Regresión Lineal

Instalar paquetes y llamar librerías

library(tidyverse)

Importar la base de datos

df <- read.csv("C:\\Users\\erik-\\OneDrive\\Documentos\\Escuela\\Universidad\\7ºSemestre\\Modulo_2\\walmart.csv")

Entender la base de datos

summary(df)

##      Store        Date            Weekly_Sales      Holiday_Flag    
##  Min.   : 1   Length:6435        Min.   : 209986   Min.   :0.00000  
##  1st Qu.:12   Class :character   1st Qu.: 553350   1st Qu.:0.00000  
##  Median :23   Mode  :character   Median : 960746   Median :0.00000  
##  Mean   :23                      Mean   :1046965   Mean   :0.06993  
##  3rd Qu.:34                      3rd Qu.:1420159   3rd Qu.:0.00000  
##  Max.   :45                      Max.   :3818687   Max.   :1.00000  
##   Temperature       Fuel_Price         CPI         Unemployment   
##  Min.   : -2.06   Min.   :2.472   Min.   :126.1   Min.   : 3.879  
##  1st Qu.: 47.46   1st Qu.:2.933   1st Qu.:131.7   1st Qu.: 6.891  
##  Median : 62.67   Median :3.445   Median :182.6   Median : 7.874  
##  Mean   : 60.66   Mean   :3.359   Mean   :171.6   Mean   : 7.999  
##  3rd Qu.: 74.94   3rd Qu.:3.735   3rd Qu.:212.7   3rd Qu.: 8.622  
##  Max.   :100.14   Max.   :4.468   Max.   :227.2   Max.   :14.313

str(df)

## 'data.frame':    6435 obs. of  8 variables:
##  $ Store       : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Date        : chr  "05-02-2010" "12-02-2010" "19-02-2010" "26-02-2010" ...
##  $ Weekly_Sales: num  1643691 1641957 1611968 1409728 1554807 ...
##  $ Holiday_Flag: int  0 1 0 0 0 0 0 0 0 0 ...
##  $ Temperature : num  42.3 38.5 39.9 46.6 46.5 ...
##  $ Fuel_Price  : num  2.57 2.55 2.51 2.56 2.62 ...
##  $ CPI         : num  211 211 211 211 211 ...
##  $ Unemployment: num  8.11 8.11 8.11 8.11 8.11 ...

df$Date <- as.Date(df$Date, format = "%d-%m-%Y")
str(df)

## 'data.frame':    6435 obs. of  8 variables:
##  $ Store       : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Date        : Date, format: "2010-02-05" "2010-02-12" ...
##  $ Weekly_Sales: num  1643691 1641957 1611968 1409728 1554807 ...
##  $ Holiday_Flag: int  0 1 0 0 0 0 0 0 0 0 ...
##  $ Temperature : num  42.3 38.5 39.9 46.6 46.5 ...
##  $ Fuel_Price  : num  2.57 2.55 2.51 2.56 2.62 ...
##  $ CPI         : num  211 211 211 211 211 ...
##  $ Unemployment: num  8.11 8.11 8.11 8.11 8.11 ...

Agregar variables a la base de datos

df$Year <-format(df$Date, "%Y")
df$Year <- as.integer(df$Year)

df$Month <-format(df$Date, "%m")
df$Month <- as.integer(df$Month)

df$WeekYear <-format(df$Date, "%W")
df$WeekYear <- as.integer(df$WeekYear)

df$WeekDay <-format(df$Date, "%u")
df$WeekDay <- as.integer(df$WeekDay)

df$Day <-format(df$Date, "%d")
df$Day <- as.integer(df$Day)

summary(df)

##      Store         Date             Weekly_Sales      Holiday_Flag    
##  Min.   : 1   Min.   :2010-02-05   Min.   : 209986   Min.   :0.00000  
##  1st Qu.:12   1st Qu.:2010-10-08   1st Qu.: 553350   1st Qu.:0.00000  
##  Median :23   Median :2011-06-17   Median : 960746   Median :0.00000  
##  Mean   :23   Mean   :2011-06-17   Mean   :1046965   Mean   :0.06993  
##  3rd Qu.:34   3rd Qu.:2012-02-24   3rd Qu.:1420159   3rd Qu.:0.00000  
##  Max.   :45   Max.   :2012-10-26   Max.   :3818687   Max.   :1.00000  
##   Temperature       Fuel_Price         CPI         Unemployment   
##  Min.   : -2.06   Min.   :2.472   Min.   :126.1   Min.   : 3.879  
##  1st Qu.: 47.46   1st Qu.:2.933   1st Qu.:131.7   1st Qu.: 6.891  
##  Median : 62.67   Median :3.445   Median :182.6   Median : 7.874  
##  Mean   : 60.66   Mean   :3.359   Mean   :171.6   Mean   : 7.999  
##  3rd Qu.: 74.94   3rd Qu.:3.735   3rd Qu.:212.7   3rd Qu.: 8.622  
##  Max.   :100.14   Max.   :4.468   Max.   :227.2   Max.   :14.313  
##       Year          Month           WeekYear        WeekDay       Day       
##  Min.   :2010   Min.   : 1.000   Min.   : 1.00   Min.   :5   Min.   : 1.00  
##  1st Qu.:2010   1st Qu.: 4.000   1st Qu.:14.00   1st Qu.:5   1st Qu.: 8.00  
##  Median :2011   Median : 6.000   Median :26.00   Median :5   Median :16.00  
##  Mean   :2011   Mean   : 6.448   Mean   :25.82   Mean   :5   Mean   :15.68  
##  3rd Qu.:2012   3rd Qu.: 9.000   3rd Qu.:38.00   3rd Qu.:5   3rd Qu.:23.00  
##  Max.   :2012   Max.   :12.000   Max.   :52.00   Max.   :5   Max.   :31.00

str(df)

## 'data.frame':    6435 obs. of  13 variables:
##  $ Store       : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Date        : Date, format: "2010-02-05" "2010-02-12" ...
##  $ Weekly_Sales: num  1643691 1641957 1611968 1409728 1554807 ...
##  $ Holiday_Flag: int  0 1 0 0 0 0 0 0 0 0 ...
##  $ Temperature : num  42.3 38.5 39.9 46.6 46.5 ...
##  $ Fuel_Price  : num  2.57 2.55 2.51 2.56 2.62 ...
##  $ CPI         : num  211 211 211 211 211 ...
##  $ Unemployment: num  8.11 8.11 8.11 8.11 8.11 ...
##  $ Year        : int  2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 ...
##  $ Month       : int  2 2 2 2 3 3 3 3 4 4 ...
##  $ WeekYear    : int  5 6 7 8 9 10 11 12 13 14 ...
##  $ WeekDay     : int  5 5 5 5 5 5 5 5 5 5 ...
##  $ Day         : int  5 12 19 26 5 12 19 26 2 9 ...

Crear el modelo

regression <- lm(Weekly_Sales ~., data = df)
summary(regression)

## 
## Call:
## lm(formula = Weekly_Sales ~ ., data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1094800  -382464   -42860   375406  2587123 
## 
## Coefficients: (2 not defined because of singularities)
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -2.384e+09  9.127e+09  -0.261   0.7940    
## Store        -1.538e+04  5.202e+02 -29.576  < 2e-16 ***
## Date         -3.399e+03  1.266e+04  -0.268   0.7883    
## Holiday_Flag  4.773e+04  2.706e+04   1.763   0.0779 .  
## Temperature  -1.817e+03  4.053e+02  -4.484 7.47e-06 ***
## Fuel_Price    6.124e+04  2.876e+04   2.130   0.0332 *  
## CPI          -2.109e+03  1.928e+02 -10.941  < 2e-16 ***
## Unemployment -2.209e+04  3.967e+03  -5.569 2.67e-08 ***
## Year          1.212e+06  4.633e+06   0.262   0.7937    
## Month         1.177e+05  3.858e+05   0.305   0.7604    
## WeekYear             NA         NA      NA       NA    
## WeekDay              NA         NA      NA       NA    
## Day           2.171e+03  1.269e+04   0.171   0.8642    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 520900 on 6424 degrees of freedom
## Multiple R-squared:  0.1495, Adjusted R-squared:  0.1482 
## F-statistic:   113 on 10 and 6424 DF,  p-value: < 2.2e-16

Resumen del modelo

df_ajustada <- df %>% select(-Date,-Fuel_Price,-Year:-Day)
regression_ajustada <- lm(Weekly_Sales ~., data = df_ajustada)
summary(regression_ajustada)

## 
## Call:
## lm(formula = Weekly_Sales ~ ., data = df_ajustada)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1035858  -392195   -40416   371110  2711797 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2031943.1    50654.7  40.114  < 2e-16 ***
## Store         -15373.4      521.3 -29.488  < 2e-16 ***
## Holiday_Flag   72218.3    25911.0   2.787  0.00533 ** 
## Temperature     -929.0      369.1  -2.517  0.01186 *  
## CPI            -2345.9      180.2 -13.019  < 2e-16 ***
## Unemployment  -22198.9     3755.9  -5.910 3.59e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 523100 on 6429 degrees of freedom
## Multiple R-squared:  0.1415, Adjusted R-squared:  0.1408 
## F-statistic: 211.9 on 5 and 6429 DF,  p-value: < 2.2e-16

Conclusiones

Nuestro modelo de regresión lineal detecta que las variables con mayor significancia para el modelo que predice las ventas semanales de Walmart son:

• La tienda
• CPI
• Desmpleo

Esto nos demuestra que hay variables externas que tienen un gran efecto en la predicción de las ventas de una tienda. De igual forma por el estadístico p del modelo podemos concluir que el modelo es significatne aunque habría que compararlo con otro modelo de predicción y utilizar otras métricas de error.