319
## 1539 210 194.04976 191.75201
## 1540 390 507.38369 504.06820
## 1541 390 507.38369 504.06820
## 1542 250 311.10508 295.74978
## 1543 270 424.49165 408.64684
## 1544 265 346.79798 341.98833
## 1545 240 324.41482 318.98431
## 1546 580 574.13586 569.71933
## 1547 206 414.20628 403.19226
## 1548 180 311.21121 314.43574
## 1549 240 150.97532 150.45407
## 1550 215 281.75851 278.92869
## 1551 280 253.30283 249.68321
## 1552 590 484.12986 474.90907
## 1553 400 438.51856 441.48843
## 1554 480 424.25637 408.09573
## 1555 295 363.27727 358.92312
## 1556 230 267.54600 264.32313
## 1557 250 211.54016 196.24053
## 1558 660 835.76448 849.98732
## 1559 220 239.98933 225.56094
## 1560 235 262.81234 259.45824
## 1561 210 172.79631 169.90826
## 1562 280 336.12195 331.01428
## 1563 300 481.97620 458.27792
## 1564 270 320.52582 305.41639
## 1565 221 315.87410 300.69490
## 1566 179 323.02840 308.10805
## 1567 750 613.62706 628.86080
## 1568 260 320.54104 324.02392
## 1569 660 672.21255 679.42398
## 1570 270 208.14351 206.23733
## 1571 850 719.80168 734.22931
## 1572 830 722.28442 718.20212
## 1573 845 638.07184 635.45838
## 1574 850 699.58942 694.87187
## 1575 270 320.52582 305.41639
## 1576 330 346.42887 350.63078
## 1577 275 328.79023 313.91237
## 1578 650 554.04442 557.26493
## 1579 195 256.95839 272.17327
## 1580 210 251.03165 247.35186
## 1581 225 404.48928 388.14011
## 1582 295 444.25992 446.55401
## 1583 365 463.76827 464.46859
## 1584 320 439.11198 439.12395
## 1585 310 304.09086 298.90179
## 1586 200 183.43401 180.84169
## 1587 200 183.43401 180.84169
## 1588 190 175.17890 172.35745
## 1589 220 306.42659 290.97666
## 1590 220 306.42659 290.97666
## 1591 149 110.35359 119.12908
## 1592 280 210.49012 208.64926
## 1593 290 363.28991 358.93631
## 1594 290 279.27048 276.37167
## 1595 325 320.44211 323.92040
## 1596 220 287.66690 285.00015
## 1597 425 465.99053 466.75621
## 1598 185 294.84098 292.37138
## 1599 255 404.45196 406.47436
## 1600 285 278.37166 309.98975
## 1601 836 722.25211 736.76435
## 1602 280 394.98858 396.74789
## 1603 165 228.29300 232.18331
## 1604 400 442.42364 442.53396
## 1605 690 630.50917 627.67123
## 1606 255 210.52283 208.68246
## 1607 245 322.92732 307.91926
## 1608 220 287.66690 285.00015
## 1609 250 105.90871 135.67480
## 1610 420 273.16754 270.09783
## 1611 651 577.23812 607.77631
## 1612 230 404.48306 388.12584
## 1613 360 365.47813 361.18252
## 1614 295 411.48019 413.69860
## 1615 155 222.40995 226.13659
## 1616 168 133.49717 132.48396
## 1617 180 191.72062 189.35832
## 1618 236 271.08288 267.95780
## 1619 120 108.80865 125.78649
## 1620 480 346.15826 350.34475
## 1621 335 466.19882 448.52558
## 1622 240 366.57030 370.51527
## 1623 598 472.69462 492.06808
## 1624 770 541.91423 531.24032
## 1625 125 161.08036 157.86873
## 1626 160 103.93776 120.71040
## 1627 280 485.20901 486.50056
## 1628 300 411.47432 413.69259
## 1629 590 541.15017 549.23180
## 1630 560 540.03777 548.09778
## 1631 150 176.40110 173.61427
## 1632 125 104.05706 102.22370
## 1633 90 99.44238 97.47836
## 1634 370 729.22466 720.49849
## 1635 285 203.40612 219.89524
## 1636 290 299.23160 302.12143
## 1637 1050 824.39203 843.15441
## 1638 590 528.13302 535.85239
## 1639 594 575.24450 570.85959
## 1640 113 92.25994 90.09816
## 1641 240 257.67766 243.73819
## 1642 600 652.48110 665.23269
## 1643 600 569.27470 564.72290
## 1644 580 572.94945 587.22102
## 1645 590 568.14491 582.26981
## 1646 260 316.99652 320.38065
## 1647 245 363.40364 359.05503
## 1648 126 155.17691 170.48890
## 1649 152 234.22820 219.71259
## 1650 300 369.17984 364.98898
## 1651 560 568.31852 582.47838
## 1652 222 222.67014 218.20081
## 1653 235 166.86398 182.36670
## 1654 300 241.00014 245.23874
## 1655 225 228.57183 242.92052
## 1656 235 228.55818 242.89490
## 1657 245 234.45085 230.30832
## 1658 240 483.49939 493.07423
## 1659 220 181.05188 178.39316
## 1660 215 227.40445 241.73096
## 1661 200 217.54909 215.06714
## 1662 530 424.20035 426.77125
## 1663 420 271.98899 268.88636
## 1664 235 175.13222 190.87353
## 1665 220 227.39757 241.71812
## 1666 230 226.20258 240.47715
## 1667 200 227.42510 241.76949
## 1668 208 227.41409 241.74894
## 1669 310 370.33737 366.17824
## 1670 350 453.94893 457.34996
## 1671 910 591.17883 600.52413
## 1672 215 239.21431 235.20616
## 1673 260 173.92521 189.59607
## 1674 105 113.59360 112.02323
## 1675 140 119.39288 117.98614
## 1676 250 239.16895 253.79455
## 1677 204 260.49138 275.79898
## 1678 350 475.27045 460.75262
## 1679 214 239.21561 235.20755
## 1680 900 695.72551 709.43031
## 1681 230 241.14990 245.39585
## 1682 850 596.61899 601.03968
## 1683 358 226.87446 225.49125
## 1684 165 240.10733 244.32712
## 1685 570 536.46577 544.42290
## 1686 125 54.44250 64.62943
## 1687 150 109.89071 108.22116
## 1688 350 256.32103 270.54404
## 1689 320 454.64505 434.37600
## 1690 220 243.93194 240.05461
## 1691 135 86.35041 78.75992
## 1692 260 260.41555 256.99425
## 1693 140 108.74090 107.03866
## 1694 210 252.21292 248.56589
## 1695 225 324.13991 309.19220
## 1696 550 553.06664 542.83764
## 1697 155 203.56164 201.52714
## 1698 201 236.87063 232.79816
## 1699 220 269.92441 266.76755
## 1700 450 501.32501 489.67877
## 1701 1350 749.15520 763.79993
## 1702 165 109.83995 108.17015
## 1703 260 173.92521 189.59607
## 1704 285 389.08745 390.68274
## 1705 290 334.50776 318.93704
## 1706 240 134.42823 133.44743
## 1707 115 101.72379 118.50149
## 1708 125 104.05706 102.22370
## 1709 238 329.93276 332.85531
## 1710 238 258.08265 254.59733
## 1711 160 290.00001 274.15958
## 1712 136 62.68398 54.42697
## 1713 165 216.84995 250.01399
## 1714 170 156.30510 171.59149
## 1715 230 175.13740 172.31410
## 1716 290 301.59421 304.54962
## 1717 190 164.55036 180.04833
## 1718 260 288.59244 285.12575
## 1719 300 292.40767 280.78625
## 1720 600 529.83183 545.80134
## 1721 230 293.42331 296.15189
## 1722 305 261.53529 258.14376
## 1723 180 239.25968 235.25480
## 1724 180 177.55084 174.79544
## 1725 388 272.71138 277.82408
## 1726 334 217.48965 215.84450
## 1727 420 414.87642 417.18948
## 1728 420 370.05427 384.50086
## 1729 135 163.43015 160.28353
## 1730 240 269.89513 266.73711
## 1731 130 181.14478 178.48977
## 1732 125 100.50574 98.57380
## 1733 165 240.10733 244.32712
## 1734 210 240.01079 225.59455
## 1735 210 180.51933 167.32025
## 1736 140 106.37350 123.24842
## 1737 230 306.36431 298.99522
## 1738 220 235.26147 220.69570
## 1739 155 161.47797 187.52336
## 1740 165 163.81059 189.89185
## 1741 321 491.47645 467.98041
## 1742 100 161.10865 157.89852
## 1743 237 405.65307 407.70875
## 1744 140 166.96641 163.91789
## 1745 150 221.24064 243.85167
## 1746 240 199.91886 197.78404
## 1747 240 202.27958 200.21028
## 1748 160 183.47545 180.88469
## 1749 240 245.08729 259.89699
## 1750 210 258.00067 253.68304
## 1751 260 186.91336 202.95981
## 1752 495 538.66682 552.76161
## 1753 260 334.99271 348.59419
## 1754 520 697.93415 694.60553
## 1755 650 497.41559 499.06311
## 1756 110 92.27049 108.77968
## 1757 220 184.59396 182.03366
## 1758 115 104.09115 102.25798
## 1759 450 678.27791 684.14815
## 1760 123 177.60972 156.31717
## 1761 125 126.55840 154.58027
## 1762 180 224.71472 228.50507
## 1763 233 265.01810 260.89579
## 1764 219 300.86445 294.77756
## 1765 185 181.08801 178.43073
## 1766 138 158.70442 155.42637
## 1767 220 322.96561 307.99077
## 1768 175 172.83288 169.94654
## 1769 195 284.04150 267.97666
## 1770 185 181.08801 178.43073
## 1771 185 224.70324 228.49318
## 1772 235 178.67486 194.51883
## 1773 250 276.97131 274.00904
## 1774 220 184.59396 182.03366
## 1775 250 320.55626 305.47364
## 1776 190 169.27448 147.54816
## 1777 315 253.25712 249.63483
## 1778 140 253.52341 267.89376
## 1779 220 184.59396 182.03366
## 1780 280 340.60470 344.64648
## 1781 475 578.39438 581.46370
## 1782 215 203.48986 201.45392
## 1783 490 617.18843 620.73948
## 1784 90 105.35984 103.55999
## 1785 185 181.08801 178.43073
## 1786 190 136.96914 136.05425
## 1787 200 224.66881 209.81819
## 1788 185 177.54568 174.79005
## 1789 260 385.71394 377.61258
## 1790 210 240.01079 225.59455
## 1791 240 385.62202 368.70157
## 1792 130 181.14478 178.48977
## 1793 190 228.61959 224.31837
## 1794 230 267.15839 272.12982
## 1795 230 267.15839 272.12982
## 1796 155 165.76950 162.68736
## 1797 175 222.45041 202.36669
## 1798 260 361.78380 347.04043
## 1799 122 168.16626 165.15148
## 1800 260 228.52407 224.21528
## 1801 95 51.00534 61.11013
## 1802 230 330.34733 325.08303
## 1803 158 174.03137 171.17863
## 1804 170 244.82354 230.59181
## 1805 330 448.10611 456.63004
## 1806 750 478.28021 479.40401
## 1807 220 225.92495 224.51057
## 1808 105 102.94164 119.77051
## 1809 175 181.09833 178.44146
## 1810 230 107.25198 124.01087
## 1811 575 661.94085 626.11985
## 1812 128 153.99397 169.26889
## 1813 130 116.30829 106.59865
## 1814 230 265.02833 260.90632
## 1815 200 217.68388 216.04084
## 1816 205 240.40823 236.43382
## 1817 205 228.59912 224.29628
## 1818 199 312.36351 297.11284
## 1819 145 166.96102 163.91223
## 1820 220 278.09522 261.81864
## 1821 218 216.76953 230.78621
## 1822 475 619.96800 629.51749
## 1823 190 169.27448 166.28893
## 1824 198 318.27195 321.69320
## 1825 200 368.04684 369.05286
## 1826 210 264.02861 260.70886
## 1827 225 192.85284 190.52186
## 1828 225 177.50436 174.74697
## 1829 377 453.88091 462.55169
## 1830 344 361.97080 357.57835
## 1831 420 619.94545 601.40042
## 1832 410 669.40706 665.29509
## 1833 220 365.83368 361.55313
## 1834 185 232.97441 218.38352
## 1835 200 324.17834 327.76449
## 1836 199 324.17988 309.26658
## 1837 170 181.10349 178.44683
## 1838 290 254.47065 250.88312
## 1839 185 244.79165 249.14124
## 1840 185 244.79165 230.54200
## 1841 180 242.43864 246.72281
## 1842 115 60.39839 52.08288
## 1843 150 175.22039 172.40080
## 1844 250 234.44426 248.93324
## 1845 200 376.27615 377.51172
## 1846 200 376.27615 377.51172
## 1847 365 453.91167 443.93695
## 1848 225 179.86597 177.17423
## 1849 310 294.34775 272.27048
## 1850 240 179.85049 177.15812
## 1851 230 287.52059 308.92812
## 1852 350 360.77309 356.34709
## 1853 145 103.98889 102.15514
## 1854 240 198.73850 196.57091
## 1855 130 124.16083 122.88545
## 1856 285 460.00704 468.88619
## 1857 310 514.28781 524.72155
## 1858 185 243.97697 240.10271
## 1859 175 227.45951 241.83370
## 1860 305 483.97393 485.23238Podemos construir un dataframe en los resultados que identificamos: el precio leal y los precios obtenidos para los dos modelos con las variables de la zona norte.
##metricas de validación para (numericas)
MAE_simple=mean(abs(resultados$precio_msimple-resultados$precio_real))
MAE_simple## [1] 58.65593MAPE_simple=MAE_simple/mean(resultados$precio_real)*100
MAPE_simple## [1] 18.74465MAE_multi=mean(abs(resultados$precio_mmulti-resultados$precio_real),na.rm = TRUE)
MAE_multi## [1] 58.53344MAPE_multi=MAE_multi/mean(resultados$precio_real)*100
MAPE_multi## [1] 18.7055data.frame(MAE_simple,MAE_multi)## MAE_simple MAE_multi
## 1 58.65593 58.53344data.frame(MAPE_simple,MAPE_multi)## MAPE_simple MAPE_multi
## 1 18.74465 18.7055Para el caso del error de predicción (MAE) en el caso del los dos modelos podemos evidenciar que es casi igual y unicamente varia en decimas. Es por esto que en el caso de usar cualquiera de los dos modelos se puede tener un error de predicción de alrededor 58 millones de pesos.
Y para el caso del error procentual de los modelos (MAPE) podemos ver que el modelo simple y el modelo multiple se equivoca en 18.7%.