Examen - Análisis descriptivo de datos utilizando R / Métodos estadísticos Multivariantes
Autor: José Palma B.
05-Septiembre-2024
# Como primer paso se carga la base de datos "bd_mtcars" => MTCars.csv
bd_mtcars <- read.csv(url("https://raw.githubusercontent.com/geovannychoez/prueba/master/MTCars.csv"), header = TRUE)
# Luego cargamos la base de datos "bd_usedcars" => UsedCars.csv
bd_usedcars <- read.csv(url("https://raw.githubusercontent.com/geovannychoez/prueba/master/UsedCars.csv"), header = TRUE)1) Análisis descriptivo únicamente a través de matriz gráfica de correlaciones
Set de datos bd_mtcars
Análisis descriptivo solo para las variables cuantitativas, seleccionamos las columnas utilizando select_if() de dplyr.
# Instalar y cargar la librería dplyr
library(dplyr)##
## Adjuntando el paquete: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union# Se selecciona solo las columnas cuantitativas
bd_mtcars_quantitative <- bd_mtcars %>%
select(car_ID, symboling, wheelbase, carlength, carwidth, carheight, curbweight,
enginesize, boreratio, stroke, compressionratio, horsepower, peakrpm,
citympg, highwaympg, price)
# Resumen de las variables cuantitativas
summary(bd_mtcars_quantitative)## car_ID symboling wheelbase carlength
## Min. : 1 Min. :-2.0000 Min. : 86.60 Min. :141.1
## 1st Qu.: 52 1st Qu.: 0.0000 1st Qu.: 94.50 1st Qu.:166.3
## Median :103 Median : 1.0000 Median : 97.00 Median :173.2
## Mean :103 Mean : 0.8341 Mean : 98.76 Mean :174.0
## 3rd Qu.:154 3rd Qu.: 2.0000 3rd Qu.:102.40 3rd Qu.:183.1
## Max. :205 Max. : 3.0000 Max. :120.90 Max. :208.1
## carwidth carheight curbweight enginesize boreratio
## Min. :60.30 Min. :47.80 Min. :1488 Min. : 61.0 Min. :2.54
## 1st Qu.:64.10 1st Qu.:52.00 1st Qu.:2145 1st Qu.: 97.0 1st Qu.:3.15
## Median :65.50 Median :54.10 Median :2414 Median :120.0 Median :3.31
## Mean :65.91 Mean :53.72 Mean :2556 Mean :126.9 Mean :3.33
## 3rd Qu.:66.90 3rd Qu.:55.50 3rd Qu.:2935 3rd Qu.:141.0 3rd Qu.:3.58
## Max. :72.30 Max. :59.80 Max. :4066 Max. :326.0 Max. :3.94
## stroke compressionratio horsepower peakrpm
## Min. :2.070 Min. : 7.00 Min. : 48.0 Min. :4150
## 1st Qu.:3.110 1st Qu.: 8.60 1st Qu.: 70.0 1st Qu.:4800
## Median :3.290 Median : 9.00 Median : 95.0 Median :5200
## Mean :3.255 Mean :10.14 Mean :104.1 Mean :5125
## 3rd Qu.:3.410 3rd Qu.: 9.40 3rd Qu.:116.0 3rd Qu.:5500
## Max. :4.170 Max. :23.00 Max. :288.0 Max. :6600
## citympg highwaympg price
## Min. :13.00 Min. :16.00 Min. : 5118
## 1st Qu.:19.00 1st Qu.:25.00 1st Qu.: 7788
## Median :24.00 Median :30.00 Median :10295
## Mean :25.22 Mean :30.75 Mean :13277
## 3rd Qu.:30.00 3rd Qu.:34.00 3rd Qu.:16503
## Max. :49.00 Max. :54.00 Max. :45400Se gráfica la correlación entre las variables cuantitativas del data set ‘bd_mtcars’.
# Genera la matriz de correlación
cor_matrix <- cor(bd_mtcars_quantitative[, sapply(bd_mtcars_quantitative, is.numeric)])
# Instalar y cargar la librería corrplot
library(corrplot)## corrplot 0.94 loaded# Matriz de correlación bd_mtcars
corrplot(cor_matrix, method = "circle", type = "upper", tl.cex = 0.8, addCoef.col = "blue")
Set de datos bd_usedcars
# Instalar y cargar la librería dplyr
library(dplyr)
# Filtrar solo las columnas cuantitativas
bd_usedcars_quantitative <- bd_usedcars %>%
select(Price, Year, Kilometer, Engine, Max.Power, Max.Torque, Length, Width, Height,
Seating.Capacity, Fuel.Tank.Capacity)
# Visualizamos el resumen solo de las variables cuantitativas
summary(bd_usedcars_quantitative)## Price Year Kilometer Engine
## Min. : 49000 Min. :1988 Min. : 0 Length:1874
## 1st Qu.: 500000 1st Qu.:2015 1st Qu.: 28020 Class :character
## Median : 842500 Median :2017 Median : 48798 Mode :character
## Mean : 1718279 Mean :2017 Mean : 53178
## 3rd Qu.: 1908250 3rd Qu.:2019 3rd Qu.: 71000
## Max. :35000000 Max. :2022 Max. :2000000
## Max.Power Max.Torque Length Width
## Length:1874 Length:1874 Min. :3099 Min. :1475
## Class :character Class :character 1st Qu.:3985 1st Qu.:1695
## Mode :character Mode :character Median :4360 Median :1770
## Mean :4282 Mean :1768
## 3rd Qu.:4620 3rd Qu.:1831
## Max. :5569 Max. :2220
## Height Seating.Capacity Fuel.Tank.Capacity
## Min. :1213 Min. :2.000 Min. : 15.00
## 1st Qu.:1485 1st Qu.:5.000 1st Qu.: 42.00
## Median :1544 Median :5.000 Median : 50.00
## Mean :1589 Mean :5.295 Mean : 52.22
## 3rd Qu.:1671 3rd Qu.:5.000 3rd Qu.: 60.00
## Max. :1995 Max. :8.000 Max. :105.00# Instalar y cargar librería dplyr
library(dplyr)
# Las variables cuantitativas deben estar en formato numérico
bd_usedcars_numeric <- bd_usedcars %>%
mutate(Price = as.numeric(Price),
Year = as.numeric(Year),
Kilometer = as.numeric(Kilometer),
Length = as.numeric(Length),
Width = as.numeric(Width),
Height = as.numeric(Height),
Seating.Capacity = as.numeric(Seating.Capacity),
Fuel.Tank.Capacity = as.numeric(Fuel.Tank.Capacity),
Engine = as.numeric(gsub(" cc", "", Engine)),
Max.Power = as.numeric(gsub(" bhp @.*", "", Max.Power)),
Max.Torque = as.numeric(gsub(" Nm @.*", "", Max.Torque)))## Warning: There were 2 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `Max.Power = as.numeric(gsub(" bhp @.*", "", Max.Power))`.
## Caused by warning:
## ! NAs introducidos por coerción
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 1 remaining warning.# Verificar transformación exitosa
head(bd_usedcars_numeric)## Make Model Price Year Kilometer
## 1 Honda Amaze 1.2 VX i-VTEC 505000 2017 87150
## 2 Maruti Suzuki Swift DZire VDI 450000 2014 75000
## 3 Hyundai i10 Magna 1.2 Kappa2 220000 2011 67000
## 4 Toyota Glanza G 799000 2019 37500
## 5 Toyota Innova 2.4 VX 7 STR [2016-2020] 1950000 2018 69000
## 6 Maruti Suzuki Ciaz ZXi 675000 2017 73315
## Fuel.Type Transmission Location Color Owner Seller.Type Engine Max.Power
## 1 Petrol Manual Pune Grey First Corporate 1198 87
## 2 Diesel Manual Ludhiana White Second Individual 1248 74
## 3 Petrol Manual Lucknow Maroon First Individual 1197 79
## 4 Petrol Manual Mangalore Red First Individual 1197 82
## 5 Diesel Manual Mumbai Grey First Individual 2393 148
## 6 Petrol Manual Pune Grey First Individual 1373 91
## Max.Torque Drivetrain Length Width Height Seating.Capacity Fuel.Tank.Capacity
## 1 109.0000 FWD 3990 1680 1505 5 35
## 2 190.0000 FWD 3995 1695 1555 5 42
## 3 112.7619 FWD 3585 1595 1550 5 35
## 4 113.0000 FWD 3995 1745 1510 5 37
## 5 343.0000 RWD 4735 1830 1795 7 55
## 6 130.0000 FWD 4490 1730 1485 5 43# Instalar y cargar librería corrplot
library(corrplot)
# Seleccionar las variables cuantitativas
bd_usedcars_quantitative <- bd_usedcars_numeric %>%
select(Price, Year, Kilometer, Length, Width, Height, Seating.Capacity, Fuel.Tank.Capacity, Engine, Max.Power, Max.Torque)
# Calcular la matriz de correlación
cor_matrix <- cor(bd_usedcars_quantitative, use = "complete.obs")
# Crea Matriz de correlación bd_usedcars
corrplot(cor_matrix,
method = "circle",
type = "upper",
tl.col = "purple",
tl.srt = 45,
title = "Matriz de Correlación base de datos bd_usedcars",
addCoef.col = "blue")
Matriz gráfica de correlaciones importantes (final)
Base de datos bd_mtcars
bd_mtcars <- read.csv(url("https://raw.githubusercontent.com/geovannychoez/prueba/master/MTCars.csv"), header = TRUE)
names(bd_mtcars) <- c('car_ID', 'symboling', 'CarName', 'fueltype', 'aspiration','doornumber','carbody',
'drivewheel', 'enginelocation', 'wheelbase', 'carlength', 'carwidth', 'carheight',
'curbweight','enginetype','cylindrenumber', 'enginesize','fuelsystem','boreratio',
'stroke', 'compressionratio', 'horsepower', 'peakrpm', 'citympg', 'highwaympg', 'price')
data_all_mtcars <- na.omit(bd_mtcars[, c('price','enginesize','carwidth','carlength',
'wheelbase','carheight','car_ID')])
corrplot.mixed(cor(data_all_mtcars),
lower = "number",
upper = "circle",
tl.col = "black")
Analisis El gráfico Matriz Correlación del set de
datos bd_mtcars, nos indica que la variable
price está altamente correlacionado de forma positiva con
las variables enginesize, horsepower,
curbweight, carwidth y carlength.
Se concluye que los vehículos con dimensiones más amplias, motores
grandes, mayor potencia, mayor peso tienen el precio más altos.
Matriz gráfica de correlaciones importantes (final)
Base de datos bd_usedcars
# Cargamos la base de datos "bd_usedcars" => UsedCars.csv
bd_usedcars <- read.csv(url("https://raw.githubusercontent.com/geovannychoez/prueba/master/UsedCars.csv"), header = TRUE)
names(bd_usedcars) <- c('Make','Model','Price','Year','Kilometer',
'Fuel.Type','Transmission','Location','Color','Owner',
'Seller.Type','Engine','Max.Power','Max.Torque','Drivetrain',
'Length','Width','Heigth','Seating.Capcity','Fuel.Tank.Capacite')
data_all_cuantitativas <- na.omit(bd_usedcars[, c('Fuel.Tank.Capacite','Length','Width',
'Price','Seating.Capcity','Year','Kilometer','Heigth')])
corrplot.mixed(cor(data_all_cuantitativas),
lower = "number",
upper = "circle",
tl.col = "black")
Analisis El gráfico matriz de correlación para el
set de datos bd_usedcars, nos indica que la variable
Price esta altamente correlacionada de forma positiva con
las variables Fuel.Tank.Capacity, Length,
Width y Seating.Capcity.
La correlación positiva con Length y Width
indica que los vehículos más grandes suelen tener precios más altos. La
relación con Price y Seating.Capcity indica
que la capacidad del vehiculo aumentan el precio.
La correlación positiva más cercana a 1 es entre
Fuel.Tank.Capacity y la variable Length
————————————————————————————-
ANÁLISIS REGRESIÓN LINEAL MÚLTIPLE (INICIAL) bd_mtcars
————————————————————————————-
# Como primer paso se carga la base de datos "bd_mtcars" => MTCars.csv
bd_mtcars <- read.csv(url("https://raw.githubusercontent.com/geovannychoez/prueba/master/MTCars.csv"), header = TRUE)
names(bd_mtcars) <- c('car_ID', 'symboling', 'CarName', 'fueltype', 'aspiration','doornumber','carbody',
'drivewheel', 'enginelocation', 'wheelbase', 'carlength', 'carwidth', 'carheight',
'curbweight','enginetype','cylindrenumber', 'enginesize','fuelsystem','boreratio',
'stroke', 'compressionratio', 'horsepower', 'peakrpm', 'citympg', 'highwaympg', 'price')
# Se crea la variable 'data_correlacion1' con el data set bd_mtcars.
data_correlacion <- na.omit(bd_mtcars[, c('price','enginesize','carwidth','carlength','car_ID')])1) Ecuación matemática del modelo (y=x1+x2+x3+x4)
Primer Modelo
Se crea la variable ‘modelo’ usando el dataset ‘data_correlacion’, se define las variables independientes y dependiente.
Variable Dependiente ‘y’: price Modelo de regresión para predecir el precio usando las variables independientes.
Variables Independientes ‘x’: ‘enginesize’,‘carwidth’,‘carlength’,‘car_ID’
y=x1+x2+x3+x4
X=as.matrix(cbind("ones"=c(1:1),data_correlacion[,2:5]))
X## ones enginesize carwidth carlength car_ID
## 1 1 130 64.1 168.8 1
## 2 1 130 64.1 168.8 2
## 3 1 152 65.5 171.2 3
## 4 1 109 66.2 176.6 4
## 5 1 136 66.4 176.6 5
## 6 1 136 66.3 177.3 6
## 7 1 136 71.4 192.7 7
## 8 1 136 71.4 192.7 8
## 9 1 131 71.4 192.7 9
## 10 1 131 67.9 178.2 10
## 11 1 108 64.8 176.8 11
## 12 1 108 64.8 176.8 12
## 13 1 164 64.8 176.8 13
## 14 1 164 64.8 176.8 14
## 15 1 164 66.9 189.0 15
## 16 1 209 66.9 189.0 16
## 17 1 209 67.9 193.8 17
## 18 1 209 70.9 197.0 18
## 19 1 61 60.3 141.1 19
## 20 1 90 63.6 155.9 20
## 21 1 90 63.6 158.8 21
## 22 1 90 63.8 157.3 22
## 23 1 90 63.8 157.3 23
## 24 1 98 63.8 157.3 24
## 25 1 90 63.8 157.3 25
## 26 1 90 63.8 157.3 26
## 27 1 90 63.8 157.3 27
## 28 1 98 63.8 157.3 28
## 29 1 122 64.6 174.6 29
## 30 1 156 66.3 173.2 30
## 31 1 92 63.9 144.6 31
## 32 1 92 63.9 144.6 32
## 33 1 79 64.0 150.0 33
## 34 1 92 64.0 150.0 34
## 35 1 92 64.0 150.0 35
## 36 1 92 64.0 163.4 36
## 37 1 92 63.9 157.1 37
## 38 1 110 65.2 167.5 38
## 39 1 110 65.2 167.5 39
## 40 1 110 65.2 175.4 40
## 41 1 110 62.5 175.4 41
## 42 1 110 65.2 175.4 42
## 43 1 110 66.0 169.1 43
## 44 1 111 61.8 170.7 44
## 45 1 90 63.6 155.9 45
## 46 1 90 63.6 155.9 46
## 47 1 119 65.2 172.6 47
## 48 1 258 69.6 199.6 48
## 49 1 258 69.6 199.6 49
## 50 1 326 70.6 191.7 50
## 51 1 91 64.2 159.1 51
## 52 1 91 64.2 159.1 52
## 53 1 91 64.2 159.1 53
## 54 1 91 64.2 166.8 54
## 55 1 91 64.2 166.8 55
## 56 1 70 65.7 169.0 56
## 57 1 70 65.7 169.0 57
## 58 1 70 65.7 169.0 58
## 59 1 80 65.7 169.0 59
## 60 1 122 66.5 177.8 60
## 61 1 122 66.5 177.8 61
## 62 1 122 66.5 177.8 62
## 63 1 122 66.5 177.8 63
## 64 1 122 66.5 177.8 64
## 65 1 122 66.5 177.8 65
## 66 1 140 66.1 175.0 66
## 67 1 134 66.1 175.0 67
## 68 1 183 70.3 190.9 68
## 69 1 183 70.3 190.9 69
## 70 1 183 70.3 187.5 70
## 71 1 183 71.7 202.6 71
## 72 1 234 71.7 202.6 72
## 73 1 234 70.5 180.3 73
## 74 1 308 71.7 208.1 74
## 75 1 304 72.0 199.2 75
## 76 1 140 68.0 178.4 76
## 77 1 92 64.4 157.3 77
## 78 1 92 64.4 157.3 78
## 79 1 92 64.4 157.3 79
## 80 1 98 63.8 157.3 80
## 81 1 110 65.4 173.0 81
## 82 1 122 65.4 173.0 82
## 83 1 156 66.3 173.2 83
## 84 1 156 66.3 173.2 84
## 85 1 156 66.3 173.2 85
## 86 1 122 65.4 172.4 86
## 87 1 122 65.4 172.4 87
## 88 1 110 65.4 172.4 88
## 89 1 110 65.4 172.4 89
## 90 1 97 63.8 165.3 90
## 91 1 103 63.8 165.3 91
## 92 1 97 63.8 165.3 92
## 93 1 97 63.8 165.3 93
## 94 1 97 63.8 170.2 94
## 95 1 97 63.8 165.3 95
## 96 1 97 63.8 165.6 96
## 97 1 97 63.8 165.3 97
## 98 1 97 63.8 170.2 98
## 99 1 97 63.8 162.4 99
## 100 1 120 65.2 173.4 100
## 101 1 120 65.2 173.4 101
## 102 1 181 66.5 181.7 102
## 103 1 181 66.5 184.6 103
## 104 1 181 66.5 184.6 104
## 105 1 181 67.9 170.7 105
## 106 1 181 67.9 170.7 106
## 107 1 181 67.9 178.5 107
## 108 1 120 68.4 186.7 108
## 109 1 152 68.4 186.7 109
## 110 1 120 68.4 198.9 110
## 111 1 152 68.4 198.9 111
## 112 1 120 68.4 186.7 112
## 113 1 152 68.4 186.7 113
## 114 1 120 68.4 198.9 114
## 115 1 152 68.4 198.9 115
## 116 1 120 68.4 186.7 116
## 117 1 152 68.4 186.7 117
## 118 1 134 68.3 186.7 118
## 119 1 90 63.8 157.3 119
## 120 1 98 63.8 157.3 120
## 121 1 90 63.8 157.3 121
## 122 1 90 63.8 167.3 122
## 123 1 98 63.8 167.3 123
## 124 1 122 64.6 174.6 124
## 125 1 156 66.3 173.2 125
## 126 1 151 68.3 168.9 126
## 127 1 194 65.0 168.9 127
## 128 1 194 65.0 168.9 128
## 129 1 194 65.0 168.9 129
## 130 1 203 72.3 175.7 130
## 131 1 132 66.5 181.5 131
## 132 1 132 66.6 176.8 132
## 133 1 121 66.5 186.6 133
## 134 1 121 66.5 186.6 134
## 135 1 121 66.5 186.6 135
## 136 1 121 66.5 186.6 136
## 137 1 121 66.5 186.6 137
## 138 1 121 66.5 186.6 138
## 139 1 97 63.4 156.9 139
## 140 1 108 63.6 157.9 140
## 141 1 108 63.8 157.3 141
## 142 1 108 65.4 172.0 142
## 143 1 108 65.4 172.0 143
## 144 1 108 65.4 172.0 144
## 145 1 108 65.4 172.0 145
## 146 1 108 65.4 172.0 146
## 147 1 108 65.4 173.5 147
## 148 1 108 65.4 173.5 148
## 149 1 108 65.4 173.6 149
## 150 1 108 65.4 173.6 150
## 151 1 92 63.6 158.7 151
## 152 1 92 63.6 158.7 152
## 153 1 92 63.6 158.7 153
## 154 1 92 63.6 169.7 154
## 155 1 92 63.6 169.7 155
## 156 1 92 63.6 169.7 156
## 157 1 98 64.4 166.3 157
## 158 1 98 64.4 166.3 158
## 159 1 110 64.4 166.3 159
## 160 1 110 64.4 166.3 160
## 161 1 98 64.4 166.3 161
## 162 1 98 64.4 166.3 162
## 163 1 98 64.4 166.3 163
## 164 1 98 64.0 168.7 164
## 165 1 98 64.0 168.7 165
## 166 1 98 64.0 168.7 166
## 167 1 98 64.0 168.7 167
## 168 1 146 65.6 176.2 168
## 169 1 146 65.6 176.2 169
## 170 1 146 65.6 176.2 170
## 171 1 146 65.6 176.2 171
## 172 1 146 65.6 176.2 172
## 173 1 146 65.6 176.2 173
## 174 1 122 66.5 175.6 174
## 175 1 110 66.5 175.6 175
## 176 1 122 66.5 175.6 176
## 177 1 122 66.5 175.6 177
## 178 1 122 66.5 175.6 178
## 179 1 171 67.7 183.5 179
## 180 1 171 67.7 183.5 180
## 181 1 171 66.5 187.8 181
## 182 1 161 66.5 187.8 182
## 183 1 97 65.5 171.7 183
## 184 1 109 65.5 171.7 184
## 185 1 97 65.5 171.7 185
## 186 1 109 65.5 171.7 186
## 187 1 109 65.5 171.7 187
## 188 1 97 65.5 171.7 188
## 189 1 109 65.5 171.7 189
## 190 1 109 64.2 159.3 190
## 191 1 109 64.0 165.7 191
## 192 1 136 66.9 180.2 192
## 193 1 97 66.9 180.2 193
## 194 1 109 66.9 183.1 194
## 195 1 141 67.2 188.8 195
## 196 1 141 67.2 188.8 196
## 197 1 141 67.2 188.8 197
## 198 1 141 67.2 188.8 198
## 199 1 130 67.2 188.8 199
## 200 1 130 67.2 188.8 200
## 201 1 141 68.9 188.8 201
## 202 1 141 68.8 188.8 202
## 203 1 173 68.9 188.8 203
## 204 1 145 68.9 188.8 204
## 205 1 141 68.9 188.8 205A=t(X)%*%X
A#Matriz de COV## ones enginesize carwidth carlength car_ID
## ones 205.0 26016 13511.1 35680.1 21115
## enginesize 26016.0 3655380 1728059.8 4599686.4 2662549
## carwidth 13511.1 1728060 891425.7 2356138.3 1393003
## carlength 35680.1 4599686 2356138.3 6241145.9 3700527
## car_ID 21115.0 2662549 1393003.3 3700526.9 2892755InvA=solve(A)
InvA## ones enginesize carwidth carlength
## ones 10.1154226552 4.445802e-03 -1.957667e-01 1.287297e-02
## enginesize 0.0044458025 6.512097e-06 -6.522458e-05 -5.881241e-06
## carwidth -0.1957667107 -6.522458e-05 4.404468e-03 -5.001652e-04
## carlength 0.0128729663 -5.881241e-06 -5.001652e-04 1.218060e-04
## car_ID -0.0001235502 4.873728e-07 7.852178e-06 -3.515124e-06
## car_ID
## ones -1.235502e-04
## enginesize 4.873728e-07
## carwidth 7.852178e-06
## carlength -3.515124e-06
## car_ID 1.514407e-06tXy=t(X)%*%as.matrix(data_correlacion[,1])
tXy## [,1]
## ones 2721726
## enginesize 404731766
## carwidth 182037637
## carlength 487445423
## car_ID 269790652InvA%*%tXy## [,1]
## ones -64610.63040
## enginesize 127.28328
## carwidth 872.36463
## carlength 32.92191
## car_ID -14.48069FUNCIÓN LINEAL DEL MODELO: Ecuación matemática que describe la relación entre las variables independientes ‘curbweight’,‘enginesize’,‘horsepower’ y la variable dependiente ‘price’. La relación se asume lineal, lo que significa que los cambios en las variables independientes afectan la variable dependiente de manera proporcional.
modelo=lm(data_correlacion$price~data_correlacion$enginesize+data_correlacion$carwidth+data_correlacion$carlength+data_correlacion$car_ID)
modelo##
## Call:
## lm(formula = data_correlacion$price ~ data_correlacion$enginesize +
## data_correlacion$carwidth + data_correlacion$carlength +
## data_correlacion$car_ID)
##
## Coefficients:
## (Intercept) data_correlacion$enginesize
## -64610.63 127.28
## data_correlacion$carwidth data_correlacion$carlength
## 872.36 32.92
## data_correlacion$car_ID
## -14.48Prueba de hipótesis global - Prueba F
F-statistic: 205.5 on 4 and 200 DF. => significancia global del modelo.
p-value: < 2.2e-16 => significancia estadística de cada uno de los predictores (variables independientes ‘enginesize’,‘carwidth’,‘carlength’,‘car_ID’) del modelo.
Prueba de hipótesis individuales - Prueba t
(Intercept) 4.44e-08
data_correlacion$enginesize < 2e-16
data_correlacion$carwidth 0.000297
data_correlacion$carlength 0.404300 Se descarta la variable carlength
data_correlacion$car_ID 0.001157
Coeficiente de Determinación (R2)
Multiple R-squared (R2): 0.8043 => Variabilidad de la variable dependiente a partir de las variables independientes => 80.43 %
Ajusted R-squared (R2 ajustado): 0.8004 => versión ajustada del Multiple R-squared => 80.04 %
summary(modelo)##
## Call:
## lm(formula = data_correlacion$price ~ data_correlacion$enginesize +
## data_correlacion$carwidth + data_correlacion$carlength +
## data_correlacion$car_ID)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8059.8 -2047.0 -337.5 1522.0 16549.5
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -64610.630 11352.006 -5.692 4.44e-08 ***
## data_correlacion$enginesize 127.283 9.108 13.974 < 2e-16 ***
## data_correlacion$carwidth 872.365 236.879 3.683 0.000297 ***
## data_correlacion$carlength 32.922 39.393 0.836 0.404300
## data_correlacion$car_ID -14.481 4.392 -3.297 0.001157 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3569 on 200 degrees of freedom
## Multiple R-squared: 0.8043, Adjusted R-squared: 0.8004
## F-statistic: 205.5 on 4 and 200 DF, p-value: < 2.2e-16————————————————————————————-
ANÁLISIS REGRESIÓN LINEAL MÚLTIPLE (FINAL) bd_mtcars
————————————————————————————-
# Como primer paso se carga la base de datos "bd_mtcars" => MTCars.csv
bd_mtcars <- read.csv(url("https://raw.githubusercontent.com/geovannychoez/prueba/master/MTCars.csv"), header = TRUE)
names(bd_mtcars) <- c('car_ID', 'symboling', 'CarName', 'fueltype', 'aspiration','doornumber','carbody',
'drivewheel', 'enginelocation', 'wheelbase', 'carlength', 'carwidth', 'carheight',
'curbweight','enginetype','cylindrenumber', 'enginesize','fuelsystem','boreratio',
'stroke', 'compressionratio', 'horsepower', 'peakrpm', 'citympg', 'highwaympg', 'price')
# Se crea la variable 'data_correlacion1' con el data set bd_mtcars.
data_correlacion <- na.omit(bd_mtcars[, c('price','enginesize','carwidth','car_ID')])1) Ecuación matemática del modelo (y=x1+x2+x3)
Modelo Final
Se crea la variable ‘modelo’ usando el dataset ‘data_correlacion’, se define las variables independientes y dependiente.
Variable Dependiente ‘y’: price Modelo de regresión para predecir el precio usando las variables independientes.
Variables Independientes ‘x’: ‘enginesize’,‘carwidth’,‘car_ID’
y=x1+x2+x3
X=as.matrix(cbind("ones"=c(1:1),data_correlacion[,2:4]))
X## ones enginesize carwidth car_ID
## 1 1 130 64.1 1
## 2 1 130 64.1 2
## 3 1 152 65.5 3
## 4 1 109 66.2 4
## 5 1 136 66.4 5
## 6 1 136 66.3 6
## 7 1 136 71.4 7
## 8 1 136 71.4 8
## 9 1 131 71.4 9
## 10 1 131 67.9 10
## 11 1 108 64.8 11
## 12 1 108 64.8 12
## 13 1 164 64.8 13
## 14 1 164 64.8 14
## 15 1 164 66.9 15
## 16 1 209 66.9 16
## 17 1 209 67.9 17
## 18 1 209 70.9 18
## 19 1 61 60.3 19
## 20 1 90 63.6 20
## 21 1 90 63.6 21
## 22 1 90 63.8 22
## 23 1 90 63.8 23
## 24 1 98 63.8 24
## 25 1 90 63.8 25
## 26 1 90 63.8 26
## 27 1 90 63.8 27
## 28 1 98 63.8 28
## 29 1 122 64.6 29
## 30 1 156 66.3 30
## 31 1 92 63.9 31
## 32 1 92 63.9 32
## 33 1 79 64.0 33
## 34 1 92 64.0 34
## 35 1 92 64.0 35
## 36 1 92 64.0 36
## 37 1 92 63.9 37
## 38 1 110 65.2 38
## 39 1 110 65.2 39
## 40 1 110 65.2 40
## 41 1 110 62.5 41
## 42 1 110 65.2 42
## 43 1 110 66.0 43
## 44 1 111 61.8 44
## 45 1 90 63.6 45
## 46 1 90 63.6 46
## 47 1 119 65.2 47
## 48 1 258 69.6 48
## 49 1 258 69.6 49
## 50 1 326 70.6 50
## 51 1 91 64.2 51
## 52 1 91 64.2 52
## 53 1 91 64.2 53
## 54 1 91 64.2 54
## 55 1 91 64.2 55
## 56 1 70 65.7 56
## 57 1 70 65.7 57
## 58 1 70 65.7 58
## 59 1 80 65.7 59
## 60 1 122 66.5 60
## 61 1 122 66.5 61
## 62 1 122 66.5 62
## 63 1 122 66.5 63
## 64 1 122 66.5 64
## 65 1 122 66.5 65
## 66 1 140 66.1 66
## 67 1 134 66.1 67
## 68 1 183 70.3 68
## 69 1 183 70.3 69
## 70 1 183 70.3 70
## 71 1 183 71.7 71
## 72 1 234 71.7 72
## 73 1 234 70.5 73
## 74 1 308 71.7 74
## 75 1 304 72.0 75
## 76 1 140 68.0 76
## 77 1 92 64.4 77
## 78 1 92 64.4 78
## 79 1 92 64.4 79
## 80 1 98 63.8 80
## 81 1 110 65.4 81
## 82 1 122 65.4 82
## 83 1 156 66.3 83
## 84 1 156 66.3 84
## 85 1 156 66.3 85
## 86 1 122 65.4 86
## 87 1 122 65.4 87
## 88 1 110 65.4 88
## 89 1 110 65.4 89
## 90 1 97 63.8 90
## 91 1 103 63.8 91
## 92 1 97 63.8 92
## 93 1 97 63.8 93
## 94 1 97 63.8 94
## 95 1 97 63.8 95
## 96 1 97 63.8 96
## 97 1 97 63.8 97
## 98 1 97 63.8 98
## 99 1 97 63.8 99
## 100 1 120 65.2 100
## 101 1 120 65.2 101
## 102 1 181 66.5 102
## 103 1 181 66.5 103
## 104 1 181 66.5 104
## 105 1 181 67.9 105
## 106 1 181 67.9 106
## 107 1 181 67.9 107
## 108 1 120 68.4 108
## 109 1 152 68.4 109
## 110 1 120 68.4 110
## 111 1 152 68.4 111
## 112 1 120 68.4 112
## 113 1 152 68.4 113
## 114 1 120 68.4 114
## 115 1 152 68.4 115
## 116 1 120 68.4 116
## 117 1 152 68.4 117
## 118 1 134 68.3 118
## 119 1 90 63.8 119
## 120 1 98 63.8 120
## 121 1 90 63.8 121
## 122 1 90 63.8 122
## 123 1 98 63.8 123
## 124 1 122 64.6 124
## 125 1 156 66.3 125
## 126 1 151 68.3 126
## 127 1 194 65.0 127
## 128 1 194 65.0 128
## 129 1 194 65.0 129
## 130 1 203 72.3 130
## 131 1 132 66.5 131
## 132 1 132 66.6 132
## 133 1 121 66.5 133
## 134 1 121 66.5 134
## 135 1 121 66.5 135
## 136 1 121 66.5 136
## 137 1 121 66.5 137
## 138 1 121 66.5 138
## 139 1 97 63.4 139
## 140 1 108 63.6 140
## 141 1 108 63.8 141
## 142 1 108 65.4 142
## 143 1 108 65.4 143
## 144 1 108 65.4 144
## 145 1 108 65.4 145
## 146 1 108 65.4 146
## 147 1 108 65.4 147
## 148 1 108 65.4 148
## 149 1 108 65.4 149
## 150 1 108 65.4 150
## 151 1 92 63.6 151
## 152 1 92 63.6 152
## 153 1 92 63.6 153
## 154 1 92 63.6 154
## 155 1 92 63.6 155
## 156 1 92 63.6 156
## 157 1 98 64.4 157
## 158 1 98 64.4 158
## 159 1 110 64.4 159
## 160 1 110 64.4 160
## 161 1 98 64.4 161
## 162 1 98 64.4 162
## 163 1 98 64.4 163
## 164 1 98 64.0 164
## 165 1 98 64.0 165
## 166 1 98 64.0 166
## 167 1 98 64.0 167
## 168 1 146 65.6 168
## 169 1 146 65.6 169
## 170 1 146 65.6 170
## 171 1 146 65.6 171
## 172 1 146 65.6 172
## 173 1 146 65.6 173
## 174 1 122 66.5 174
## 175 1 110 66.5 175
## 176 1 122 66.5 176
## 177 1 122 66.5 177
## 178 1 122 66.5 178
## 179 1 171 67.7 179
## 180 1 171 67.7 180
## 181 1 171 66.5 181
## 182 1 161 66.5 182
## 183 1 97 65.5 183
## 184 1 109 65.5 184
## 185 1 97 65.5 185
## 186 1 109 65.5 186
## 187 1 109 65.5 187
## 188 1 97 65.5 188
## 189 1 109 65.5 189
## 190 1 109 64.2 190
## 191 1 109 64.0 191
## 192 1 136 66.9 192
## 193 1 97 66.9 193
## 194 1 109 66.9 194
## 195 1 141 67.2 195
## 196 1 141 67.2 196
## 197 1 141 67.2 197
## 198 1 141 67.2 198
## 199 1 130 67.2 199
## 200 1 130 67.2 200
## 201 1 141 68.9 201
## 202 1 141 68.8 202
## 203 1 173 68.9 203
## 204 1 145 68.9 204
## 205 1 141 68.9 205A=t(X)%*%X
A#Matriz de COV## ones enginesize carwidth car_ID
## ones 205.0 26016 13511.1 21115
## enginesize 26016.0 3655380 1728059.8 2662549
## carwidth 13511.1 1728060 891425.7 1393003
## car_ID 21115.0 2662549 1393003.3 2892755InvA=solve(A)
InvA## ones enginesize carwidth car_ID
## ones 8.7549543259 5.067356e-03 -1.429072e-01 2.479426e-04
## enginesize 0.0050673564 6.228129e-06 -8.937438e-05 3.176498e-07
## carwidth -0.1429071867 -8.937438e-05 2.350668e-03 -6.581774e-06
## car_ID 0.0002479426 3.176498e-07 -6.581774e-06 1.412966e-06tXy=t(X)%*%as.matrix(data_correlacion[,1])
tXy## [,1]
## ones 2721726
## enginesize 404731766
## carwidth 182037637
## car_ID 269790652InvA%*%tXy## [,1]
## ones -68089.95407
## enginesize 128.87287
## carwidth 1007.54998
## car_ID -13.53061FUNCIÓN LINEAL DEL MODELO: Ecuación matemática que describe la relación entre las variables independientes ‘curbweight’,‘enginesize’,‘horsepower’ y la variable dependiente ‘price’. La relación se asume lineal, lo que significa que los cambios en las variables independientes afectan la variable dependiente de manera proporcional.
modelo=lm(data_correlacion$price~data_correlacion$enginesize+data_correlacion$carwidth+data_correlacion$car_ID)
modelo##
## Call:
## lm(formula = data_correlacion$price ~ data_correlacion$enginesize +
## data_correlacion$carwidth + data_correlacion$car_ID)
##
## Coefficients:
## (Intercept) data_correlacion$enginesize
## -68089.95 128.87
## data_correlacion$carwidth data_correlacion$car_ID
## 1007.55 -13.53Prueba de hipótesis global - Prueba F
F-statistic: 274.2 on 3 and 201 DF. => significancia global del modelo.
p-value: < 2.2e-16 => significancia estadística de cada uno de los predictores (variables independientes ‘curbweight’,‘enginesize’,‘horsepower’) del modelo.
Las tres variables independientes del modelo son diferentes a 0.
Prueba de hipótesis individuales - Prueba t
(Intercept) 8.07e-10
data_correlacion$enginesize < 2e-16
data_correlacion$carwidth 2.22e-08
data_correlacion$car_ID 0.00164
Coeficiente de Determinación (R2)
Multiple R-squared (R2): 0.8036 => Variabilidad de la variable dependiente a partir de las variables independientes => 80.36 %
Ajusted R-squared (R2 ajustado): 0.8007 => versión ajustada del Multiple R-squared => 80.07 %
summary(modelo)##
## Call:
## lm(formula = data_correlacion$price ~ data_correlacion$enginesize +
## data_correlacion$carwidth + data_correlacion$car_ID)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8379.1 -2121.5 -539.5 1751.9 16371.3
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -68089.954 10553.135 -6.452 8.07e-10 ***
## data_correlacion$enginesize 128.873 8.901 14.479 < 2e-16 ***
## data_correlacion$carwidth 1007.550 172.922 5.827 2.22e-08 ***
## data_correlacion$car_ID -13.531 4.240 -3.192 0.00164 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3567 on 201 degrees of freedom
## Multiple R-squared: 0.8036, Adjusted R-squared: 0.8007
## F-statistic: 274.2 on 3 and 201 DF, p-value: < 2.2e-16————————————————————————————-
ANÁLISIS REGRESIÓN LINEAL MÚLTIPLE (INICIAL) bd_mtcars
————————————————————————————-
# Cargamos la base de datos "bd_usedcars" => UsedCars.csv
bd_usedcars <- read.csv(url("https://raw.githubusercontent.com/geovannychoez/prueba/master/UsedCars.csv"), header = TRUE)
names(bd_usedcars) <- c('Make','Model','Price','Year','Kilometer',
'Fuel.Type','Transmission','Location','Color','Owner',
'Seller.Type','Engine','Max.Power','Max.Torque','Drivetrain',
'Length','Width','Heigth','Seating.Capcity','Fuel.Tank.Capacite')
# Se crea la variable 'data_correlacion1' con el data set bd_mtcars.
data_correlacion2 <- na.omit(bd_usedcars[, c('Price','Fuel.Tank.Capacite','Length','Width','Heigth')])1) Ecuación matemática del modelo (y=x1+x2+x3+x4)
Modelo Final
Se crea la variable ‘modelo’ usando el dataset ‘data_correlacion’, se define las variables independientes y dependiente.
Variable Dependiente ‘y’: price Modelo de regresión para predecir el precio usando las variables independientes.
Variables Independientes ‘x’: ‘Fuel.Tank.Capacite’,‘Length’,‘Width’
y=x1+x2+x3+x4
X=as.matrix(cbind("ones"=c(1:1),data_correlacion2[,2:5]))
X## ones Fuel.Tank.Capacite Length Width Heigth
## 1 1 35.0 3990 1680 1505
## 2 1 42.0 3995 1695 1555
## 3 1 35.0 3585 1595 1550
## 4 1 37.0 3995 1745 1510
## 5 1 55.0 4735 1830 1795
## 6 1 43.0 4490 1730 1485
## 7 1 51.0 4439 1821 1612
## 8 1 50.0 4670 1814 1476
## 9 1 50.0 4331 1822 1671
## 10 1 45.0 3985 1734 1505
## 11 1 28.0 3679 1579 1478
## 12 1 43.0 4490 1730 1485
## 13 1 50.0 4598 1894 1706
## 14 1 45.0 3971 1682 1469
## 15 1 35.0 3695 1600 1560
## 16 1 35.0 3445 1515 1475
## 17 1 37.0 3995 1745 1510
## 18 1 32.0 3655 1620 1675
## 19 1 60.0 4270 1780 1630
## 20 1 27.0 3565 1520 1564
## 21 1 55.0 4384 1699 1466
## 22 1 35.0 3610 1645 1560
## 23 1 45.0 3995 1770 1605
## 24 1 60.0 3545 1490 1475
## 25 1 43.0 3775 1680 1620
## 26 1 60.0 4270 1780 1630
## 27 1 35.0 3610 1680 1500
## 28 1 45.0 3985 1734 1505
## 29 1 40.0 3999 1734 1601
## 30 1 45.0 3995 1770 1605
## 31 1 60.0 4270 1780 1630
## 32 1 52.0 3999 1765 1708
## 33 1 35.0 3565 1525 1590
## 34 1 35.0 3746 1647 1535
## 35 1 35.0 3992 1677 1537
## 36 1 55.0 4735 1830 1795
## 37 1 66.0 4656 1890 1639
## 38 1 55.0 4270 1780 1665
## 39 1 70.0 4804 2141 1796
## 40 1 55.0 4620 1775 1475
## 41 1 63.0 4701 1826 1427
## 42 1 70.0 4082 1777 1297
## 43 1 45.0 3985 1734 1505
## 44 1 60.0 3920 1726 1930
## 45 1 37.0 3995 1745 1500
## 46 1 35.0 3600 1600 1560
## 47 1 43.0 4490 1730 1485
## 48 1 43.0 4490 1730 1485
## 49 1 60.0 4270 1780 1630
## 50 1 60.0 4270 1780 1630
## 51 1 28.0 3679 1579 1478
## 52 1 60.0 4655 1835 1760
## 53 1 35.0 3746 1647 1535
## 54 1 55.0 4585 1765 1760
## 55 1 67.0 4657 1881 1678
## 56 1 60.0 4395 1818 1640
## 57 1 60.0 4430 1817 1975
## 58 1 35.0 3610 1680 1500
## 59 1 57.0 4633 1811 1429
## 60 1 40.0 4440 1695 1495
## 61 1 45.0 3970 1682 1453
## 62 1 48.0 3995 1790 1640
## 63 1 40.0 3675 1475 1800
## 64 1 43.0 3765 1660 1520
## 65 1 67.0 4648 1881 1661
## 66 1 80.0 4795 1855 1835
## 67 1 50.0 4545 1750 1450
## 68 1 37.0 3845 1735 1530
## 69 1 37.0 3995 1775 1505
## 70 1 50.0 4456 1796 1416
## 71 1 40.0 4440 1695 1495
## 72 1 45.0 3795 1680 1427
## 73 1 40.0 3955 1694 1544
## 74 1 45.0 3970 1682 1453
## 75 1 35.0 3990 1680 1505
## 76 1 70.0 4825 1825 1480
## 77 1 57.0 3985 1820 1844
## 78 1 66.0 4596 1770 1447
## 79 1 64.0 4385 1831 1608
## 80 1 37.0 3995 1745 1500
## 81 1 63.0 4454 2044 1545
## 82 1 37.0 3995 1745 1500
## 83 1 60.0 4270 1780 1630
## 84 1 55.0 4384 1699 1466
## 85 1 66.0 4596 1770 1447
## 86 1 65.0 4825 1825 1480
## 87 1 37.0 3995 1735 1515
## 88 1 50.0 4331 1822 1671
## 89 1 35.0 3599 1495 1700
## 90 1 48.0 3995 1790 1640
## 91 1 75.0 4931 1983 1676
## 92 1 59.0 4686 1810 1409
## 93 1 45.0 3985 1734 1505
## 94 1 43.0 4375 1700 1475
## 95 1 35.0 3990 1680 1505
## 96 1 55.0 4540 1760 1480
## 97 1 45.0 3985 1734 1505
## 98 1 43.0 3765 1660 1520
## 99 1 60.0 4270 1780 1630
## 100 1 65.0 4915 1874 1455
## 101 1 63.0 4454 2044 1545
## 102 1 42.0 3995 1821 1627
## 103 1 37.0 3840 1735 1530
## 104 1 57.0 3985 1820 1844
## 105 1 42.0 4420 1695 1480
## 106 1 80.0 4879 1854 1474
## 107 1 80.0 4705 1840 1850
## 108 1 44.0 3995 1706 1570
## 109 1 55.0 4386 1699 1466
## 110 1 35.0 3395 1490 1475
## 111 1 45.0 4265 1695 1685
## 112 1 45.0 3795 1680 1427
## 113 1 50.0 4456 1796 1416
## 114 1 50.0 4598 1894 1706
## 115 1 37.0 3995 1775 1505
## 116 1 45.0 3985 1734 1505
## 117 1 45.0 3970 1682 1453
## 118 1 42.0 3995 1695 1555
## 119 1 35.0 3565 1525 1590
## 120 1 43.0 3765 1660 1520
## 121 1 50.0 4300 1790 1635
## 122 1 55.0 4318 1805 1548
## 123 1 75.0 5052 1968 1740
## 124 1 37.0 3995 1775 1505
## 125 1 43.0 4370 1700 1475
## 126 1 35.0 3599 1495 1700
## 127 1 60.0 4495 1817 1975
## 128 1 43.0 3765 1660 1520
## 129 1 80.0 4795 1855 1835
## 130 1 70.0 4663 1898 1659
## 131 1 50.0 4360 1822 1695
## 132 1 42.0 3995 1695 1555
## 133 1 55.0 4270 1780 1665
## 134 1 43.0 3765 1660 1520
## 135 1 60.0 4395 1818 1640
## 136 1 45.0 4440 1729 1475
## 137 1 45.0 3995 1710 1505
## 138 1 75.0 4933 1874 1455
## 139 1 45.0 4585 1866 1774
## 140 1 50.0 4315 1800 1645
## 141 1 37.0 3995 1745 1500
## 142 1 80.0 5063 1860 1494
## 143 1 45.0 4296 1695 1685
## 144 1 43.0 4370 1700 1475
## 145 1 43.0 4370 1700 1475
## 146 1 70.0 4600 2069 1724
## 147 1 80.0 4795 1855 1835
## 148 1 93.0 4819 2141 1796
## 149 1 43.0 3995 1660 1520
## 150 1 70.0 5453 1899 1498
## 151 1 55.0 4270 1780 1665
## 152 1 48.0 4323 1809 1650
## 153 1 58.0 4630 1780 1710
## 154 1 35.0 3395 1490 1475
## 155 1 50.0 4315 1822 1695
## 156 1 43.0 3765 1660 1520
## 157 1 40.0 4440 1695 1495
## 158 1 66.0 4686 1810 1442
## 159 1 40.0 3985 1734 1505
## 160 1 45.0 4000 1642 1522
## 161 1 55.0 4386 1699 1466
## 162 1 45.0 3995 1790 1647
## 163 1 70.0 4585 1890 1785
## 164 1 57.0 4633 1811 1429
## 165 1 50.0 4417 1804 1494
## 166 1 65.0 4915 1874 1455
## 167 1 60.0 4430 1817 1975
## 168 1 80.0 4705 1840 1850
## 169 1 45.0 3985 1734 1505
## 170 1 52.0 3999 1765 1708
## 171 1 100.0 5089 1983 1737
## 172 1 66.0 4686 1810 1442
## 173 1 27.0 3565 1520 1564
## 174 1 60.0 4456 1820 1995
## 175 1 60.0 4655 1835 1760
## 176 1 43.0 3760 1690 1530
## 177 1 37.0 3840 1735 1530
## 178 1 40.0 4440 1695 1495
## 179 1 50.0 4315 1822 1695
## 180 1 64.0 4385 1831 1608
## 181 1 95.0 4781 1911 1774
## 182 1 60.0 4370 1783 1458
## 183 1 65.0 4899 2094 1464
## 184 1 42.0 3995 1695 1555
## 185 1 60.0 4456 1820 1995
## 186 1 42.0 4420 1695 1480
## 187 1 66.0 4596 1770 1447
## 188 1 60.0 4270 1780 1630
## 189 1 80.0 4868 1854 1471
## 190 1 70.0 4804 2141 1796
## 191 1 35.0 3395 1490 1475
## 192 1 45.0 3995 1710 1505
## 193 1 55.0 4413 1699 1466
## 194 1 44.0 3994 1811 1607
## 195 1 42.0 3995 1695 1555
## 196 1 42.0 3995 1695 1555
## 197 1 45.0 3995 1790 1647
## 198 1 55.0 4413 1699 1466
## 199 1 64.0 4649 1860 1366
## 200 1 37.0 3805 1680 1520
## 201 1 80.0 5157 2183 1659
## 202 1 55.0 4735 1830 1795
## 203 1 60.0 4270 1780 1630
## 204 1 80.0 4795 1855 1835
## 205 1 42.0 4420 1695 1480
## 206 1 28.0 3679 1579 1478
## 207 1 75.0 4915 1874 1455
## 208 1 50.0 4661 1894 1786
## 209 1 65.0 4915 1874 1455
## 210 1 35.0 3610 1680 1500
## 211 1 42.0 3850 1695 1530
## 212 1 60.0 4456 1820 1995
## 213 1 55.0 4735 1830 1795
## 214 1 35.0 3995 1695 1501
## 215 1 93.0 4819 2141 1796
## 216 1 60.0 4395 1818 1640
## 217 1 80.0 5005 1981 1693
## 218 1 80.0 4795 1855 1835
## 219 1 100.0 4846 1939 1702
## 220 1 55.0 4735 1830 1795
## 221 1 80.0 4695 1840 1850
## 222 1 100.0 5089 1983 1737
## 223 1 60.0 3655 1620 1675
## 224 1 35.0 3545 1490 1475
## 225 1 43.0 4490 1730 1485
## 226 1 37.0 3840 1735 1530
## 227 1 43.0 4370 1700 1475
## 228 1 66.0 4702 1810 1434
## 229 1 90.0 4868 1854 1471
## 230 1 44.0 3994 1811 1607
## 231 1 35.0 3395 1490 1475
## 232 1 70.0 4585 1890 1785
## 233 1 50.0 4598 1894 1706
## 234 1 42.0 4386 1683 1603
## 235 1 37.0 3827 1742 1615
## 236 1 43.0 3765 1660 1520
## 237 1 40.0 4440 1695 1495
## 238 1 37.0 3995 1745 1500
## 239 1 82.0 4731 2071 1651
## 240 1 104.0 4879 2073 1803
## 241 1 80.0 4705 1840 1850
## 242 1 28.0 3679 1579 1478
## 243 1 51.0 4439 1821 1612
## 244 1 64.0 4385 1831 1608
## 245 1 35.0 3520 1475 1690
## 246 1 40.0 3985 1734 1505
## 247 1 70.0 4585 1890 1785
## 248 1 43.0 3765 1660 1520
## 249 1 42.0 3995 1695 1555
## 250 1 85.0 4846 2155 1705
## 251 1 50.0 4331 1822 1671
## 252 1 28.0 3679 1579 1478
## 253 1 50.0 4300 1790 1635
## 254 1 57.0 3985 1820 1844
## 255 1 65.0 4600 2069 1724
## 256 1 37.0 3995 1745 1510
## 257 1 60.0 4270 1780 1630
## 258 1 55.0 4735 1830 1795
## 259 1 45.0 3970 1682 1453
## 260 1 65.0 4825 1860 1840
## 261 1 35.0 3620 1475 1460
## 262 1 55.0 4620 1775 1475
## 263 1 35.0 3585 1595 1550
## 264 1 60.0 4788 1903 1791
## 265 1 35.0 3565 1595 1550
## 266 1 60.0 4270 1780 1630
## 267 1 100.0 5130 1934 1850
## 268 1 64.0 4385 1831 1608
## 269 1 45.0 3970 1682 1453
## 270 1 56.0 4795 1967 1416
## 271 1 64.0 4385 1831 1608
## 272 1 43.0 4370 1700 1475
## 273 1 45.0 3995 1770 1605
## 274 1 48.0 3995 1790 1640
## 275 1 67.0 4648 1881 1661
## 276 1 40.0 3999 1734 1601
## 277 1 65.0 4936 1868 1479
## 278 1 35.0 3990 1680 1505
## 279 1 50.0 4598 1894 1706
## 280 1 68.0 4491 1852 1304
## 281 1 35.0 3599 1495 1700
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## 791 1 80.0 5063 1860 1494
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## 852 1 55.0 4735 1830 1795
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## 855 1 55.0 4655 1965 1922
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## 859 1 45.0 3987 1687 1495
## 860 1 64.0 4385 1831 1608
## 861 1 40.0 3999 1734 1601
## 862 1 66.0 4686 1810 1442
## 863 1 50.0 4456 1796 1416
## 864 1 50.0 4424 1804 1494
## 865 1 40.0 4440 1695 1495
## 866 1 43.0 3765 1660 1520
## 867 1 48.0 4300 1765 1590
## 868 1 75.0 4933 1874 1455
## 869 1 40.0 3675 1475 1800
## 870 1 60.0 4695 1890 1755
## 871 1 65.0 4969 2139 1420
## 872 1 42.0 4440 1695 1485
## 873 1 100.0 5089 1983 1737
## 874 1 43.0 3765 1660 1520
## 875 1 65.0 4600 2069 1724
## 876 1 80.0 4795 1855 1835
## 877 1 42.0 3995 1695 1555
## 878 1 60.0 4270 1780 1630
## 879 1 45.0 4296 1695 1685
## 880 1 35.0 3610 1645 1560
## 881 1 45.0 3995 1770 1605
## 882 1 40.0 4549 1748 1489
## 883 1 50.0 4300 1790 1635
## 884 1 43.0 4375 1700 1475
## 885 1 42.0 3995 1695 1555
## 886 1 55.0 4384 1699 1466
## 887 1 40.0 4440 1695 1495
## 888 1 55.0 4735 1830 1795
## 889 1 82.5 5399 1948 1550
## 890 1 64.0 4385 1831 1608
## 891 1 66.0 4861 1864 1483
## 892 1 64.0 4385 1831 1608
## 893 1 45.0 3971 1682 1469
## 894 1 40.0 4440 1695 1495
## 895 1 55.0 4270 1780 1665
## 896 1 45.0 3985 1734 1505
## 897 1 42.0 3995 1821 1627
## 898 1 32.0 3495 1550 1500
## 899 1 44.0 3994 1811 1607
## 900 1 43.0 4375 1700 1475
## 901 1 42.0 3850 1695 1530
## 902 1 70.0 4600 2069 1724
## 903 1 40.0 4440 1695 1495
## 904 1 40.0 3886 1695 1525
## 905 1 37.0 3995 1745 1510
## 906 1 80.0 5063 1860 1494
## 907 1 50.0 4500 1790 1675
## 908 1 40.0 4440 1695 1495
## 909 1 64.0 4690 1880 1690
## 910 1 55.0 4735 1830 1795
## 911 1 37.0 3995 1745 1510
## 912 1 32.0 3655 1620 1675
## 913 1 64.0 4690 1880 1690
## 914 1 55.0 4735 1830 1795
## 915 1 65.0 4915 1874 1455
## 916 1 42.0 3850 1695 1530
## 917 1 56.0 4640 1845 1645
## 918 1 55.0 4735 1830 1795
## 919 1 66.0 4658 1890 1644
## 920 1 48.0 3995 1790 1640
## 921 1 35.0 3565 1525 1590
## 922 1 45.0 3985 1734 1505
## 923 1 42.0 4420 1695 1480
## 924 1 50.0 4315 1822 1695
## 925 1 50.0 4221 1760 1612
## 926 1 35.0 3620 1475 1460
## 927 1 45.0 3995 1760 1555
## 928 1 60.0 4720 1835 1760
## 929 1 28.0 3679 1579 1478
## 930 1 82.0 4838 1915 1837
## 931 1 57.0 3985 1820 1844
## 932 1 42.0 4440 1695 1485
## 933 1 45.0 3985 1734 1505
## 934 1 80.0 4705 1840 1850
## 935 1 70.0 4660 1890 1760
## 936 1 60.0 4456 1820 1930
## 937 1 66.0 4686 1810 1442
## 938 1 75.0 4629 1898 1653
## 939 1 43.0 4370 1700 1475
## 940 1 28.0 3679 1579 1478
## 941 1 50.0 4598 1894 1706
## 942 1 60.0 3920 1710 1930
## 943 1 50.0 4456 1796 1416
## 944 1 60.9 4784 2080 1391
## 945 1 82.0 4731 2071 1651
## 946 1 35.0 3495 1475 1460
## 947 1 37.0 3995 1735 1515
## 948 1 55.0 4413 1699 1466
## 949 1 60.0 4838 1817 1482
## 950 1 44.0 3821 1727 1414
## 951 1 80.0 4795 1855 1835
## 952 1 48.0 3995 1790 1640
## 953 1 67.5 4635 1865 1484
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## 955 1 65.0 4696 1923 1624
## 956 1 80.0 4795 1855 1835
## 957 1 35.0 3599 1495 1700
## 958 1 65.0 4696 1923 1624
## 959 1 37.0 3995 1745 1500
## 960 1 40.0 3675 1475 1800
## 961 1 37.0 3995 1745 1500
## 962 1 35.0 3599 1495 1700
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## 964 1 35.0 3599 1495 1700
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## 966 1 35.0 3585 1595 1550
## 967 1 42.0 3995 1695 1555
## 968 1 48.0 3995 1790 1640
## 969 1 27.0 3565 1520 1564
## 970 1 35.0 3395 1490 1475
## 971 1 55.0 4386 1699 1466
## 972 1 80.0 4705 1840 1850
## 973 1 50.0 4456 1796 1416
## 974 1 60.0 4395 1818 1640
## 975 1 70.0 4804 2141 1796
## 976 1 45.0 3985 1734 1505
## 977 1 37.0 3995 1745 1500
## 978 1 42.0 3995 1695 1555
## 979 1 45.0 3995 1710 1505
## 980 1 93.0 4819 2141 1796
## 981 1 64.0 4385 1831 1608
## 982 1 50.0 4315 1800 1645
## 983 1 50.0 4620 1800 1465
## 984 1 45.0 4250 1670 1370
## 985 1 55.0 4270 1780 1665
## 986 1 35.0 3585 1595 1550
## 987 1 27.0 3565 1520 1564
## 988 1 55.0 4735 1830 1795
## 989 1 50.0 4975 1865 1445
## 990 1 42.0 3995 1695 1555
## 991 1 45.0 3995 1760 1555
## 992 1 64.0 4385 1831 1608
## 993 1 60.0 4456 1820 1995
## 994 1 43.0 4490 1730 1485
## 995 1 50.0 4315 1822 1695
## 996 1 27.0 3565 1520 1564
## 997 1 47.0 4299 1822 1557
## 998 1 42.0 4440 1695 1485
## 999 1 80.0 4705 1840 1850
## 1000 1 65.0 4735 1830 1795
## 1001 1 32.0 3515 1500 1510
## 1002 1 35.0 3990 1680 1505
## 1003 1 37.0 3995 1745 1510
## 1004 1 60.0 4456 1820 1995
## 1005 1 43.0 3765 1660 1520
## 1006 1 40.0 3675 1475 1800
## 1007 1 66.0 4686 1810 1442
## 1008 1 45.0 3985 1734 1505
## 1009 1 65.0 4899 2094 1464
## 1010 1 63.0 4701 1826 1427
## 1011 1 40.0 4440 1695 1495
## 1012 1 37.0 3840 1735 1530
## 1013 1 42.0 3995 1695 1555
## 1014 1 40.0 3675 1475 1825
## 1015 1 32.0 3495 1550 1500
## 1016 1 43.0 3765 1660 1520
## 1017 1 54.0 4762 1847 1433
## 1018 1 37.0 3840 1735 1530
## 1019 1 52.0 3999 1765 1708
## 1020 1 50.0 4315 1822 1695
## 1021 1 56.0 4795 1967 1416
## 1022 1 93.0 4819 2141 1796
## 1023 1 45.0 3970 1682 1453
## 1024 1 35.0 3545 1490 1475
## 1025 1 42.0 4425 1730 1495
## 1026 1 40.0 3999 1734 1601
## 1027 1 63.0 4454 2044 1545
## 1028 1 60.0 4456 1820 1995
## 1029 1 35.0 3990 1680 1505
## 1030 1 45.0 4445 1775 1700
## 1031 1 57.0 4633 1811 1429
## 1032 1 43.0 3765 1660 1520
## 1033 1 50.0 4526 1800 1420
## 1034 1 48.0 3995 1790 1640
## 1035 1 45.0 3970 1682 1453
## 1036 1 35.0 3746 1647 1535
## 1037 1 57.0 4360 2120 1635
## 1038 1 60.0 4430 1817 1975
## 1039 1 66.0 4656 1890 1639
## 1040 1 55.0 4390 1699 1467
## 1041 1 95.0 4781 1911 1774
## 1042 1 44.0 3982 1727 1425
## 1043 1 55.0 4540 1760 1480
## 1044 1 43.0 4370 1700 1475
## 1045 1 58.0 4935 1850 1895
## 1046 1 35.0 3600 1600 1560
## 1047 1 56.0 4530 1775 1470
## 1048 1 40.0 4440 1695 1495
## 1049 1 50.0 4315 1822 1695
## 1050 1 35.0 3695 1600 1560
## 1051 1 50.0 4315 1800 1637
## 1052 1 83.0 5252 1899 1457
## 1053 1 43.0 4375 1700 1475
## 1054 1 43.0 4370 1700 1475
## 1055 1 85.0 4986 1995 1705
## 1056 1 37.0 3845 1735 1530
## 1057 1 68.0 4752 1918 1621
## 1058 1 35.0 3585 1595 1550
## 1059 1 40.0 4440 1695 1495
## 1060 1 37.0 3995 1735 1515
## 1061 1 50.0 4598 1894 1706
## 1062 1 60.0 4405 1818 1640
## 1063 1 43.0 4370 1700 1475
## 1064 1 55.0 4413 1699 1466
## 1065 1 43.0 4375 1700 1475
## 1066 1 60.0 4270 1780 1630
## 1067 1 83.0 4935 2004 1696
## 1068 1 45.0 4445 1775 1700
## 1069 1 35.0 3993 1677 1532
## 1070 1 43.0 4370 1700 1475
## 1071 1 75.0 4933 1874 1455
## 1072 1 55.0 4270 1780 1665
## 1073 1 45.0 3995 1710 1505
## 1074 1 40.0 4440 1695 1495
## 1075 1 50.0 4456 1796 1416
## 1076 1 42.0 3850 1695 1530
## 1077 1 43.0 4490 1730 1485
## 1078 1 70.0 4585 1890 1785
## 1079 1 45.0 3985 1734 1505
## 1080 1 60.0 3920 1710 1930
## 1081 1 37.0 3995 1775 1505
## 1082 1 50.0 4300 1790 1635
## 1083 1 63.0 4701 1826 1427
## 1084 1 67.0 4648 1881 1661
## 1085 1 65.0 4936 1868 1479
## 1086 1 60.0 4270 1780 1630
## 1087 1 75.0 5052 1968 1740
## 1088 1 45.0 3995 1770 1605
## 1089 1 70.0 4585 1890 1785
## 1090 1 35.0 3995 1635 1490
## 1091 1 45.0 3995 1770 1605
## 1092 1 37.0 3995 1775 1505
## 1093 1 35.0 3995 1695 1501
## 1094 1 37.0 3995 1745 1500
## 1095 1 64.0 4385 1831 1608
## 1096 1 50.0 4225 1760 1612
## 1097 1 43.0 4375 1700 1475
## 1098 1 70.0 4695 1815 1840
## 1099 1 45.0 3985 1734 1505
## 1100 1 60.0 4655 1835 1760
## 1101 1 50.0 4300 1790 1635
## 1102 1 42.0 3850 1695 1530
## 1103 1 42.0 4425 1730 1495
## 1104 1 50.0 4670 1814 1476
## 1105 1 37.0 3840 1735 1530
## 1106 1 60.0 4270 1780 1630
## 1107 1 80.0 4892 1860 1837
## 1108 1 57.0 4633 1811 1429
## 1109 1 43.0 4490 1730 1485
## 1110 1 40.0 4440 1695 1495
## 1111 1 35.0 3599 1495 1700
## 1112 1 35.0 3585 1595 1550
## 1113 1 52.0 3999 1765 1708
## 1114 1 75.0 4933 1874 1455
## 1115 1 50.0 4315 1822 1695
## 1116 1 45.0 4296 1695 1685
## 1117 1 42.0 3850 1695 1530
## 1118 1 83.0 5252 1899 1457
## 1119 1 60.0 4270 1780 1630
## 1120 1 45.0 4296 1695 1685
## 1121 1 37.0 3995 1745 1500
## 1122 1 80.0 4903 1869 1837
## 1123 1 57.0 4633 1811 1429
## 1124 1 50.0 4225 1760 1612
## 1125 1 45.0 3995 1790 1647
## 1126 1 71.0 4486 1839 1672
## 1127 1 50.0 4670 1814 1476
## 1128 1 66.0 4861 1864 1483
## 1129 1 42.0 3850 1695 1530
## 1130 1 42.0 4386 1683 1603
## 1131 1 35.0 3395 1490 1475
## 1132 1 35.0 3599 1495 1700
## 1133 1 82.5 5569 1948 1550
## 1134 1 66.0 4596 1770 1447
## 1135 1 64.0 4690 1880 1690
## 1136 1 60.0 3610 1645 1560
## 1137 1 66.0 4581 1770 1447
## 1138 1 42.0 3995 1695 1555
## 1139 1 35.0 3600 1600 1560
## 1140 1 60.0 3655 1620 1675
## 1141 1 35.0 3585 1595 1550
## 1142 1 37.0 3995 1735 1515
## 1143 1 28.0 3679 1579 1478
## 1144 1 48.0 4300 1765 1590
## 1145 1 42.0 3850 1695 1530
## 1146 1 60.0 4395 1818 1640
## 1147 1 65.0 4600 2173 1690
## 1148 1 60.0 4270 1780 1630
## 1149 1 55.0 4540 1760 1480
## 1150 1 43.0 4490 1730 1485
## 1151 1 50.0 4300 1790 1635
## 1152 1 35.0 3600 1600 1560
## 1153 1 43.0 4160 1690 1530
## 1154 1 35.0 3520 1475 1690
## 1155 1 43.0 4490 1730 1485
## 1156 1 40.0 3999 1734 1601
## 1157 1 40.0 4440 1695 1495
## 1158 1 42.0 3850 1695 1530
## 1159 1 51.0 4447 1821 1598
## 1160 1 54.0 4379 1801 1281
## 1161 1 43.0 4160 1690 1530
## 1162 1 35.0 3600 1600 1560
## 1163 1 45.0 3795 1680 1427
## 1164 1 60.0 4270 1780 1630
## 1165 1 40.0 4440 1695 1495
## 1166 1 80.0 5063 1860 1494
## 1167 1 35.0 3995 1695 1501
## 1168 1 63.0 4454 2044 1545
## 1169 1 35.0 3395 1490 1475
## 1170 1 37.0 3995 1745 1500
## 1171 1 50.0 4490 1735 1560
## 1172 1 45.0 3775 1695 1510
## 1173 1 45.0 4440 1729 1475
## 1174 1 66.0 4686 1810 1442
## 1175 1 80.0 4705 1840 1850
## 1176 1 35.0 3565 1595 1550
## 1177 1 80.0 4795 1855 1835
## 1178 1 65.0 4915 1820 1450
## 1179 1 48.0 4300 1765 1590
## 1180 1 60.0 3995 1835 1839
## 1181 1 45.0 3995 1760 1555
## 1182 1 66.0 4686 1810 1442
## 1183 1 35.0 3620 1475 1460
## 1184 1 50.0 4417 1804 1494
## 1185 1 60.0 3995 1795 1817
## 1186 1 105.0 5199 2220 1840
## 1187 1 80.0 4903 1869 1837
## 1188 1 60.0 4655 1835 1760
## 1189 1 45.0 4395 1735 1690
## 1190 1 65.0 4600 2069 1724
## 1191 1 43.0 4375 1700 1475
## 1192 1 66.0 5067 2091 1457
## 1193 1 105.0 4999 2220 1835
## 1194 1 43.0 3765 1660 1520
## 1195 1 60.0 4720 1835 1760
## 1196 1 40.0 4440 1695 1495
## 1197 1 60.0 3610 1645 1560
## 1198 1 37.0 3995 1745 1500
## 1199 1 43.0 4375 1700 1475
## 1200 1 45.0 3970 1682 1453
## 1201 1 60.0 4456 1820 1995
## 1202 1 77.0 5255 2105 1460
## 1203 1 37.0 3995 1745 1500
## 1204 1 70.0 4804 2141 1796
## 1205 1 35.0 3395 1490 1475
## 1206 1 80.0 4795 1855 1835
## 1207 1 45.0 3995 1770 1605
## 1208 1 43.0 3765 1660 1520
## 1209 1 35.0 3990 1680 1505
## 1210 1 50.0 4331 1822 1671
## 1211 1 45.0 4445 1775 1700
## 1212 1 50.0 4456 1796 1416
## 1213 1 66.0 4596 1770 1447
## 1214 1 80.0 4795 1855 1835
## 1215 1 35.0 3565 1525 1590
## 1216 1 60.0 4270 1780 1630
## 1217 1 55.0 4735 1830 1795
## 1218 1 90.0 5265 1949 1471
## 1219 1 40.0 3955 1694 1544
## 1220 1 100.0 5089 1983 1737
## 1221 1 32.0 3495 1550 1500
## 1222 1 64.0 4385 1831 1608
## 1223 1 40.0 4440 1695 1495
## 1224 1 42.0 3850 1695 1530
## 1225 1 52.0 3998 1765 1647
## 1226 1 57.0 4360 2120 1635
## 1227 1 45.0 3985 1734 1505
## 1228 1 28.0 3429 1560 1541
## 1229 1 43.0 3765 1660 1520
## 1230 1 55.0 4384 1699 1466
## 1231 1 93.0 4819 2141 1796
## 1232 1 66.0 4656 1890 1639
## 1233 1 50.0 4300 1790 1635
## 1234 1 43.0 3995 1660 1520
## 1235 1 52.0 3998 1765 1647
## 1236 1 48.0 3995 1790 1640
## 1237 1 55.0 4735 1830 1795
## 1238 1 50.0 4456 1796 1416
## 1239 1 48.0 3995 1790 1640
## 1240 1 42.0 3850 1695 1530
## 1241 1 28.0 3595 1475 1700
## 1242 1 45.0 3795 1680 1427
## 1243 1 35.0 3395 1490 1475
## 1244 1 55.0 4384 1699 1466
## 1245 1 82.5 5569 1948 1550
## 1246 1 90.0 5207 2157 1823
## 1247 1 66.0 4861 1864 1483
## 1248 1 35.0 3395 1490 1475
## 1249 1 35.0 3746 1647 1535
## 1250 1 40.0 3955 1694 1544
## 1251 1 70.0 4850 1960 1845
## 1252 1 70.0 4804 2141 1796
## 1253 1 63.0 4701 1826 1427
## 1254 1 60.0 5115 1985 1755
## 1255 1 45.0 4296 1695 1685
## 1256 1 50.0 4417 1804 1494
## 1257 1 43.0 4490 1730 1485
## 1258 1 43.0 3765 1660 1520
## 1259 1 60.0 4456 1820 1995
## 1260 1 48.0 3995 1790 1640
## 1261 1 35.0 3992 1677 1537
## 1262 1 63.0 4454 2044 1545
## 1263 1 65.0 4696 1923 1624
## 1264 1 35.0 3545 1490 1475
## 1265 1 40.0 4440 1695 1495
## 1266 1 55.0 4585 1765 1760
## 1267 1 50.0 4292 1780 1433
## 1268 1 48.0 3995 1790 1640
## 1269 1 55.0 4390 1699 1467
## 1270 1 35.0 3600 1600 1560
## 1271 1 50.0 4545 1750 1450
## 1272 1 65.0 4899 2094 1464
## 1273 1 60.0 3610 1645 1560
## 1274 1 66.0 4861 1864 1483
## 1275 1 32.0 3495 1550 1500
## 1276 1 60.0 4720 1835 1760
## 1277 1 57.0 4360 2120 1635
## 1278 1 60.0 3545 1490 1475
## 1279 1 43.0 3765 1660 1520
## 1280 1 40.0 3886 1695 1525
## 1281 1 35.0 3585 1595 1550
## 1282 1 60.0 4430 1817 1975
## 1283 1 42.0 3995 1695 1555
## 1284 1 67.0 4657 1881 1678
## 1285 1 35.0 3585 1595 1550
## 1286 1 45.0 3995 1770 1605
## 1287 1 42.0 3850 1695 1530
## 1288 1 60.0 4270 1780 1630
## 1289 1 44.0 3995 1706 1570
## 1290 1 45.0 4265 1695 1685
## 1291 1 70.0 4585 1890 1785
## 1292 1 60.0 4370 1783 1458
## 1293 1 37.0 3995 1745 1500
## 1294 1 60.0 4270 1780 1630
## 1295 1 48.0 4300 1765 1590
## 1296 1 35.0 3715 1635 1565
## 1297 1 45.0 3985 1734 1505
## 1298 1 35.0 3395 1490 1475
## 1299 1 50.0 4424 1804 1494
## 1300 1 65.0 4915 1874 1455
## 1301 1 65.0 4899 2094 1464
## 1302 1 35.0 3545 1490 1475
## 1303 1 40.0 3675 1475 1800
## 1304 1 55.0 4735 1830 1795
## 1305 1 65.0 4915 1820 1450
## 1306 1 40.0 4440 1695 1495
## 1307 1 55.0 4655 1965 1922
## 1308 1 48.0 4300 1765 1590
## 1309 1 40.0 4440 1695 1495
## 1310 1 35.0 3585 1595 1550
## 1311 1 35.0 3545 1490 1475
## 1312 1 63.0 4701 1826 1427
## 1313 1 57.0 3985 1820 1844
## 1314 1 50.0 4315 1800 1645
## 1315 1 66.0 4693 1810 1402
## 1316 1 70.0 4585 1890 1785
## 1317 1 60.0 3995 1835 1839
## 1318 1 70.0 4663 1893 1659
## 1319 1 57.0 3985 1820 1844
## 1320 1 60.0 4270 1780 1630
## 1321 1 66.0 4658 1890 1644
## 1322 1 60.0 4624 2031 1429
## 1323 1 57.0 3985 1820 1855
## 1324 1 45.0 3995 1760 1555
## 1325 1 63.0 4454 2044 1545
## 1326 1 70.0 4804 2141 1796
## 1327 1 50.0 4424 1804 1494
## 1328 1 43.0 4370 1700 1475
## 1329 1 75.0 5052 1968 1740
## 1330 1 60.0 4270 1780 1630
## 1331 1 48.0 3995 1790 1640
## 1332 1 35.0 3600 1475 1595
## 1333 1 51.0 4439 1821 1612
## 1334 1 63.0 4454 2044 1545
## 1335 1 75.0 4933 1874 1455
## 1336 1 48.0 3995 1790 1640
## 1337 1 42.0 4420 1695 1480
## 1338 1 42.0 4420 1695 1480
## 1339 1 55.0 4386 1699 1466
## 1340 1 41.0 3805 1665 1525
## 1341 1 35.0 3990 1680 1505
## 1342 1 57.0 4633 1811 1429
## 1343 1 55.0 4735 1830 1795
## 1344 1 42.0 3850 1695 1530
## 1345 1 42.0 3850 1695 1530
## 1346 1 50.0 4331 1822 1671
## 1347 1 35.0 3746 1647 1535
## 1348 1 35.0 3600 1600 1560
## 1349 1 32.0 3700 1690 1595
## 1350 1 64.0 4385 1831 1608
## 1351 1 45.0 3971 1682 1469
## 1352 1 37.0 3995 1745 1500
## 1353 1 60.0 4270 1780 1630
## 1354 1 75.0 5052 1968 1740
## 1355 1 43.0 4370 1700 1475
## 1356 1 44.0 3982 1727 1425
## 1357 1 43.0 4160 1690 1530
## 1358 1 35.0 3565 1595 1550
## 1359 1 43.0 3995 1660 1520
## 1360 1 35.0 3620 1475 1460
## 1361 1 42.0 4440 1695 1485
## 1362 1 66.0 4596 1770 1447
## 1363 1 42.0 3850 1695 1530
## 1364 1 42.0 3995 1695 1555
## 1365 1 50.0 4975 1865 1445
## 1366 1 37.0 3995 1775 1505
## 1367 1 45.0 3971 1682 1469
## 1368 1 43.0 3765 1660 1520
## 1369 1 50.0 4659 1814 1476
## 1370 1 50.0 4417 1804 1494
## 1371 1 66.0 4658 1890 1644
## 1372 1 43.0 4490 1730 1485
## 1373 1 60.0 3805 1680 1520
## 1374 1 35.0 3495 1475 1460
## 1375 1 35.0 3995 1695 1501
## 1376 1 43.0 4370 1700 1475
## 1377 1 80.0 4705 1840 1850
## 1378 1 70.0 4585 1890 1785
## 1379 1 50.0 4315 1800 1645
## 1380 1 60.0 4430 1817 1975
## 1381 1 35.0 3585 1595 1550
## 1382 1 45.0 3985 1734 1505
## 1383 1 80.0 4795 1855 1835
## 1384 1 55.0 4270 1780 1665
## 1385 1 40.0 4440 1695 1495
## 1386 1 35.0 3565 1595 1550
## 1387 1 80.0 4922 2004 1745
## 1388 1 55.0 4963 1879 1443
## 1389 1 43.0 3995 1660 1520
## 1390 1 43.0 4370 1700 1475
## 1391 1 80.0 4892 1860 1837
## 1392 1 43.0 4370 1700 1475
## 1393 1 55.0 4270 1780 1665
## 1394 1 35.0 3585 1595 1550
## 1395 1 55.0 4620 1775 1475
## 1396 1 48.0 3995 1790 1640
## 1397 1 50.0 4456 1796 1416
## 1398 1 37.0 3995 1745 1510
## 1399 1 45.0 3987 1698 1483
## 1400 1 66.0 4596 2020 1447
## 1401 1 45.0 3970 1682 1453
## 1402 1 52.0 3998 1765 1647
## 1403 1 28.0 3679 1579 1478
## 1404 1 43.0 4375 1700 1475
## 1405 1 78.0 4755 1900 1785
## 1406 1 63.0 4454 2044 1545
## 1407 1 50.0 4456 1796 1416
## 1408 1 37.0 3995 1735 1515
## 1409 1 75.0 5052 1968 1740
## 1410 1 42.0 3850 1695 1530
## 1411 1 45.0 3995 1682 1483
## 1412 1 40.0 4549 1748 1489
## 1413 1 80.0 4868 1854 1470
## 1414 1 43.0 4490 1730 1485
## 1415 1 50.0 4598 1894 1706
## 1416 1 43.0 3765 1660 1520
## 1417 1 43.0 3765 1660 1520
## 1418 1 42.0 4440 1695 1485
## 1419 1 57.0 4633 1811 1429
## 1420 1 80.0 4705 1840 1850
## 1421 1 60.0 4270 1780 1630
## 1422 1 50.0 4598 1894 1706
## 1423 1 55.0 4585 1765 1760
## 1424 1 45.0 3985 1734 1505
## 1425 1 66.0 4686 1810 1442
## 1426 1 43.0 4490 1730 1485
## 1427 1 65.0 4600 2069 1690
## 1428 1 55.0 4735 1830 1795
## 1429 1 45.0 4296 1695 1685
## 1430 1 41.0 4425 1695 1505
## 1431 1 35.0 3990 1680 1505
## 1432 1 45.0 3971 1682 1469
## 1433 1 35.0 3995 1695 1501
## 1434 1 43.0 3995 1660 1520
## 1435 1 55.0 4384 1699 1466
## 1436 1 55.0 4390 1699 1467
## 1437 1 90.0 5207 2157 1823
## 1438 1 75.0 4629 1898 1653
## 1439 1 40.0 4440 1695 1495
## 1440 1 43.0 3765 1660 1520
## 1441 1 43.0 4370 1700 1475
## 1442 1 55.0 4318 1805 1548
## 1443 1 70.0 4585 1890 1785
## 1444 1 42.0 4420 1695 1480
## 1445 1 45.0 3895 1735 1555
## 1446 1 62.0 4475 1850 1660
## 1447 1 42.0 3995 1695 1555
## 1448 1 42.0 3995 1695 1555
## 1449 1 35.0 3585 1595 1550
## 1450 1 42.0 3995 1821 1627
## 1451 1 60.0 4270 1780 1630
## 1452 1 35.0 3565 1525 1590
## 1453 1 60.0 4107 1745 1880
## 1454 1 52.0 3999 1765 1708
## 1455 1 35.0 3640 1595 1520
## 1456 1 54.0 4425 1863 1652
## 1457 1 35.0 3620 1475 1460
## 1458 1 48.0 3995 1790 1640
## 1459 1 66.0 4658 1890 1644
## 1460 1 48.0 4300 1765 1590
## 1461 1 45.0 4265 1695 1685
## 1462 1 80.0 5063 1860 1494
## 1463 1 66.0 4658 1890 1644
## 1464 1 75.0 4629 1898 1653
## 1465 1 40.0 4440 1695 1495
## 1466 1 50.0 4456 1796 1416
## 1467 1 70.0 4950 1845 1475
## 1468 1 45.0 4440 1729 1475
## 1469 1 45.0 4395 1735 1690
## 1470 1 65.0 4899 2094 1464
## 1471 1 35.0 3990 1680 1505
## 1472 1 43.0 4490 1730 1485
## 1473 1 48.0 3995 1790 1640
## 1474 1 43.0 4160 1690 1530
## 1475 1 100.0 5120 1934 1850
## 1476 1 65.0 4915 1874 1455
## 1477 1 60.0 4456 1820 1930
## 1478 1 63.0 4701 1826 1427
## 1479 1 32.0 3495 1550 1500
## 1480 1 50.0 4315 1822 1695
## 1481 1 45.0 4395 1735 1690
## 1482 1 43.0 4549 1796 1446
## 1483 1 45.0 3985 1734 1505
## 1484 1 55.0 4270 1780 1665
## 1485 1 65.0 4600 2069 1690
## 1486 1 28.0 3679 1579 1478
## 1487 1 45.0 4296 1695 1685
## 1488 1 35.0 3565 1595 1550
## 1489 1 43.0 3765 1660 1520
## 1490 1 55.0 4585 1760 1760
## 1491 1 93.0 4819 2141 1796
## 1492 1 43.0 4490 1730 1485
## 1493 1 37.0 3995 1735 1515
## 1494 1 35.0 3785 1635 1485
## 1495 1 70.0 4585 1890 1785
## 1496 1 63.0 4701 1826 1427
## 1497 1 43.0 4490 1730 1485
## 1498 1 37.0 3995 1745 1510
## 1499 1 35.0 3599 1495 1700
## 1500 1 60.0 4788 1903 1791
## 1501 1 80.0 4705 1840 1850
## 1502 1 43.0 3775 1680 1620
## 1503 1 55.0 4390 1699 1467
## 1504 1 37.0 3995 1775 1505
## 1505 1 55.0 4735 1830 1795
## 1506 1 43.0 4549 1796 1446
## 1507 1 44.0 3994 1811 1607
## 1508 1 40.0 3985 1734 1505
## 1509 1 35.0 3585 1595 1550
## 1510 1 81.0 4882 1894 1848
## 1511 1 42.0 3995 1821 1627
## 1512 1 45.0 4265 1695 1510
## 1513 1 42.0 3850 1695 1530
## 1514 1 35.0 3990 1680 1505
## 1515 1 60.0 4456 1820 1995
## 1516 1 45.0 3995 1770 1605
## 1517 1 35.0 3620 1475 1460
## 1518 1 35.0 3990 1680 1505
## 1519 1 45.0 3995 1682 1483
## 1520 1 60.0 4655 1835 1760
## 1521 1 35.0 3599 1495 1700
## 1522 1 35.0 3585 1595 1550
## 1523 1 35.0 3695 1600 1560
## 1524 1 43.0 4490 1730 1485
## 1525 1 93.0 4819 2141 1796
## 1526 1 42.0 4420 1695 1480
## 1527 1 50.0 4315 1800 1645
## 1528 1 65.0 3995 1680 1520
## 1529 1 35.0 3565 1595 1550
## 1530 1 65.0 4899 2094 1464
## 1531 1 40.0 4440 1695 1495
## 1532 1 50.0 4315 1822 1695
## 1533 1 65.0 4936 1868 1479
## 1534 1 42.0 3850 1695 1530
## 1535 1 63.0 4454 2044 1545
## 1536 1 40.0 3955 1694 1544
## 1537 1 65.0 4600 2069 1724
## 1538 1 64.0 4385 1831 1608
## 1539 1 65.0 4936 1868 1479
## 1540 1 55.0 4735 1830 1795
## 1541 1 52.0 3999 1765 1708
## 1542 1 43.0 4370 1700 1475
## 1543 1 45.0 3995 1710 1505
## 1544 1 45.0 4265 1695 1510
## 1545 1 57.0 3985 1820 1844
## 1546 1 48.0 3995 1790 1640
## 1547 1 35.0 3545 1490 1475
## 1548 1 35.0 3585 1595 1550
## 1549 1 83.0 5252 1899 1457
## 1550 1 70.0 4585 1890 1785
## 1551 1 35.0 3565 1595 1550
## 1552 1 42.0 3850 1695 1530
## 1553 1 45.0 3995 1710 1505
## 1554 1 66.0 4869 1864 1469
## 1555 1 63.0 4701 1826 1427
## 1556 1 42.0 3995 1695 1555
## 1557 1 45.0 3995 1760 1555
## 1558 1 35.0 3715 1635 1565
## 1559 1 57.0 3985 1820 1855
## 1560 1 32.0 3655 1620 1675
## 1561 1 80.0 4903 1869 1837
## 1562 1 80.0 4795 1855 1835
## 1563 1 66.0 4686 1810 1442
## 1564 1 37.0 3995 1745 1500
## 1565 1 50.0 4315 1822 1695
## 1566 1 35.0 3600 1600 1560
## 1567 1 50.0 4689 1814 1496
## 1568 1 65.0 4936 1868 1479
## 1569 1 40.0 3955 1694 1544
## 1570 1 45.0 3985 1734 1505
## 1571 1 60.0 4270 1780 1630
## 1572 1 60.0 4270 1780 1630
## 1573 1 50.0 4331 1822 1671
## 1574 1 60.9 4784 2080 1391
## 1575 1 50.0 4300 1790 1635
## 1576 1 35.0 3695 1600 1560
## 1577 1 66.0 4988 1890 1435
## 1578 1 80.0 4705 1840 1850
## 1579 1 35.0 3990 1680 1505
## 1580 1 55.0 4735 1830 1795
## 1581 1 57.0 5140 1928 1901
## 1582 1 42.0 4420 1695 1480
## 1583 1 50.0 4456 1796 1416
## 1584 1 60.0 4456 1820 1995
## 1585 1 45.0 3995 1770 1605
## 1586 1 35.0 3636 1475 1670
## 1587 1 48.0 3995 1790 1640
## 1588 1 42.0 3995 1695 1555
## 1589 1 45.0 4296 1695 1685
## 1590 1 83.0 5151 2000 1805
## 1591 1 55.0 4270 1780 1665
## 1592 1 28.0 3679 1579 1478
## 1593 1 45.0 4440 1729 1475
## 1594 1 54.0 4762 1847 1433
## 1595 1 61.0 4454 1798 1545
## 1596 1 80.0 4892 1860 1837
## 1597 1 60.0 4708 1891 1676
## 1598 1 60.0 3995 1835 1839
## 1599 1 50.0 4570 1800 1465
## 1600 1 43.0 4370 1700 1475
## 1601 1 40.0 3991 1750 1605
## 1602 1 55.0 4735 1830 1795
## 1603 1 43.0 4490 1730 1485
## 1604 1 43.0 4375 1700 1475
## 1605 1 40.0 4440 1695 1495
## 1606 1 60.0 4430 1817 1975
## 1607 1 42.0 3995 1695 1555
## 1608 1 37.0 3845 1735 1530
## 1609 1 63.0 4655 1965 1922
## 1610 1 70.0 4585 1890 1785
## 1611 1 37.0 3995 1735 1515
## 1612 1 43.0 3765 1660 1520
## 1613 1 55.0 4963 1879 1443
## 1614 1 44.0 3850 1727 1414
## 1615 1 45.0 4440 1729 1475
## 1616 1 80.0 5246 1899 1494
## 1617 1 40.0 3955 1694 1544
## 1618 1 93.0 4924 2157 1772
## 1619 1 42.0 3850 1695 1530
## 1620 1 42.0 3850 1695 1530
## 1621 1 70.0 4644 1891 1713
## 1622 1 67.0 4657 1881 1678
## 1623 1 60.0 4456 1820 1930
## 1624 1 71.0 4953 2008 1776
## 1625 1 75.0 4933 1874 1455
## 1626 1 93.0 4819 2141 1796
## 1627 1 66.0 4686 1810 1442
## 1628 1 28.0 3679 1579 1478
## 1629 1 50.0 4424 1804 1494
## 1630 1 57.0 3985 1820 1844
## 1631 1 35.0 3600 1600 1560
## 1632 1 35.0 3395 1490 1475
## 1633 1 57.0 3985 1820 1920
## 1634 1 45.0 4265 1695 1685
## 1635 1 70.0 4695 1815 1840
## 1636 1 80.0 4705 1840 1850
## 1637 1 43.0 3765 1660 1520
## 1638 1 60.0 4270 1780 1630
## 1639 1 43.0 4370 1700 1475
## 1640 1 66.0 4596 1770 1447
## 1641 1 80.0 5063 1860 1494
## 1642 1 55.0 3985 1850 1880
## 1643 1 35.0 3695 1600 1560
## 1644 1 60.0 4395 1818 1640
## 1645 1 48.0 4300 1765 1590
## 1646 1 35.0 3600 1600 1560
## 1647 1 35.0 3520 1475 1660
## 1648 1 90.0 5226 2120 1479
## 1649 1 75.0 4918 1983 1696
## 1650 1 45.0 3775 1695 1510
## 1651 1 55.0 4735 1830 1795
## 1652 1 40.0 3955 1694 1544
## 1653 1 42.0 3995 1695 1555
## 1654 1 70.0 4585 1890 1785
## 1655 1 43.0 4490 1730 1485
## 1656 1 60.0 4788 1903 1791
## 1657 1 64.0 4385 1831 1608
## 1658 1 50.0 4526 1800 1420
## 1659 1 63.0 4701 1826 1427
## 1660 1 43.0 4549 1796 1446
## 1661 1 48.0 3995 1790 1640
## 1662 1 55.0 4540 1760 1480
## 1663 1 37.0 3995 1745 1500
## 1664 1 42.0 3850 1695 1530
## 1665 1 60.0 4456 1820 1995
## 1666 1 70.0 4585 1890 1785
## 1667 1 37.0 3995 1745 1500
## 1668 1 40.0 3999 1734 1601
## 1669 1 55.0 3985 1850 1880
## 1670 1 40.0 4440 1695 1495
## 1671 1 28.0 3679 1579 1478
## 1672 1 42.0 3995 1695 1555
## 1673 1 54.0 4726 1842 1427
## 1674 1 50.0 4659 1814 1476
## 1675 1 50.0 4500 1790 1675
## 1676 1 50.0 4315 1800 1645
## 1677 1 80.0 4795 1855 1835
## 1678 1 43.0 3765 1660 1520
## 1679 1 75.0 4933 1874 1455
## 1680 1 40.0 4440 1695 1495
## 1681 1 70.0 4585 1890 1785
## 1682 1 66.0 4963 1868 1467
## 1683 1 73.0 4939 1886 1457
## 1684 1 50.0 4300 1790 1635
## 1685 1 28.0 3679 1579 1478
## 1686 1 50.0 4331 1822 1671
## 1687 1 55.0 4386 1699 1466
## 1688 1 40.0 3955 1694 1544
## 1689 1 44.0 3994 1811 1607
## 1690 1 45.0 3985 1734 1505
## 1691 1 70.0 4585 1890 1785
## 1692 1 45.0 4265 1695 1685
## 1693 1 43.0 4375 1700 1475
## 1694 1 42.0 4453 1735 1666
## 1695 1 60.0 3995 1835 1839
## 1696 1 48.0 3995 1790 1640
## 1697 1 60.0 4370 1783 1458
## 1698 1 35.0 3600 1600 1560
## 1699 1 50.0 4670 1814 1476
## 1700 1 42.0 4420 1695 1480
## 1701 1 43.0 3995 1660 1520
## 1702 1 55.0 4735 1830 1795
## 1703 1 55.0 4386 1699 1466
## 1704 1 43.0 4370 1700 1475
## 1705 1 35.0 3395 1490 1475
## 1706 1 43.0 4375 1700 1475
## 1707 1 40.0 3995 1704 1525
## 1708 1 44.0 3982 1727 1425
## 1709 1 75.0 4933 1874 1455
## 1710 1 50.0 4500 1790 1675
## 1711 1 50.0 4315 1800 1645
## 1712 1 37.0 3805 1680 1520
## 1713 1 55.0 4585 1765 1760
## 1714 1 35.0 3445 1515 1475
## 1715 1 35.0 3395 1490 1475
## 1716 1 35.0 3620 1475 1460
## 1717 1 45.0 4440 1729 1475
## 1718 1 78.0 4936 1868 1479
## 1719 1 45.0 3971 1682 1469
## 1720 1 48.0 3995 1790 1640
## 1721 1 67.0 4657 1881 1678
## 1722 1 64.0 4385 1831 1608
## 1723 1 50.0 4331 1822 1671
## 1724 1 32.0 3495 1550 1500
## 1725 1 37.0 3995 1735 1515
## 1726 1 60.0 4456 1820 1995
## 1727 1 50.0 4424 1804 1494
## 1728 1 35.0 3793 1665 1587
## 1729 1 80.0 5246 1899 1494
## 1730 1 57.0 3985 1820 1844
## 1731 1 35.0 3565 1595 1550
## 1732 1 80.0 4903 1869 1837
## 1733 1 35.0 3600 1600 1560
## 1734 1 38.0 3495 1495 1518
## 1735 1 37.0 3805 1680 1520
## 1736 1 58.0 4545 1820 1685
## 1737 1 42.0 3995 1695 1555
## 1738 1 64.0 4385 1831 1608
## 1739 1 35.0 3395 1490 1475
## 1740 1 28.0 3679 1579 1478
## 1741 1 52.0 3999 1765 1708
## 1742 1 50.0 4359 2010 1557
## 1743 1 43.0 3995 1660 1520
## 1744 1 40.0 4440 1695 1495
## 1745 1 60.0 4270 1780 1630
## 1746 1 50.0 4456 1796 1416
## 1747 1 43.0 4375 1700 1475
## 1748 1 70.0 5246 1899 1494
## 1749 1 42.0 3995 1695 1555
## 1750 1 80.0 4879 1854 1474
## 1751 1 50.0 4670 1814 1476
## 1752 1 35.0 3610 1645 1560
## 1753 1 45.0 4265 1695 1685
## 1754 1 80.0 4892 1860 1837
## 1755 1 56.0 4795 1967 1416
## 1756 1 80.0 4795 1855 1835
## 1757 1 55.0 4620 1775 1475
## 1758 1 37.0 3990 1755 1523
## 1759 1 54.0 4425 1863 1652
## 1760 1 43.0 4490 1730 1485
## 1761 1 40.0 3999 1734 1601
## 1762 1 35.0 3565 1595 1550
## 1763 1 42.0 3995 1695 1555
## 1764 1 35.0 3395 1490 1475
## 1765 1 43.0 4375 1700 1475
## 1766 1 32.0 3495 1550 1500
## 1767 1 75.0 4933 1874 1455
## 1768 1 60.0 4456 1820 1995
## 1769 1 35.0 3599 1495 1700
## 1770 1 44.0 3994 1811 1607
## 1771 1 35.0 3695 1600 1560
## 1772 1 60.0 4655 1835 1760
## 1773 1 60.0 4270 1780 1630
## 1774 1 35.0 3599 1495 1700
## 1775 1 35.0 3675 1715 1655
## 1776 1 40.0 4440 1695 1495
## 1777 1 43.0 4370 1700 1475
## 1778 1 35.0 3990 1680 1505
## 1779 1 45.0 3995 1770 1605
## 1780 1 55.0 4270 1780 1665
## 1781 1 35.0 3565 1595 1550
## 1782 1 45.0 4445 1775 1700
## 1783 1 45.0 4296 1695 1685
## 1784 1 28.0 3679 1579 1478
## 1785 1 37.0 3995 1745 1500
## 1786 1 45.0 3985 1734 1505
## 1787 1 28.0 3679 1579 1478
## 1788 1 65.0 4735 1830 1795
## 1789 1 41.0 4425 1695 1505
## 1790 1 93.0 4819 2141 1796
## 1791 1 35.0 3610 1680 1500
## 1792 1 48.0 3995 1790 1640
## 1793 1 42.0 3850 1695 1530
## 1794 1 43.0 4490 1730 1485
## 1795 1 42.0 3850 1695 1530
## 1796 1 56.0 4630 1777 1432
## 1797 1 57.0 3985 1820 1844
## 1798 1 65.0 4600 2069 1724
## 1799 1 52.0 3999 1765 1708
## 1800 1 80.0 5063 1860 1494
## 1801 1 77.0 4879 2073 1780
## 1802 1 93.0 4819 2141 1796
## 1803 1 66.0 4686 1810 1442
## 1804 1 43.0 4490 1730 1485
## 1805 1 32.0 3700 1690 1595
## 1806 1 52.0 3999 1765 1708
## 1807 1 66.0 4658 1890 1644
## 1808 1 28.0 3679 1579 1478
## 1809 1 55.0 4386 1699 1466
## 1810 1 42.0 3995 1695 1555
## 1811 1 35.0 3610 1680 1500
## 1812 1 43.0 3765 1660 1520
## 1813 1 60.0 3655 1620 1675
## 1814 1 40.0 4320 1764 1486
## 1815 1 50.0 4424 1804 1494
## 1816 1 35.0 3599 1495 1700
## 1817 1 80.0 4795 1855 1835
## 1818 1 48.0 3995 1790 1640
## 1819 1 35.0 3395 1490 1475
## 1820 1 43.0 3995 1660 1520
## 1821 1 48.0 3995 1790 1640
## 1822 1 42.0 4440 1695 1485
## 1823 1 43.0 4490 1730 1485
## 1824 1 43.0 3765 1660 1520
## 1825 1 60.0 4405 1818 1640
## 1826 1 60.0 4395 1818 1640
## 1827 1 42.0 4440 1695 1485
## 1828 1 55.0 4384 1699 1466
## 1829 1 80.0 4818 1822 1420
## 1830 1 42.0 3995 1695 1555
## 1831 1 35.0 3600 1600 1560
## 1832 1 80.0 5063 1860 1494
## 1833 1 54.0 4726 1842 1427
## 1834 1 28.0 3429 1560 1541
## 1835 1 67.0 4657 1881 1678
## 1836 1 42.0 3850 1695 1530
## 1837 1 47.0 4097 1789 1561
## 1838 1 70.0 4585 1890 1785
## 1839 1 70.0 4585 1890 1785
## 1840 1 52.0 3999 1765 1708
## 1841 1 50.0 4300 1790 1635
## 1842 1 80.0 4795 1855 1835
## 1843 1 50.0 4315 1800 1645
## 1844 1 70.0 4585 1890 1785
## 1845 1 55.0 4655 1965 1922
## 1846 1 45.0 3775 1695 1510
## 1847 1 32.0 3495 1550 1500
## 1848 1 40.0 4440 1695 1495
## 1849 1 45.0 4265 1695 1510
## 1850 1 45.0 3995 1790 1647
## 1851 1 42.0 3995 1695 1555
## 1852 1 80.0 4879 1854 1474
## 1853 1 42.0 3995 1695 1555
## 1854 1 80.0 4695 1840 1850
## 1855 1 40.0 4440 1695 1495
## 1856 1 60.0 4395 1818 1640
## 1857 1 50.0 4359 2010 1557
## 1858 1 40.0 4440 1695 1495
## 1859 1 66.0 4686 1810 1442
## 1860 1 42.0 4249 1690 1503
## 1861 1 66.0 4686 1810 1442
## 1862 1 60.0 4695 1890 1755
## 1863 1 35.0 3599 1495 1700
## 1864 1 48.0 3995 1790 1640
## 1865 1 40.0 4440 1695 1495
## 1866 1 43.0 3765 1660 1520
## 1867 1 100.0 5130 1934 1850
## 1868 1 60.0 4270 1780 1630
## 1869 1 48.0 3995 1790 1640
## 1870 1 43.0 3775 1680 1620
## 1871 1 70.0 4585 1890 1785
## 1872 1 32.0 3495 1550 1500
## 1873 1 45.0 3795 1680 1427
## 1874 1 65.0 4936 1868 1479A=t(X)%*%X
A#Matriz de COV## ones Fuel.Tank.Capacite Length Width
## ones 1874.0 97855.3 8023555 3313019
## Fuel.Tank.Capacite 97855.3 5540618.9 429004132 175949670
## Length 8023555.0 429004131.7 34709363925 14270287180
## Width 3313019.0 175949669.5 14270287180 5889353051
## Heigth 2977726.0 157052090.3 12770588762 5275108831
## Heigth
## ones 2977726
## Fuel.Tank.Capacite 157052090
## Length 12770588762
## Width 5275108831
## Heigth 4765458664InvA=solve(A)
InvA## ones Fuel.Tank.Capacite Length Width
## ones 2.768619e-01 1.171014e-03 -2.026171e-05 -8.800667e-05
## Fuel.Tank.Capacite 1.171014e-03 9.351030e-06 -1.718318e-07 -3.264468e-07
## Length -2.026171e-05 -1.718318e-07 1.096082e-08 -1.528789e-08
## Width -8.800667e-05 -3.264468e-07 -1.528789e-08 1.041158e-07
## Heigth -5.987469e-05 -2.180529e-07 5.873404e-09 -8.531833e-09
## Heigth
## ones -5.987469e-05
## Fuel.Tank.Capacite -2.180529e-07
## Length 5.873404e-09
## Width -8.531833e-09
## Heigth 3.851373e-08tXy=t(X)%*%as.matrix(data_correlacion2[,1])
tXy## [,1]
## ones 3.220055e+09
## Fuel.Tank.Capacite 2.085380e+11
## Length 1.491434e+13
## Width 6.037127e+12
## Heigth 5.173438e+12InvA%*%tXy## [,1]
## ones -7544065.3603
## Fuel.Tank.Capacite 59132.4074
## Length 486.9388
## Width 4949.9942
## Heigth -2933.5108FUNCIÓN LINEAL DEL MODELO: Ecuación matemática que describe la relación entre las variables independientes ‘curbweight’,‘enginesize’,‘horsepower’ y la variable dependiente ‘price’. La relación se asume lineal, lo que significa que los cambios en las variables independientes afectan la variable dependiente de manera proporcional.
modelo2=lm(data_correlacion2$Price~data_correlacion2$Fuel.Tank.Capacite+data_correlacion2$Length+data_correlacion2$Width+data_correlacion2$Heigth)
modelo2##
## Call:
## lm(formula = data_correlacion2$Price ~ data_correlacion2$Fuel.Tank.Capacite +
## data_correlacion2$Length + data_correlacion2$Width + data_correlacion2$Heigth)
##
## Coefficients:
## (Intercept) data_correlacion2$Fuel.Tank.Capacite
## -7544065.4 59132.4
## data_correlacion2$Length data_correlacion2$Width
## 486.9 4950.0
## data_correlacion2$Heigth
## -2933.5Prueba de hipótesis global - Prueba F
F-statistic: 319.4 on 4 and 1869 DF. => significancia global del modelo.
p-value: < 2.2e-16 => significancia estadística de cada uno de los predictores (variables independientes ‘Fuel.Tank.Capacite’,‘Length’,‘Width’,‘Heigth’) del modelo.
Las tres variables independientes del modelo son diferentes a 0.
Prueba de hipótesis individuales - Prueba t
(Intercept) 2.97e-14
data_correlacion2$Fuel.Tank.Capacite < 2e-16
data_correlacion2$Length 0.013
data_correlacion2$Width 4.57e-16
data_correlacion2$Heigth 2.42e-15
Coeficiente de Determinación (R2)
Multiple R-squared (R2): 0.406 => Variabilidad de la variable dependiente a partir de las variables independientes => 40.60 %
Ajusted R-squared (R2 ajustado): 0.4047 => versión ajustada del Multiple R-squared => 40.47 %
summary(modelo2)##
## Call:
## lm(formula = data_correlacion2$Price ~ data_correlacion2$Fuel.Tank.Capacite +
## data_correlacion2$Length + data_correlacion2$Width + data_correlacion2$Heigth)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4982919 -750418 -210502 407446 29603361
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7544065.4 984908.7 -7.660 2.97e-14 ***
## data_correlacion2$Fuel.Tank.Capacite 59132.4 5723.9 10.331 < 2e-16 ***
## data_correlacion2$Length 486.9 196.0 2.485 0.013 *
## data_correlacion2$Width 4950.0 604.0 8.196 4.57e-16 ***
## data_correlacion2$Heigth -2933.5 367.3 -7.986 2.42e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1872000 on 1869 degrees of freedom
## Multiple R-squared: 0.406, Adjusted R-squared: 0.4047
## F-statistic: 319.4 on 4 and 1869 DF, p-value: < 2.2e-16————————————————————————————-
ANÁLISIS REGRESIÓN LINEAL MÚLTIPLE (FINAL) bd_mtcars
————————————————————————————-
# Cargamos la base de datos "bd_usedcars" => UsedCars.csv
bd_usedcars <- read.csv(url("https://raw.githubusercontent.com/geovannychoez/prueba/master/UsedCars.csv"), header = TRUE)
names(bd_usedcars) <- c('Make','Model','Price','Year','Kilometer',
'Fuel.Type','Transmission','Location','Color','Owner',
'Seller.Type','Engine','Max.Power','Max.Torque','Drivetrain',
'Length','Width','Heigth','Seating.Capcity','Fuel.Tank.Capacite')
# Se crea la variable 'data_correlacion1' con el data set bd_mtcars.
data_correlacion2 <- na.omit(bd_usedcars[, c('Price','Fuel.Tank.Capacite','Length','Width')])1) Ecuación matemática del modelo (y=x1+x2+x3)
Modelo Final
Se crea la variable ‘modelo’ usando el dataset ‘data_correlacion’, se define las variables independientes y dependiente.
Variable Dependiente ‘y’: price Modelo de regresión para predecir el precio usando las variables independientes.
Variables Independientes ‘x’: ‘Fuel.Tank.Capacite’,‘Length’,‘Width’
y=x1+x2+x3
X=as.matrix(cbind("ones"=c(1:1),data_correlacion2[,2:4]))
X## ones Fuel.Tank.Capacite Length Width
## 1 1 35.0 3990 1680
## 2 1 42.0 3995 1695
## 3 1 35.0 3585 1595
## 4 1 37.0 3995 1745
## 5 1 55.0 4735 1830
## 6 1 43.0 4490 1730
## 7 1 51.0 4439 1821
## 8 1 50.0 4670 1814
## 9 1 50.0 4331 1822
## 10 1 45.0 3985 1734
## 11 1 28.0 3679 1579
## 12 1 43.0 4490 1730
## 13 1 50.0 4598 1894
## 14 1 45.0 3971 1682
## 15 1 35.0 3695 1600
## 16 1 35.0 3445 1515
## 17 1 37.0 3995 1745
## 18 1 32.0 3655 1620
## 19 1 60.0 4270 1780
## 20 1 27.0 3565 1520
## 21 1 55.0 4384 1699
## 22 1 35.0 3610 1645
## 23 1 45.0 3995 1770
## 24 1 60.0 3545 1490
## 25 1 43.0 3775 1680
## 26 1 60.0 4270 1780
## 27 1 35.0 3610 1680
## 28 1 45.0 3985 1734
## 29 1 40.0 3999 1734
## 30 1 45.0 3995 1770
## 31 1 60.0 4270 1780
## 32 1 52.0 3999 1765
## 33 1 35.0 3565 1525
## 34 1 35.0 3746 1647
## 35 1 35.0 3992 1677
## 36 1 55.0 4735 1830
## 37 1 66.0 4656 1890
## 38 1 55.0 4270 1780
## 39 1 70.0 4804 2141
## 40 1 55.0 4620 1775
## 41 1 63.0 4701 1826
## 42 1 70.0 4082 1777
## 43 1 45.0 3985 1734
## 44 1 60.0 3920 1726
## 45 1 37.0 3995 1745
## 46 1 35.0 3600 1600
## 47 1 43.0 4490 1730
## 48 1 43.0 4490 1730
## 49 1 60.0 4270 1780
## 50 1 60.0 4270 1780
## 51 1 28.0 3679 1579
## 52 1 60.0 4655 1835
## 53 1 35.0 3746 1647
## 54 1 55.0 4585 1765
## 55 1 67.0 4657 1881
## 56 1 60.0 4395 1818
## 57 1 60.0 4430 1817
## 58 1 35.0 3610 1680
## 59 1 57.0 4633 1811
## 60 1 40.0 4440 1695
## 61 1 45.0 3970 1682
## 62 1 48.0 3995 1790
## 63 1 40.0 3675 1475
## 64 1 43.0 3765 1660
## 65 1 67.0 4648 1881
## 66 1 80.0 4795 1855
## 67 1 50.0 4545 1750
## 68 1 37.0 3845 1735
## 69 1 37.0 3995 1775
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## 71 1 40.0 4440 1695
## 72 1 45.0 3795 1680
## 73 1 40.0 3955 1694
## 74 1 45.0 3970 1682
## 75 1 35.0 3990 1680
## 76 1 70.0 4825 1825
## 77 1 57.0 3985 1820
## 78 1 66.0 4596 1770
## 79 1 64.0 4385 1831
## 80 1 37.0 3995 1745
## 81 1 63.0 4454 2044
## 82 1 37.0 3995 1745
## 83 1 60.0 4270 1780
## 84 1 55.0 4384 1699
## 85 1 66.0 4596 1770
## 86 1 65.0 4825 1825
## 87 1 37.0 3995 1735
## 88 1 50.0 4331 1822
## 89 1 35.0 3599 1495
## 90 1 48.0 3995 1790
## 91 1 75.0 4931 1983
## 92 1 59.0 4686 1810
## 93 1 45.0 3985 1734
## 94 1 43.0 4375 1700
## 95 1 35.0 3990 1680
## 96 1 55.0 4540 1760
## 97 1 45.0 3985 1734
## 98 1 43.0 3765 1660
## 99 1 60.0 4270 1780
## 100 1 65.0 4915 1874
## 101 1 63.0 4454 2044
## 102 1 42.0 3995 1821
## 103 1 37.0 3840 1735
## 104 1 57.0 3985 1820
## 105 1 42.0 4420 1695
## 106 1 80.0 4879 1854
## 107 1 80.0 4705 1840
## 108 1 44.0 3995 1706
## 109 1 55.0 4386 1699
## 110 1 35.0 3395 1490
## 111 1 45.0 4265 1695
## 112 1 45.0 3795 1680
## 113 1 50.0 4456 1796
## 114 1 50.0 4598 1894
## 115 1 37.0 3995 1775
## 116 1 45.0 3985 1734
## 117 1 45.0 3970 1682
## 118 1 42.0 3995 1695
## 119 1 35.0 3565 1525
## 120 1 43.0 3765 1660
## 121 1 50.0 4300 1790
## 122 1 55.0 4318 1805
## 123 1 75.0 5052 1968
## 124 1 37.0 3995 1775
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## 126 1 35.0 3599 1495
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## 130 1 70.0 4663 1898
## 131 1 50.0 4360 1822
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## 140 1 50.0 4315 1800
## 141 1 37.0 3995 1745
## 142 1 80.0 5063 1860
## 143 1 45.0 4296 1695
## 144 1 43.0 4370 1700
## 145 1 43.0 4370 1700
## 146 1 70.0 4600 2069
## 147 1 80.0 4795 1855
## 148 1 93.0 4819 2141
## 149 1 43.0 3995 1660
## 150 1 70.0 5453 1899
## 151 1 55.0 4270 1780
## 152 1 48.0 4323 1809
## 153 1 58.0 4630 1780
## 154 1 35.0 3395 1490
## 155 1 50.0 4315 1822
## 156 1 43.0 3765 1660
## 157 1 40.0 4440 1695
## 158 1 66.0 4686 1810
## 159 1 40.0 3985 1734
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## 161 1 55.0 4386 1699
## 162 1 45.0 3995 1790
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## 166 1 65.0 4915 1874
## 167 1 60.0 4430 1817
## 168 1 80.0 4705 1840
## 169 1 45.0 3985 1734
## 170 1 52.0 3999 1765
## 171 1 100.0 5089 1983
## 172 1 66.0 4686 1810
## 173 1 27.0 3565 1520
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## 175 1 60.0 4655 1835
## 176 1 43.0 3760 1690
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## 178 1 40.0 4440 1695
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## 182 1 60.0 4370 1783
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## 191 1 35.0 3395 1490
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## 205 1 42.0 4420 1695
## 206 1 28.0 3679 1579
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## 208 1 50.0 4661 1894
## 209 1 65.0 4915 1874
## 210 1 35.0 3610 1680
## 211 1 42.0 3850 1695
## 212 1 60.0 4456 1820
## 213 1 55.0 4735 1830
## 214 1 35.0 3995 1695
## 215 1 93.0 4819 2141
## 216 1 60.0 4395 1818
## 217 1 80.0 5005 1981
## 218 1 80.0 4795 1855
## 219 1 100.0 4846 1939
## 220 1 55.0 4735 1830
## 221 1 80.0 4695 1840
## 222 1 100.0 5089 1983
## 223 1 60.0 3655 1620
## 224 1 35.0 3545 1490
## 225 1 43.0 4490 1730
## 226 1 37.0 3840 1735
## 227 1 43.0 4370 1700
## 228 1 66.0 4702 1810
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## 230 1 44.0 3994 1811
## 231 1 35.0 3395 1490
## 232 1 70.0 4585 1890
## 233 1 50.0 4598 1894
## 234 1 42.0 4386 1683
## 235 1 37.0 3827 1742
## 236 1 43.0 3765 1660
## 237 1 40.0 4440 1695
## 238 1 37.0 3995 1745
## 239 1 82.0 4731 2071
## 240 1 104.0 4879 2073
## 241 1 80.0 4705 1840
## 242 1 28.0 3679 1579
## 243 1 51.0 4439 1821
## 244 1 64.0 4385 1831
## 245 1 35.0 3520 1475
## 246 1 40.0 3985 1734
## 247 1 70.0 4585 1890
## 248 1 43.0 3765 1660
## 249 1 42.0 3995 1695
## 250 1 85.0 4846 2155
## 251 1 50.0 4331 1822
## 252 1 28.0 3679 1579
## 253 1 50.0 4300 1790
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## 255 1 65.0 4600 2069
## 256 1 37.0 3995 1745
## 257 1 60.0 4270 1780
## 258 1 55.0 4735 1830
## 259 1 45.0 3970 1682
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## 263 1 35.0 3585 1595
## 264 1 60.0 4788 1903
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## 266 1 60.0 4270 1780
## 267 1 100.0 5130 1934
## 268 1 64.0 4385 1831
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## 273 1 45.0 3995 1770
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## 275 1 67.0 4648 1881
## 276 1 40.0 3999 1734
## 277 1 65.0 4936 1868
## 278 1 35.0 3990 1680
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## 280 1 68.0 4491 1852
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## 283 1 62.0 4475 1850
## 284 1 45.0 3995 1710
## 285 1 60.0 4370 1783
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## 304 1 35.0 3610 1680
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## 308 1 57.0 4936 1868
## 309 1 55.0 4655 1965
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## 312 1 80.0 4922 2004
## 313 1 52.0 3999 1765
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## 443 1 93.0 4891 2003
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## 1266 1 55.0 4585 1765
## 1267 1 50.0 4292 1780
## 1268 1 48.0 3995 1790
## 1269 1 55.0 4390 1699
## 1270 1 35.0 3600 1600
## 1271 1 50.0 4545 1750
## 1272 1 65.0 4899 2094
## 1273 1 60.0 3610 1645
## 1274 1 66.0 4861 1864
## 1275 1 32.0 3495 1550
## 1276 1 60.0 4720 1835
## 1277 1 57.0 4360 2120
## 1278 1 60.0 3545 1490
## 1279 1 43.0 3765 1660
## 1280 1 40.0 3886 1695
## 1281 1 35.0 3585 1595
## 1282 1 60.0 4430 1817
## 1283 1 42.0 3995 1695
## 1284 1 67.0 4657 1881
## 1285 1 35.0 3585 1595
## 1286 1 45.0 3995 1770
## 1287 1 42.0 3850 1695
## 1288 1 60.0 4270 1780
## 1289 1 44.0 3995 1706
## 1290 1 45.0 4265 1695
## 1291 1 70.0 4585 1890
## 1292 1 60.0 4370 1783
## 1293 1 37.0 3995 1745
## 1294 1 60.0 4270 1780
## 1295 1 48.0 4300 1765
## 1296 1 35.0 3715 1635
## 1297 1 45.0 3985 1734
## 1298 1 35.0 3395 1490
## 1299 1 50.0 4424 1804
## 1300 1 65.0 4915 1874
## 1301 1 65.0 4899 2094
## 1302 1 35.0 3545 1490
## 1303 1 40.0 3675 1475
## 1304 1 55.0 4735 1830
## 1305 1 65.0 4915 1820
## 1306 1 40.0 4440 1695
## 1307 1 55.0 4655 1965
## 1308 1 48.0 4300 1765
## 1309 1 40.0 4440 1695
## 1310 1 35.0 3585 1595
## 1311 1 35.0 3545 1490
## 1312 1 63.0 4701 1826
## 1313 1 57.0 3985 1820
## 1314 1 50.0 4315 1800
## 1315 1 66.0 4693 1810
## 1316 1 70.0 4585 1890
## 1317 1 60.0 3995 1835
## 1318 1 70.0 4663 1893
## 1319 1 57.0 3985 1820
## 1320 1 60.0 4270 1780
## 1321 1 66.0 4658 1890
## 1322 1 60.0 4624 2031
## 1323 1 57.0 3985 1820
## 1324 1 45.0 3995 1760
## 1325 1 63.0 4454 2044
## 1326 1 70.0 4804 2141
## 1327 1 50.0 4424 1804
## 1328 1 43.0 4370 1700
## 1329 1 75.0 5052 1968
## 1330 1 60.0 4270 1780
## 1331 1 48.0 3995 1790
## 1332 1 35.0 3600 1475
## 1333 1 51.0 4439 1821
## 1334 1 63.0 4454 2044
## 1335 1 75.0 4933 1874
## 1336 1 48.0 3995 1790
## 1337 1 42.0 4420 1695
## 1338 1 42.0 4420 1695
## 1339 1 55.0 4386 1699
## 1340 1 41.0 3805 1665
## 1341 1 35.0 3990 1680
## 1342 1 57.0 4633 1811
## 1343 1 55.0 4735 1830
## 1344 1 42.0 3850 1695
## 1345 1 42.0 3850 1695
## 1346 1 50.0 4331 1822
## 1347 1 35.0 3746 1647
## 1348 1 35.0 3600 1600
## 1349 1 32.0 3700 1690
## 1350 1 64.0 4385 1831
## 1351 1 45.0 3971 1682
## 1352 1 37.0 3995 1745
## 1353 1 60.0 4270 1780
## 1354 1 75.0 5052 1968
## 1355 1 43.0 4370 1700
## 1356 1 44.0 3982 1727
## 1357 1 43.0 4160 1690
## 1358 1 35.0 3565 1595
## 1359 1 43.0 3995 1660
## 1360 1 35.0 3620 1475
## 1361 1 42.0 4440 1695
## 1362 1 66.0 4596 1770
## 1363 1 42.0 3850 1695
## 1364 1 42.0 3995 1695
## 1365 1 50.0 4975 1865
## 1366 1 37.0 3995 1775
## 1367 1 45.0 3971 1682
## 1368 1 43.0 3765 1660
## 1369 1 50.0 4659 1814
## 1370 1 50.0 4417 1804
## 1371 1 66.0 4658 1890
## 1372 1 43.0 4490 1730
## 1373 1 60.0 3805 1680
## 1374 1 35.0 3495 1475
## 1375 1 35.0 3995 1695
## 1376 1 43.0 4370 1700
## 1377 1 80.0 4705 1840
## 1378 1 70.0 4585 1890
## 1379 1 50.0 4315 1800
## 1380 1 60.0 4430 1817
## 1381 1 35.0 3585 1595
## 1382 1 45.0 3985 1734
## 1383 1 80.0 4795 1855
## 1384 1 55.0 4270 1780
## 1385 1 40.0 4440 1695
## 1386 1 35.0 3565 1595
## 1387 1 80.0 4922 2004
## 1388 1 55.0 4963 1879
## 1389 1 43.0 3995 1660
## 1390 1 43.0 4370 1700
## 1391 1 80.0 4892 1860
## 1392 1 43.0 4370 1700
## 1393 1 55.0 4270 1780
## 1394 1 35.0 3585 1595
## 1395 1 55.0 4620 1775
## 1396 1 48.0 3995 1790
## 1397 1 50.0 4456 1796
## 1398 1 37.0 3995 1745
## 1399 1 45.0 3987 1698
## 1400 1 66.0 4596 2020
## 1401 1 45.0 3970 1682
## 1402 1 52.0 3998 1765
## 1403 1 28.0 3679 1579
## 1404 1 43.0 4375 1700
## 1405 1 78.0 4755 1900
## 1406 1 63.0 4454 2044
## 1407 1 50.0 4456 1796
## 1408 1 37.0 3995 1735
## 1409 1 75.0 5052 1968
## 1410 1 42.0 3850 1695
## 1411 1 45.0 3995 1682
## 1412 1 40.0 4549 1748
## 1413 1 80.0 4868 1854
## 1414 1 43.0 4490 1730
## 1415 1 50.0 4598 1894
## 1416 1 43.0 3765 1660
## 1417 1 43.0 3765 1660
## 1418 1 42.0 4440 1695
## 1419 1 57.0 4633 1811
## 1420 1 80.0 4705 1840
## 1421 1 60.0 4270 1780
## 1422 1 50.0 4598 1894
## 1423 1 55.0 4585 1765
## 1424 1 45.0 3985 1734
## 1425 1 66.0 4686 1810
## 1426 1 43.0 4490 1730
## 1427 1 65.0 4600 2069
## 1428 1 55.0 4735 1830
## 1429 1 45.0 4296 1695
## 1430 1 41.0 4425 1695
## 1431 1 35.0 3990 1680
## 1432 1 45.0 3971 1682
## 1433 1 35.0 3995 1695
## 1434 1 43.0 3995 1660
## 1435 1 55.0 4384 1699
## 1436 1 55.0 4390 1699
## 1437 1 90.0 5207 2157
## 1438 1 75.0 4629 1898
## 1439 1 40.0 4440 1695
## 1440 1 43.0 3765 1660
## 1441 1 43.0 4370 1700
## 1442 1 55.0 4318 1805
## 1443 1 70.0 4585 1890
## 1444 1 42.0 4420 1695
## 1445 1 45.0 3895 1735
## 1446 1 62.0 4475 1850
## 1447 1 42.0 3995 1695
## 1448 1 42.0 3995 1695
## 1449 1 35.0 3585 1595
## 1450 1 42.0 3995 1821
## 1451 1 60.0 4270 1780
## 1452 1 35.0 3565 1525
## 1453 1 60.0 4107 1745
## 1454 1 52.0 3999 1765
## 1455 1 35.0 3640 1595
## 1456 1 54.0 4425 1863
## 1457 1 35.0 3620 1475
## 1458 1 48.0 3995 1790
## 1459 1 66.0 4658 1890
## 1460 1 48.0 4300 1765
## 1461 1 45.0 4265 1695
## 1462 1 80.0 5063 1860
## 1463 1 66.0 4658 1890
## 1464 1 75.0 4629 1898
## 1465 1 40.0 4440 1695
## 1466 1 50.0 4456 1796
## 1467 1 70.0 4950 1845
## 1468 1 45.0 4440 1729
## 1469 1 45.0 4395 1735
## 1470 1 65.0 4899 2094
## 1471 1 35.0 3990 1680
## 1472 1 43.0 4490 1730
## 1473 1 48.0 3995 1790
## 1474 1 43.0 4160 1690
## 1475 1 100.0 5120 1934
## 1476 1 65.0 4915 1874
## 1477 1 60.0 4456 1820
## 1478 1 63.0 4701 1826
## 1479 1 32.0 3495 1550
## 1480 1 50.0 4315 1822
## 1481 1 45.0 4395 1735
## 1482 1 43.0 4549 1796
## 1483 1 45.0 3985 1734
## 1484 1 55.0 4270 1780
## 1485 1 65.0 4600 2069
## 1486 1 28.0 3679 1579
## 1487 1 45.0 4296 1695
## 1488 1 35.0 3565 1595
## 1489 1 43.0 3765 1660
## 1490 1 55.0 4585 1760
## 1491 1 93.0 4819 2141
## 1492 1 43.0 4490 1730
## 1493 1 37.0 3995 1735
## 1494 1 35.0 3785 1635
## 1495 1 70.0 4585 1890
## 1496 1 63.0 4701 1826
## 1497 1 43.0 4490 1730
## 1498 1 37.0 3995 1745
## 1499 1 35.0 3599 1495
## 1500 1 60.0 4788 1903
## 1501 1 80.0 4705 1840
## 1502 1 43.0 3775 1680
## 1503 1 55.0 4390 1699
## 1504 1 37.0 3995 1775
## 1505 1 55.0 4735 1830
## 1506 1 43.0 4549 1796
## 1507 1 44.0 3994 1811
## 1508 1 40.0 3985 1734
## 1509 1 35.0 3585 1595
## 1510 1 81.0 4882 1894
## 1511 1 42.0 3995 1821
## 1512 1 45.0 4265 1695
## 1513 1 42.0 3850 1695
## 1514 1 35.0 3990 1680
## 1515 1 60.0 4456 1820
## 1516 1 45.0 3995 1770
## 1517 1 35.0 3620 1475
## 1518 1 35.0 3990 1680
## 1519 1 45.0 3995 1682
## 1520 1 60.0 4655 1835
## 1521 1 35.0 3599 1495
## 1522 1 35.0 3585 1595
## 1523 1 35.0 3695 1600
## 1524 1 43.0 4490 1730
## 1525 1 93.0 4819 2141
## 1526 1 42.0 4420 1695
## 1527 1 50.0 4315 1800
## 1528 1 65.0 3995 1680
## 1529 1 35.0 3565 1595
## 1530 1 65.0 4899 2094
## 1531 1 40.0 4440 1695
## 1532 1 50.0 4315 1822
## 1533 1 65.0 4936 1868
## 1534 1 42.0 3850 1695
## 1535 1 63.0 4454 2044
## 1536 1 40.0 3955 1694
## 1537 1 65.0 4600 2069
## 1538 1 64.0 4385 1831
## 1539 1 65.0 4936 1868
## 1540 1 55.0 4735 1830
## 1541 1 52.0 3999 1765
## 1542 1 43.0 4370 1700
## 1543 1 45.0 3995 1710
## 1544 1 45.0 4265 1695
## 1545 1 57.0 3985 1820
## 1546 1 48.0 3995 1790
## 1547 1 35.0 3545 1490
## 1548 1 35.0 3585 1595
## 1549 1 83.0 5252 1899
## 1550 1 70.0 4585 1890
## 1551 1 35.0 3565 1595
## 1552 1 42.0 3850 1695
## 1553 1 45.0 3995 1710
## 1554 1 66.0 4869 1864
## 1555 1 63.0 4701 1826
## 1556 1 42.0 3995 1695
## 1557 1 45.0 3995 1760
## 1558 1 35.0 3715 1635
## 1559 1 57.0 3985 1820
## 1560 1 32.0 3655 1620
## 1561 1 80.0 4903 1869
## 1562 1 80.0 4795 1855
## 1563 1 66.0 4686 1810
## 1564 1 37.0 3995 1745
## 1565 1 50.0 4315 1822
## 1566 1 35.0 3600 1600
## 1567 1 50.0 4689 1814
## 1568 1 65.0 4936 1868
## 1569 1 40.0 3955 1694
## 1570 1 45.0 3985 1734
## 1571 1 60.0 4270 1780
## 1572 1 60.0 4270 1780
## 1573 1 50.0 4331 1822
## 1574 1 60.9 4784 2080
## 1575 1 50.0 4300 1790
## 1576 1 35.0 3695 1600
## 1577 1 66.0 4988 1890
## 1578 1 80.0 4705 1840
## 1579 1 35.0 3990 1680
## 1580 1 55.0 4735 1830
## 1581 1 57.0 5140 1928
## 1582 1 42.0 4420 1695
## 1583 1 50.0 4456 1796
## 1584 1 60.0 4456 1820
## 1585 1 45.0 3995 1770
## 1586 1 35.0 3636 1475
## 1587 1 48.0 3995 1790
## 1588 1 42.0 3995 1695
## 1589 1 45.0 4296 1695
## 1590 1 83.0 5151 2000
## 1591 1 55.0 4270 1780
## 1592 1 28.0 3679 1579
## 1593 1 45.0 4440 1729
## 1594 1 54.0 4762 1847
## 1595 1 61.0 4454 1798
## 1596 1 80.0 4892 1860
## 1597 1 60.0 4708 1891
## 1598 1 60.0 3995 1835
## 1599 1 50.0 4570 1800
## 1600 1 43.0 4370 1700
## 1601 1 40.0 3991 1750
## 1602 1 55.0 4735 1830
## 1603 1 43.0 4490 1730
## 1604 1 43.0 4375 1700
## 1605 1 40.0 4440 1695
## 1606 1 60.0 4430 1817
## 1607 1 42.0 3995 1695
## 1608 1 37.0 3845 1735
## 1609 1 63.0 4655 1965
## 1610 1 70.0 4585 1890
## 1611 1 37.0 3995 1735
## 1612 1 43.0 3765 1660
## 1613 1 55.0 4963 1879
## 1614 1 44.0 3850 1727
## 1615 1 45.0 4440 1729
## 1616 1 80.0 5246 1899
## 1617 1 40.0 3955 1694
## 1618 1 93.0 4924 2157
## 1619 1 42.0 3850 1695
## 1620 1 42.0 3850 1695
## 1621 1 70.0 4644 1891
## 1622 1 67.0 4657 1881
## 1623 1 60.0 4456 1820
## 1624 1 71.0 4953 2008
## 1625 1 75.0 4933 1874
## 1626 1 93.0 4819 2141
## 1627 1 66.0 4686 1810
## 1628 1 28.0 3679 1579
## 1629 1 50.0 4424 1804
## 1630 1 57.0 3985 1820
## 1631 1 35.0 3600 1600
## 1632 1 35.0 3395 1490
## 1633 1 57.0 3985 1820
## 1634 1 45.0 4265 1695
## 1635 1 70.0 4695 1815
## 1636 1 80.0 4705 1840
## 1637 1 43.0 3765 1660
## 1638 1 60.0 4270 1780
## 1639 1 43.0 4370 1700
## 1640 1 66.0 4596 1770
## 1641 1 80.0 5063 1860
## 1642 1 55.0 3985 1850
## 1643 1 35.0 3695 1600
## 1644 1 60.0 4395 1818
## 1645 1 48.0 4300 1765
## 1646 1 35.0 3600 1600
## 1647 1 35.0 3520 1475
## 1648 1 90.0 5226 2120
## 1649 1 75.0 4918 1983
## 1650 1 45.0 3775 1695
## 1651 1 55.0 4735 1830
## 1652 1 40.0 3955 1694
## 1653 1 42.0 3995 1695
## 1654 1 70.0 4585 1890
## 1655 1 43.0 4490 1730
## 1656 1 60.0 4788 1903
## 1657 1 64.0 4385 1831
## 1658 1 50.0 4526 1800
## 1659 1 63.0 4701 1826
## 1660 1 43.0 4549 1796
## 1661 1 48.0 3995 1790
## 1662 1 55.0 4540 1760
## 1663 1 37.0 3995 1745
## 1664 1 42.0 3850 1695
## 1665 1 60.0 4456 1820
## 1666 1 70.0 4585 1890
## 1667 1 37.0 3995 1745
## 1668 1 40.0 3999 1734
## 1669 1 55.0 3985 1850
## 1670 1 40.0 4440 1695
## 1671 1 28.0 3679 1579
## 1672 1 42.0 3995 1695
## 1673 1 54.0 4726 1842
## 1674 1 50.0 4659 1814
## 1675 1 50.0 4500 1790
## 1676 1 50.0 4315 1800
## 1677 1 80.0 4795 1855
## 1678 1 43.0 3765 1660
## 1679 1 75.0 4933 1874
## 1680 1 40.0 4440 1695
## 1681 1 70.0 4585 1890
## 1682 1 66.0 4963 1868
## 1683 1 73.0 4939 1886
## 1684 1 50.0 4300 1790
## 1685 1 28.0 3679 1579
## 1686 1 50.0 4331 1822
## 1687 1 55.0 4386 1699
## 1688 1 40.0 3955 1694
## 1689 1 44.0 3994 1811
## 1690 1 45.0 3985 1734
## 1691 1 70.0 4585 1890
## 1692 1 45.0 4265 1695
## 1693 1 43.0 4375 1700
## 1694 1 42.0 4453 1735
## 1695 1 60.0 3995 1835
## 1696 1 48.0 3995 1790
## 1697 1 60.0 4370 1783
## 1698 1 35.0 3600 1600
## 1699 1 50.0 4670 1814
## 1700 1 42.0 4420 1695
## 1701 1 43.0 3995 1660
## 1702 1 55.0 4735 1830
## 1703 1 55.0 4386 1699
## 1704 1 43.0 4370 1700
## 1705 1 35.0 3395 1490
## 1706 1 43.0 4375 1700
## 1707 1 40.0 3995 1704
## 1708 1 44.0 3982 1727
## 1709 1 75.0 4933 1874
## 1710 1 50.0 4500 1790
## 1711 1 50.0 4315 1800
## 1712 1 37.0 3805 1680
## 1713 1 55.0 4585 1765
## 1714 1 35.0 3445 1515
## 1715 1 35.0 3395 1490
## 1716 1 35.0 3620 1475
## 1717 1 45.0 4440 1729
## 1718 1 78.0 4936 1868
## 1719 1 45.0 3971 1682
## 1720 1 48.0 3995 1790
## 1721 1 67.0 4657 1881
## 1722 1 64.0 4385 1831
## 1723 1 50.0 4331 1822
## 1724 1 32.0 3495 1550
## 1725 1 37.0 3995 1735
## 1726 1 60.0 4456 1820
## 1727 1 50.0 4424 1804
## 1728 1 35.0 3793 1665
## 1729 1 80.0 5246 1899
## 1730 1 57.0 3985 1820
## 1731 1 35.0 3565 1595
## 1732 1 80.0 4903 1869
## 1733 1 35.0 3600 1600
## 1734 1 38.0 3495 1495
## 1735 1 37.0 3805 1680
## 1736 1 58.0 4545 1820
## 1737 1 42.0 3995 1695
## 1738 1 64.0 4385 1831
## 1739 1 35.0 3395 1490
## 1740 1 28.0 3679 1579
## 1741 1 52.0 3999 1765
## 1742 1 50.0 4359 2010
## 1743 1 43.0 3995 1660
## 1744 1 40.0 4440 1695
## 1745 1 60.0 4270 1780
## 1746 1 50.0 4456 1796
## 1747 1 43.0 4375 1700
## 1748 1 70.0 5246 1899
## 1749 1 42.0 3995 1695
## 1750 1 80.0 4879 1854
## 1751 1 50.0 4670 1814
## 1752 1 35.0 3610 1645
## 1753 1 45.0 4265 1695
## 1754 1 80.0 4892 1860
## 1755 1 56.0 4795 1967
## 1756 1 80.0 4795 1855
## 1757 1 55.0 4620 1775
## 1758 1 37.0 3990 1755
## 1759 1 54.0 4425 1863
## 1760 1 43.0 4490 1730
## 1761 1 40.0 3999 1734
## 1762 1 35.0 3565 1595
## 1763 1 42.0 3995 1695
## 1764 1 35.0 3395 1490
## 1765 1 43.0 4375 1700
## 1766 1 32.0 3495 1550
## 1767 1 75.0 4933 1874
## 1768 1 60.0 4456 1820
## 1769 1 35.0 3599 1495
## 1770 1 44.0 3994 1811
## 1771 1 35.0 3695 1600
## 1772 1 60.0 4655 1835
## 1773 1 60.0 4270 1780
## 1774 1 35.0 3599 1495
## 1775 1 35.0 3675 1715
## 1776 1 40.0 4440 1695
## 1777 1 43.0 4370 1700
## 1778 1 35.0 3990 1680
## 1779 1 45.0 3995 1770
## 1780 1 55.0 4270 1780
## 1781 1 35.0 3565 1595
## 1782 1 45.0 4445 1775
## 1783 1 45.0 4296 1695
## 1784 1 28.0 3679 1579
## 1785 1 37.0 3995 1745
## 1786 1 45.0 3985 1734
## 1787 1 28.0 3679 1579
## 1788 1 65.0 4735 1830
## 1789 1 41.0 4425 1695
## 1790 1 93.0 4819 2141
## 1791 1 35.0 3610 1680
## 1792 1 48.0 3995 1790
## 1793 1 42.0 3850 1695
## 1794 1 43.0 4490 1730
## 1795 1 42.0 3850 1695
## 1796 1 56.0 4630 1777
## 1797 1 57.0 3985 1820
## 1798 1 65.0 4600 2069
## 1799 1 52.0 3999 1765
## 1800 1 80.0 5063 1860
## 1801 1 77.0 4879 2073
## 1802 1 93.0 4819 2141
## 1803 1 66.0 4686 1810
## 1804 1 43.0 4490 1730
## 1805 1 32.0 3700 1690
## 1806 1 52.0 3999 1765
## 1807 1 66.0 4658 1890
## 1808 1 28.0 3679 1579
## 1809 1 55.0 4386 1699
## 1810 1 42.0 3995 1695
## 1811 1 35.0 3610 1680
## 1812 1 43.0 3765 1660
## 1813 1 60.0 3655 1620
## 1814 1 40.0 4320 1764
## 1815 1 50.0 4424 1804
## 1816 1 35.0 3599 1495
## 1817 1 80.0 4795 1855
## 1818 1 48.0 3995 1790
## 1819 1 35.0 3395 1490
## 1820 1 43.0 3995 1660
## 1821 1 48.0 3995 1790
## 1822 1 42.0 4440 1695
## 1823 1 43.0 4490 1730
## 1824 1 43.0 3765 1660
## 1825 1 60.0 4405 1818
## 1826 1 60.0 4395 1818
## 1827 1 42.0 4440 1695
## 1828 1 55.0 4384 1699
## 1829 1 80.0 4818 1822
## 1830 1 42.0 3995 1695
## 1831 1 35.0 3600 1600
## 1832 1 80.0 5063 1860
## 1833 1 54.0 4726 1842
## 1834 1 28.0 3429 1560
## 1835 1 67.0 4657 1881
## 1836 1 42.0 3850 1695
## 1837 1 47.0 4097 1789
## 1838 1 70.0 4585 1890
## 1839 1 70.0 4585 1890
## 1840 1 52.0 3999 1765
## 1841 1 50.0 4300 1790
## 1842 1 80.0 4795 1855
## 1843 1 50.0 4315 1800
## 1844 1 70.0 4585 1890
## 1845 1 55.0 4655 1965
## 1846 1 45.0 3775 1695
## 1847 1 32.0 3495 1550
## 1848 1 40.0 4440 1695
## 1849 1 45.0 4265 1695
## 1850 1 45.0 3995 1790
## 1851 1 42.0 3995 1695
## 1852 1 80.0 4879 1854
## 1853 1 42.0 3995 1695
## 1854 1 80.0 4695 1840
## 1855 1 40.0 4440 1695
## 1856 1 60.0 4395 1818
## 1857 1 50.0 4359 2010
## 1858 1 40.0 4440 1695
## 1859 1 66.0 4686 1810
## 1860 1 42.0 4249 1690
## 1861 1 66.0 4686 1810
## 1862 1 60.0 4695 1890
## 1863 1 35.0 3599 1495
## 1864 1 48.0 3995 1790
## 1865 1 40.0 4440 1695
## 1866 1 43.0 3765 1660
## 1867 1 100.0 5130 1934
## 1868 1 60.0 4270 1780
## 1869 1 48.0 3995 1790
## 1870 1 43.0 3775 1680
## 1871 1 70.0 4585 1890
## 1872 1 32.0 3495 1550
## 1873 1 45.0 3795 1680
## 1874 1 65.0 4936 1868A=t(X)%*%X
A#Matriz de COV## ones Fuel.Tank.Capacite Length Width
## ones 1874.0 97855.3 8023555 3313019
## Fuel.Tank.Capacite 97855.3 5540618.9 429004132 175949670
## Length 8023555.0 429004131.7 34709363925 14270287180
## Width 3313019.0 175949669.5 14270287180 5889353051InvA=solve(A)
InvA## ones Fuel.Tank.Capacite Length Width
## ones 1.837788e-01 8.320220e-04 -1.113073e-05 -1.012705e-04
## Fuel.Tank.Capacite 8.320220e-04 8.116482e-06 -1.385784e-07 -3.747514e-07
## Length -1.113073e-05 -1.385784e-07 1.006512e-08 -1.398677e-08
## Width -1.012705e-04 -3.747514e-07 -1.398677e-08 1.022258e-07tXy=t(X)%*%as.matrix(data_correlacion2[,1])
tXy## [,1]
## ones 3.220055e+09
## Fuel.Tank.Capacite 2.085380e+11
## Length 1.491434e+13
## Width 6.037127e+12InvA%*%tXy## [,1]
## ones -1.210460e+07
## Fuel.Tank.Capacite 4.252377e+04
## Length 9.343038e+02
## Width 4.300142e+03FUNCIÓN LINEAL DEL MODELO: Ecuación matemática que describe la relación entre las variables independientes ‘curbweight’,‘enginesize’,‘horsepower’ y la variable dependiente ‘price’. La relación se asume lineal, lo que significa que los cambios en las variables independientes afectan la variable dependiente de manera proporcional.
modelo2=lm(data_correlacion2$Price~data_correlacion2$Fuel.Tank.Capacite+data_correlacion2$Length+data_correlacion2$Width)
modelo2##
## Call:
## lm(formula = data_correlacion2$Price ~ data_correlacion2$Fuel.Tank.Capacite +
## data_correlacion2$Length + data_correlacion2$Width)
##
## Coefficients:
## (Intercept) data_correlacion2$Fuel.Tank.Capacite
## -1.210e+07 4.252e+04
## data_correlacion2$Length data_correlacion2$Width
## 9.343e+02 4.300e+03Prueba de hipótesis global - Prueba F
F-statistic: 391.4 on 3 and 1870 DF. => significancia global del modelo.
p-value: < 2.2e-16 => significancia estadística de cada uno de los predictores (variables independientes ‘Fuel.Tank.Capacite’,‘Length’,‘Width’) del modelo.
Las tres variables independientes del modelo son diferentes a 0.
Prueba de hipótesis individuales - Prueba t
(Intercept) < 2e-16
data_correlacion2$Fuel.Tank.Capacite 7.30e-15
data_correlacion2$Length 1.07e-06
data_correlacion2$Width 2.22e-12
Coeficiente de Determinación (R2)
Multiple R-squared (R2): 0.3857 => Variabilidad de la variable dependiente a partir de las variables independientes => 38.57 %
Ajusted R-squared (R2 ajustado): 0.3847 => versión ajustada del Multiple R-squared => 38.47 %
summary(modelo2)##
## Call:
## lm(formula = data_correlacion2$Price ~ data_correlacion2$Fuel.Tank.Capacite +
## data_correlacion2$Length + data_correlacion2$Width)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4226517 -778163 -216094 412501 31125964
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.210e+07 8.158e+05 -14.838 < 2e-16 ***
## data_correlacion2$Fuel.Tank.Capacite 4.252e+04 5.421e+03 7.844 7.30e-15 ***
## data_correlacion2$Length 9.343e+02 1.909e+02 4.894 1.07e-06 ***
## data_correlacion2$Width 4.300e+03 6.084e+02 7.068 2.22e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1903000 on 1870 degrees of freedom
## Multiple R-squared: 0.3857, Adjusted R-squared: 0.3847
## F-statistic: 391.4 on 3 and 1870 DF, p-value: < 2.2e-16RESPUESTAS CASO DE ESTUDIO bd_mtcars
- ¿Qué variables son significativas para predecir el precio de un automóvil? La correlación más cercana a 1 es entre las variables ‘price’ y la variable enginesize con un valor de 0.87
Es decir que el tamaño del motor es la caracteristica más fuerte para determinar el precio del vehiculo.
La segunda relación más fuerte es entre ‘price’ y la variable carwidth con una correlación de 0.76
En el modelo final se descarto la correlación más debil o cercana a cero entre el precio y la variable carlength
- ¿Qué tan bien esas variables explican el precio de un automóvil? Las tres variables con mayor correlación o más cercanas a 1 respecto a la variable precio son:
‘enginesize’,‘carwidth’,‘car_ID’. Se puede concluir que el vehiculo con mayor tamaño de motor y más ancho sea el precio va ser más alto.
RESPUESTAS CASO DE ESTUDIO bd_usedcars
- ¿Qué variables son significativas para explicar el precio de un automóvil? La correlación más cercana a 1 es entre las variables ‘price’ y la variable Fuel.Tank.Capacity con un valor de 0.59
Es decir que la capacidad del tanque de combustible es la caracteristica más fuerte para determinar el precio del vehiculo.
En el modelo final se descarto la correlación más debil o cercana a cero entre el precio y la variable Heigth
- ¿Qué tan bien esas variables explican el precio de un automóvil?
La correlación más fuerte es entre ‘Fuel.Tank.Capacity’ y la variable Length con una correlación de 0.81
La segunda correlación más cercana a 1 es entre las variables Length y Width con una correlación de 0.80
Se puede concluir que entre capacidad del tanque de combustible y la variable Longitud son las más determinantes para el precio del vehiculo