Regresion Lineal

Renta de Bicis

1. Importar la base de datos

#file.choose()
df <- read.csv("C:\\Users\\jesus\\Documents\\Actividades\\rentadebicis.csv")

2. Entender la base de datos

summary(df)

##     ï..hora           dia              mes              aÃ.o     
##  Min.   : 0.00   Min.   : 1.000   Min.   : 1.000   Min.   :2011  
##  1st Qu.: 6.00   1st Qu.: 5.000   1st Qu.: 4.000   1st Qu.:2011  
##  Median :12.00   Median :10.000   Median : 7.000   Median :2012  
##  Mean   :11.54   Mean   : 9.993   Mean   : 6.521   Mean   :2012  
##  3rd Qu.:18.00   3rd Qu.:15.000   3rd Qu.:10.000   3rd Qu.:2012  
##  Max.   :23.00   Max.   :19.000   Max.   :12.000   Max.   :2012  
##     estacion     dia_de_la_semana     asueto         temperatura   
##  Min.   :1.000   Min.   :1.000    Min.   :0.00000   Min.   : 0.82  
##  1st Qu.:2.000   1st Qu.:2.000    1st Qu.:0.00000   1st Qu.:13.94  
##  Median :3.000   Median :4.000    Median :0.00000   Median :20.50  
##  Mean   :2.507   Mean   :4.014    Mean   :0.02857   Mean   :20.23  
##  3rd Qu.:4.000   3rd Qu.:6.000    3rd Qu.:0.00000   3rd Qu.:26.24  
##  Max.   :4.000   Max.   :7.000    Max.   :1.00000   Max.   :41.00  
##  sensacion_termica    humedad       velocidad_del_viento
##  Min.   : 0.76     Min.   :  0.00   Min.   : 0.000      
##  1st Qu.:16.66     1st Qu.: 47.00   1st Qu.: 7.002      
##  Median :24.24     Median : 62.00   Median :12.998      
##  Mean   :23.66     Mean   : 61.89   Mean   :12.799      
##  3rd Qu.:31.06     3rd Qu.: 77.00   3rd Qu.:16.998      
##  Max.   :45.45     Max.   :100.00   Max.   :56.997      
##  rentas_de_no_registrados rentas_de_registrados rentas_totales 
##  Min.   :  0.00           Min.   :  0.0         Min.   :  1.0  
##  1st Qu.:  4.00           1st Qu.: 36.0         1st Qu.: 42.0  
##  Median : 17.00           Median :118.0         Median :145.0  
##  Mean   : 36.02           Mean   :155.6         Mean   :191.6  
##  3rd Qu.: 49.00           3rd Qu.:222.0         3rd Qu.:284.0  
##  Max.   :367.00           Max.   :886.0         Max.   :977.0

Observaciones: 1. Los dias llegan hasta el 19 y no hasta el 31.
2. Cuál es la relación de las estaciones? 1 es primavera, 2 es verano, 3 es otoño y 4 es invierno. 3. Cuál es la relación de los días de la semana? 1 es domingo, 2 es lunes,…. y 7 es sabado

3. Generar la regresión lineal

regresion <- lm(rentas_totales ~ ï..hora + dia + mes + aÃ.o + estacion + dia_de_la_semana +   asueto + temperatura + sensacion_termica + humedad + velocidad_del_viento, data = df)
summary(regresion)

## 
## Call:
## lm(formula = rentas_totales ~ ï..hora + dia + mes + aÃ.o + estacion + 
##     dia_de_la_semana + asueto + temperatura + sensacion_termica + 
##     humedad + velocidad_del_viento, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -305.52  -93.64  -27.70   61.85  649.10 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -1.661e+05  5.496e+03 -30.217  < 2e-16 ***
## ï..hora               7.735e+00  2.070e-01  37.368  < 2e-16 ***
## dia                   3.844e-01  2.482e-01   1.549  0.12150    
## mes                   9.996e+00  1.682e+00   5.943 2.89e-09 ***
## aÃ.o                  8.258e+01  2.732e+00  30.225  < 2e-16 ***
## estacion             -7.774e+00  5.177e+00  -1.502  0.13324    
## dia_de_la_semana      4.393e-01  6.918e-01   0.635  0.52545    
## asueto               -4.864e+00  8.365e+00  -0.582  0.56089    
## temperatura           1.582e+00  1.038e+00   1.524  0.12752    
## sensacion_termica     4.748e+00  9.552e-01   4.971 6.76e-07 ***
## humedad              -2.115e+00  7.884e-02 -26.827  < 2e-16 ***
## velocidad_del_viento  5.582e-01  1.809e-01   3.086  0.00203 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 141.7 on 10874 degrees of freedom
## Multiple R-squared:  0.3891, Adjusted R-squared:  0.3885 
## F-statistic: 629.6 on 11 and 10874 DF,  p-value: < 2.2e-16

4. Ajustar la regresion lineal

regresion <- lm(rentas_totales ~ ï..hora + mes + aÃ.o + sensacion_termica + humedad + velocidad_del_viento, data = df)
summary(regresion)

## 
## Call:
## lm(formula = rentas_totales ~ ï..hora + mes + aÃ.o + sensacion_termica + 
##     humedad + velocidad_del_viento, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -308.60  -93.85  -28.34   61.05  648.09 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -1.662e+05  5.496e+03 -30.250  < 2e-16 ***
## ï..hora               7.734e+00  2.070e-01  37.364  < 2e-16 ***
## mes                   7.574e+00  4.207e-01  18.002  < 2e-16 ***
## aÃ.o                  8.266e+01  2.732e+00  30.258  < 2e-16 ***
## sensacion_termica     6.172e+00  1.689e-01  36.539  < 2e-16 ***
## humedad              -2.121e+00  7.858e-02 -26.988  < 2e-16 ***
## velocidad_del_viento  6.208e-01  1.771e-01   3.506 0.000457 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 141.7 on 10879 degrees of freedom
## Multiple R-squared:  0.3886, Adjusted R-squared:  0.3883 
## F-statistic:  1153 on 6 and 10879 DF,  p-value: < 2.2e-16

5. Construir un modelo predictivo

datos <- data.frame(ï..hora=11.54, mes=1:12, aÃ.o=2013, sensacion_termica=23.66, humedad=61.89, velocidad_del_viento=12.799)
predict(regresion, datos)

##        1        2        3        4        5        6        7        8 
## 273.6001 281.1738 288.7475 296.3213 303.8950 311.4687 319.0424 326.6161 
##        9       10       11       12 
## 334.1898 341.7635 349.3372 356.9110

Conclusiones

El modelo predictivo nos muestra las bicicletas rentadas por hora por mes, considerando las variables de sensacion termica, humedad y velocidad del viento como variables de entrada, con una R-cuadrada ajustada de 38.83%.

Renta de Casas

1. Importar la base de datos

#file.choose()
bd <- read.csv("C:\\Users\\jesus\\Documents\\Actividades\\HousePriceData.csv")

2. Entender la base de datos

summary(bd)

##  ï..Observation    Dist_Taxi      Dist_Market    Dist_Hospital  
##  Min.   :  1.0   Min.   :  146   Min.   : 1666   Min.   : 3227  
##  1st Qu.:237.0   1st Qu.: 6477   1st Qu.: 9367   1st Qu.:11302  
##  Median :469.0   Median : 8228   Median :11149   Median :13189  
##  Mean   :468.4   Mean   : 8235   Mean   :11022   Mean   :13091  
##  3rd Qu.:700.0   3rd Qu.: 9939   3rd Qu.:12675   3rd Qu.:14855  
##  Max.   :932.0   Max.   :20662   Max.   :20945   Max.   :23294  
##                                                                 
##      Carpet         Builtup        Parking          City_Category     
##  Min.   :  775   Min.   :  932   Length:905         Length:905        
##  1st Qu.: 1317   1st Qu.: 1579   Class :character   Class :character  
##  Median : 1478   Median : 1774   Mode  :character   Mode  :character  
##  Mean   : 1511   Mean   : 1794                                        
##  3rd Qu.: 1654   3rd Qu.: 1985                                        
##  Max.   :24300   Max.   :12730                                        
##  NA's   :7                                                            
##     Rainfall       House_Price       
##  Min.   :-110.0   Min.   :  1492000  
##  1st Qu.: 600.0   1st Qu.:  4623000  
##  Median : 780.0   Median :  5860000  
##  Mean   : 786.9   Mean   :  6083992  
##  3rd Qu.: 970.0   3rd Qu.:  7200000  
##  Max.   :1560.0   Max.   :150000000  
## 

Observaciones 1. La variable Rainfall tiene valores negativos. 2. Hay NA’s en la variable Carpet. 3. La variable House_Price tiene valores atipicos

3. Limpiar la base de datos

library(dplyr)

## Warning: package 'dplyr' was built under R version 4.1.3

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

# Cuantos NA's hay en la base de datos
sum(is.na(bd))

## [1] 7

# Cuantos NA's hay por variable
sapply(bd, function(x) sum(is.na(x)))

## ï..Observation      Dist_Taxi    Dist_Market  Dist_Hospital         Carpet 
##              0              0              0              0              7 
##        Builtup        Parking  City_Category       Rainfall    House_Price 
##              0              0              0              0              0

# Eliminar NA's
bd <- na.omit(bd)

# Eliminar Totales negativos
bd <- bd[bd$Rainfall>0,]

# Identificar Outliears
boxplot(bd$House_Price, horizontal=TRUE)

# Eliminar Outliers
bd <- bd[bd$House_Price<150000000,]
boxplot(bd$House_Price, horizontal=TRUE)

### 4. Generar la regresion lineal

regresion_1 <- lm(House_Price ~  Dist_Taxi + Dist_Market + Dist_Hospital + Carpet +  Builtup + Parking + City_Category + Rainfall, data = bd)
summary(regresion_1)

## 
## Call:
## lm(formula = House_Price ~ Dist_Taxi + Dist_Market + Dist_Hospital + 
##     Carpet + Builtup + Parking + City_Category + Rainfall, data = bd)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3572286  -803711   -64861   759084  4399052 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          5.611e+06  3.681e+05  15.246  < 2e-16 ***
## Dist_Taxi            3.041e+01  2.684e+01   1.133   0.2575    
## Dist_Market          1.248e+01  2.083e+01   0.599   0.5492    
## Dist_Hospital        4.862e+01  3.009e+01   1.616   0.1065    
## Carpet              -7.734e+02  3.478e+03  -0.222   0.8241    
## Builtup              1.315e+03  2.902e+03   0.453   0.6506    
## ParkingNo Parking   -6.046e+05  1.390e+05  -4.351 1.52e-05 ***
## ParkingNot Provided -4.898e+05  1.236e+05  -3.963 8.00e-05 ***
## ParkingOpen         -2.635e+05  1.126e+05  -2.340   0.0195 *  
## City_CategoryCAT B  -1.875e+06  9.607e+04 -19.517  < 2e-16 ***
## City_CategoryCAT C  -2.890e+06  1.059e+05 -27.291  < 2e-16 ***
## Rainfall            -1.260e+02  1.558e+02  -0.809   0.4187    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1223000 on 883 degrees of freedom
## Multiple R-squared:  0.5005, Adjusted R-squared:  0.4943 
## F-statistic: 80.43 on 11 and 883 DF,  p-value: < 2.2e-16

5. Construir un modelo predictivo

datos_1 <- data.frame(Dist_Taxi=8278, Dist_Market=16251, Dist_Hospital=13857, Carpet=1455, Builtup=1764, Parking="Covered", City_Category="CAT A", Rainfall=390)
predict(regresion_1, datos_1)

##       1 
## 7884599

Conclusiones

El modelo predictivo muestra el precio de la casa, considerando las demás variables como datos de entrada, con una R-cuadrada ajustada del 49.43%.