Regresión lineal

Importar base de datos

library(tidyverse)

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df= read.csv("/Users/gabrielmedina/Downloads/Walmart_Store_sales.csv")
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.   :3818686   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

Análisis exploratorio

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: NA NA ...
##  $ 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 ...

summary(df)

##      Store         Date             Weekly_Sales      Holiday_Flag    
##  Min.   : 1   Min.   :2010-02-19   Min.   : 209986   Min.   :0.00000  
##  1st Qu.:12   1st Qu.:2010-10-22   1st Qu.: 553350   1st Qu.:0.00000  
##  Median :23   Median :2011-07-04   Median : 960746   Median :0.00000  
##  Mean   :23   Mean   :2011-06-30   Mean   :1046965   Mean   :0.06993  
##  3rd Qu.:34   3rd Qu.:2012-03-16   3rd Qu.:1420159   3rd Qu.:0.00000  
##  Max.   :45   Max.   :2012-10-26   Max.   :3818686   Max.   :1.00000  
##               NA's   :2565                                            
##   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  
## 

Conversión de variables

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

df$Month=format(df$Date, "%m")
df$Monthr=as.integer(df$Month)

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

#df$WeekYear=format(df$Date, "%W")
#df$WeekYear=as.integer(df$WeekYear)

#df$WeekDay=format(df$Date, "%u")
#df$WeekDay=as.integer(df$WeekDay)

Modelo

regresion=lm(Weekly_Sales ~. , data=df)
summary(regresion)

## 
## Call:
## lm(formula = Weekly_Sales ~ ., data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1257597  -377860   -46922   353118  2344499 
## 
## Coefficients: (1 not defined because of singularities)
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   2.649e+10  2.925e+10   0.906   0.3652    
## Store        -1.514e+04  6.681e+02 -22.657  < 2e-16 ***
## Date          3.670e+04  4.059e+04   0.904   0.3660    
## Holiday_Flag -1.321e+05  5.283e+04  -2.500   0.0125 *  
## Temperature  -6.170e+02  8.634e+02  -0.715   0.4749    
## Fuel_Price    7.974e+04  4.491e+04   1.776   0.0759 .  
## CPI          -2.166e+03  2.655e+02  -8.161 4.45e-16 ***
## Unemployment -2.772e+04  5.347e+03  -5.184 2.28e-07 ***
## Year         -1.344e+07  1.485e+07  -0.905   0.3653    
## Month02      -1.010e+06  1.271e+06  -0.795   0.4268    
## Month03      -2.109e+06  2.429e+06  -0.868   0.3852    
## Month04      -3.250e+06  3.690e+06  -0.881   0.3785    
## Month05      -4.328e+06  4.907e+06  -0.882   0.3779    
## Month06      -5.417e+06  6.162e+06  -0.879   0.3794    
## Month07      -6.559e+06  7.378e+06  -0.889   0.3741    
## Month08      -7.661e+06  8.639e+06  -0.887   0.3753    
## Month09      -8.893e+06  9.897e+06  -0.899   0.3690    
## Month10      -9.966e+06  1.111e+07  -0.897   0.3699    
## Month11      -1.078e+07  1.237e+07  -0.872   0.3835    
## Month12      -1.179e+07  1.359e+07  -0.868   0.3854    
## Monthr               NA         NA      NA       NA    
## Day          -3.815e+04  4.071e+04  -0.937   0.3487    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 518300 on 3849 degrees of freedom
##   (2565 observations deleted due to missingness)
## Multiple R-squared:  0.1743, Adjusted R-squared:   0.17 
## F-statistic: 40.62 on 20 and 3849 DF,  p-value: < 2.2e-16

Modelo ajustado

ajustada=df %>% select(-Store,-Day,-Year:-Day)
ajustada_regresion=lm(Weekly_Sales ~., data=ajustada)
summary(ajustada_regresion)

## 
## Call:
## lm(formula = Weekly_Sales ~ ., data = ajustada)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1111688  -473110  -118330   390059  2800968 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2122065.27  724942.69   2.927  0.00344 ** 
## Date             -26.74      53.23  -0.502  0.61545    
## Holiday_Flag  172222.88   44490.26   3.871  0.00011 ***
## Temperature     -989.33     541.15  -1.828  0.06760 .  
## Fuel_Price     -3705.97   33393.96  -0.111  0.91164    
## CPI            -1532.67     260.00  -5.895 4.07e-09 ***
## Unemployment  -43842.71    5377.15  -8.154 4.73e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 560600 on 3863 degrees of freedom
##   (2565 observations deleted due to missingness)
## Multiple R-squared:  0.03028,    Adjusted R-squared:  0.02878 
## F-statistic: 20.11 on 6 and 3863 DF,  p-value: < 2.2e-16