Project#2 Retail Sales Forcast
Luyun Liang
4/10/2019
library(psych)
library(ISLR)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alphalibrary(fpp2)## Loading required package: forecast## Loading required package: fma## Loading required package: expsmoothlibrary(tidyr)
library(seasonal)##
## Attaching package: 'seasonal'## The following object is masked from 'package:psych':
##
## outlier#read the data
Sales_Transaction<-read.csv(file="/Users/luyunliang/Downloads/Sales_Transactions_Dataset_Weekly.csv",header = TRUE,sep = ",",stringsAsFactors = TRUE)#Exploratory data analysis
str(Sales_Transaction)## 'data.frame': 811 obs. of 107 variables:
## $ Product_Code : Factor w/ 811 levels "P1","P10","P100",..: 1 112 223 332 443 554 663 770 801 2 ...
## $ W0 : int 11 7 7 12 8 3 4 8 14 22 ...
## $ W1 : int 12 6 11 8 5 3 8 6 9 19 ...
## $ W2 : int 10 3 8 13 13 2 3 10 10 19 ...
## $ W3 : int 8 2 9 5 11 7 7 9 7 29 ...
## $ W4 : int 13 7 10 9 6 6 8 6 11 20 ...
## $ W5 : int 12 1 8 6 7 3 7 8 15 16 ...
## $ W6 : int 14 6 7 9 9 8 2 7 12 26 ...
## $ W7 : int 21 3 13 13 14 6 3 5 7 20 ...
## $ W8 : int 6 3 12 13 9 6 10 10 13 24 ...
## $ W9 : int 14 3 6 11 9 3 3 10 12 20 ...
## $ W10 : int 11 2 14 8 11 1 5 8 15 31 ...
## $ W11 : int 14 2 9 4 18 1 2 8 15 22 ...
## $ W12 : int 16 6 4 5 8 5 3 15 16 23 ...
## $ W13 : int 9 2 7 4 4 4 4 9 10 19 ...
## $ W14 : int 9 0 12 15 13 3 5 5 9 15 ...
## $ W15 : int 9 6 8 7 8 5 3 11 9 19 ...
## $ W16 : int 14 2 7 11 10 3 7 10 13 22 ...
## $ W17 : int 9 7 11 9 15 5 10 7 8 23 ...
## $ W18 : int 3 7 10 15 6 10 0 13 10 20 ...
## $ W19 : int 12 9 7 4 13 8 3 9 18 33 ...
## $ W20 : int 5 4 7 6 11 4 7 12 18 16 ...
## $ W21 : int 11 7 13 7 6 9 5 11 17 23 ...
## $ W22 : int 7 2 11 11 10 7 1 5 10 23 ...
## $ W23 : int 12 4 8 7 9 5 5 11 16 16 ...
## $ W24 : int 5 5 10 9 8 4 7 11 14 25 ...
## $ W25 : int 9 3 8 6 12 2 5 12 10 27 ...
## $ W26 : int 7 5 14 10 8 1 2 3 4 12 ...
## $ W27 : int 10 8 5 10 9 3 4 10 7 15 ...
## $ W28 : int 5 5 3 2 13 2 3 12 7 15 ...
## $ W29 : int 11 5 13 6 3 4 1 9 10 11 ...
## $ W30 : int 7 3 11 7 5 0 3 9 3 14 ...
## $ W31 : int 10 1 9 2 3 3 2 10 13 29 ...
## $ W32 : int 12 3 7 5 5 2 2 8 9 23 ...
## $ W33 : int 6 2 8 12 5 11 4 9 7 12 ...
## $ W34 : int 5 3 7 5 9 2 2 8 9 16 ...
## $ W35 : int 14 10 9 19 7 1 6 9 8 9 ...
## $ W36 : int 10 5 6 8 4 4 4 15 7 23 ...
## $ W37 : int 9 2 12 6 8 4 5 6 9 22 ...
## $ W38 : int 12 7 12 8 8 3 1 7 15 15 ...
## $ W39 : int 17 3 9 8 5 2 3 8 8 18 ...
## $ W40 : int 7 2 3 12 5 5 5 3 9 13 ...
## $ W41 : int 11 5 5 6 8 4 8 9 8 17 ...
## $ W42 : int 4 2 6 9 7 4 2 10 11 14 ...
## $ W43 : int 7 4 14 10 11 2 3 14 5 17 ...
## $ W44 : int 8 5 5 3 7 4 3 4 13 11 ...
## $ W45 : int 10 1 5 4 12 3 6 8 3 24 ...
## $ W46 : int 12 1 7 6 6 6 2 8 7 13 ...
## $ W47 : int 3 4 8 8 6 5 6 6 7 16 ...
## $ W48 : int 7 5 14 14 5 3 2 7 10 18 ...
## $ W49 : int 6 1 8 8 11 3 4 4 12 23 ...
## $ W50 : int 5 6 8 7 8 10 2 9 7 18 ...
## $ W51 : int 10 0 7 8 9 6 1 9 13 20 ...
## $ MIN : int 3 0 3 2 3 0 0 3 3 9 ...
## $ MAX : int 21 10 14 19 18 11 10 15 18 33 ...
## $ Normalized.0 : num 0.44 0.7 0.36 0.59 0.33 0.27 0.4 0.42 0.73 0.54 ...
## $ Normalized.1 : num 0.5 0.6 0.73 0.35 0.13 0.27 0.8 0.25 0.4 0.42 ...
## $ Normalized.2 : num 0.39 0.3 0.45 0.65 0.67 0.18 0.3 0.58 0.47 0.42 ...
## $ Normalized.3 : num 0.28 0.2 0.55 0.18 0.53 0.64 0.7 0.5 0.27 0.83 ...
## $ Normalized.4 : num 0.56 0.7 0.64 0.41 0.2 0.55 0.8 0.25 0.53 0.46 ...
## $ Normalized.5 : num 0.5 0.1 0.45 0.24 0.27 0.27 0.7 0.42 0.8 0.29 ...
## $ Normalized.6 : num 0.61 0.6 0.36 0.41 0.4 0.73 0.2 0.33 0.6 0.71 ...
## $ Normalized.7 : num 1 0.3 0.91 0.65 0.73 0.55 0.3 0.17 0.27 0.46 ...
## $ Normalized.8 : num 0.17 0.3 0.82 0.65 0.4 0.55 1 0.58 0.67 0.63 ...
## $ Normalized.9 : num 0.61 0.3 0.27 0.53 0.4 0.27 0.3 0.58 0.6 0.46 ...
## $ Normalized.10: num 0.44 0.2 1 0.35 0.53 0.09 0.5 0.42 0.8 0.92 ...
## $ Normalized.11: num 0.61 0.2 0.55 0.12 1 0.09 0.2 0.42 0.8 0.54 ...
## $ Normalized.12: num 0.72 0.6 0.09 0.18 0.33 0.45 0.3 1 0.87 0.58 ...
## $ Normalized.13: num 0.33 0.2 0.36 0.12 0.07 0.36 0.4 0.5 0.47 0.42 ...
## $ Normalized.14: num 0.33 0 0.82 0.76 0.67 0.27 0.5 0.17 0.4 0.25 ...
## $ Normalized.15: num 0.33 0.6 0.45 0.29 0.33 0.45 0.3 0.67 0.4 0.42 ...
## $ Normalized.16: num 0.61 0.2 0.36 0.53 0.47 0.27 0.7 0.58 0.67 0.54 ...
## $ Normalized.17: num 0.33 0.7 0.73 0.41 0.8 0.45 1 0.33 0.33 0.58 ...
## $ Normalized.18: num 0 0.7 0.64 0.76 0.2 0.91 0 0.83 0.47 0.46 ...
## $ Normalized.19: num 0.5 0.9 0.36 0.12 0.67 0.73 0.3 0.5 1 1 ...
## $ Normalized.20: num 0.11 0.4 0.36 0.24 0.53 0.36 0.7 0.75 1 0.29 ...
## $ Normalized.21: num 0.44 0.7 0.91 0.29 0.2 0.82 0.5 0.67 0.93 0.58 ...
## $ Normalized.22: num 0.22 0.2 0.73 0.53 0.47 0.64 0.1 0.17 0.47 0.58 ...
## $ Normalized.23: num 0.5 0.4 0.45 0.29 0.4 0.45 0.5 0.67 0.87 0.29 ...
## $ Normalized.24: num 0.11 0.5 0.64 0.41 0.33 0.36 0.7 0.67 0.73 0.67 ...
## $ Normalized.25: num 0.33 0.3 0.45 0.24 0.6 0.18 0.5 0.75 0.47 0.75 ...
## $ Normalized.26: num 0.22 0.5 1 0.47 0.33 0.09 0.2 0 0.07 0.13 ...
## $ Normalized.27: num 0.39 0.8 0.18 0.47 0.4 0.27 0.4 0.58 0.27 0.25 ...
## $ Normalized.28: num 0.11 0.5 0 0 0.67 0.18 0.3 0.75 0.27 0.25 ...
## $ Normalized.29: num 0.44 0.5 0.91 0.24 0 0.36 0.1 0.5 0.47 0.08 ...
## $ Normalized.30: num 0.22 0.3 0.73 0.29 0.13 0 0.3 0.5 0 0.21 ...
## $ Normalized.31: num 0.39 0.1 0.55 0 0 0.27 0.2 0.58 0.67 0.83 ...
## $ Normalized.32: num 0.5 0.3 0.36 0.18 0.13 0.18 0.2 0.42 0.4 0.58 ...
## $ Normalized.33: num 0.17 0.2 0.45 0.59 0.13 1 0.4 0.5 0.27 0.13 ...
## $ Normalized.34: num 0.11 0.3 0.36 0.18 0.4 0.18 0.2 0.42 0.4 0.29 ...
## $ Normalized.35: num 0.61 1 0.55 1 0.27 0.09 0.6 0.5 0.33 0 ...
## $ Normalized.36: num 0.39 0.5 0.27 0.35 0.07 0.36 0.4 1 0.27 0.58 ...
## $ Normalized.37: num 0.33 0.2 0.82 0.24 0.33 0.36 0.5 0.25 0.4 0.54 ...
## $ Normalized.38: num 0.5 0.7 0.82 0.35 0.33 0.27 0.1 0.33 0.8 0.25 ...
## $ Normalized.39: num 0.78 0.3 0.55 0.35 0.13 0.18 0.3 0.42 0.33 0.38 ...
## $ Normalized.40: num 0.22 0.2 0 0.59 0.13 0.45 0.5 0 0.4 0.17 ...
## $ Normalized.41: num 0.44 0.5 0.18 0.24 0.33 0.36 0.8 0.5 0.33 0.33 ...
## $ Normalized.42: num 0.06 0.2 0.27 0.41 0.27 0.36 0.2 0.58 0.53 0.21 ...
## $ Normalized.43: num 0.22 0.4 1 0.47 0.53 0.18 0.3 0.92 0.13 0.33 ...
## [list output truncated]summary(Sales_Transaction)## Product_Code W0 W1 W2
## P1 : 1 Min. : 0.000 Min. : 0.000 Min. : 0.00
## P10 : 1 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.00
## P100 : 1 Median : 3.000 Median : 3.000 Median : 3.00
## P101 : 1 Mean : 8.903 Mean : 9.129 Mean : 9.39
## P102 : 1 3rd Qu.:12.000 3rd Qu.:12.000 3rd Qu.:12.00
## P103 : 1 Max. :54.000 Max. :53.000 Max. :56.00
## (Other):805
## W3 W4 W5 W6
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.00
## Median : 4.000 Median : 4.000 Median : 3.000 Median : 4.00
## Mean : 9.718 Mean : 9.575 Mean : 9.466 Mean : 9.72
## 3rd Qu.:13.000 3rd Qu.:13.000 3rd Qu.:12.500 3rd Qu.:13.00
## Max. :59.000 Max. :61.000 Max. :52.000 Max. :56.00
##
## W7 W8 W9 W10
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.00
## Median : 4.000 Median : 4.000 Median : 4.000 Median : 4.00
## Mean : 9.586 Mean : 9.784 Mean : 9.682 Mean : 9.79
## 3rd Qu.:12.500 3rd Qu.:13.000 3rd Qu.:13.000 3rd Qu.:13.00
## Max. :62.000 Max. :63.000 Max. :52.000 Max. :56.00
##
## W11 W12 W13 W14
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000
## Median : 4.000 Median : 3.000 Median : 4.000 Median : 4.000
## Mean : 9.678 Mean : 9.827 Mean : 9.687 Mean : 9.908
## 3rd Qu.:13.000 3rd Qu.:13.000 3rd Qu.:13.000 3rd Qu.:13.000
## Max. :57.000 Max. :61.000 Max. :55.000 Max. :57.000
##
## W15 W16 W17 W18
## Min. : 0.00 Min. : 0.00 Min. : 0.000 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0.00
## Median : 4.00 Median : 4.00 Median : 4.000 Median : 4.00
## Mean :10.05 Mean :10.03 Mean : 9.905 Mean :10.01
## 3rd Qu.:14.00 3rd Qu.:13.00 3rd Qu.:13.000 3rd Qu.:13.00
## Max. :59.00 Max. :62.00 Max. :67.000 Max. :57.00
##
## W19 W20 W21 W22
## Min. : 0.000 Min. : 0.00 Min. : 0.00 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000
## Median : 4.000 Median : 4.00 Median : 4.00 Median : 4.000
## Mean : 9.645 Mean : 9.85 Mean : 9.71 Mean : 9.903
## 3rd Qu.:13.000 3rd Qu.:13.00 3rd Qu.:13.00 3rd Qu.:13.000
## Max. :56.000 Max. :64.00 Max. :58.00 Max. :51.000
##
## W23 W24 W25 W26
## Min. : 0.000 Min. : 0.00 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.: 1.00 1st Qu.: 1.000 1st Qu.: 0.000
## Median : 4.000 Median : 5.00 Median : 5.000 Median : 3.000
## Mean : 9.862 Mean :10.17 Mean : 8.893 Mean : 6.951
## 3rd Qu.:14.000 3rd Qu.:16.00 3rd Qu.:15.000 3rd Qu.: 9.000
## Max. :72.000 Max. :64.00 Max. :64.000 Max. :46.000
##
## W27 W28 W29 W30
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000
## Median : 3.000 Median : 3.000 Median : 3.000 Median : 3.000
## Mean : 7.194 Mean : 7.383 Mean : 7.339 Mean : 7.608
## 3rd Qu.:10.000 3rd Qu.: 9.000 3rd Qu.:10.000 3rd Qu.:10.000
## Max. :47.000 Max. :44.000 Max. :42.000 Max. :48.000
##
## W31 W32 W33 W34
## Min. : 0.00 Min. : 0.00 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0.000
## Median : 3.00 Median : 3.00 Median : 3.000 Median : 3.000
## Mean : 7.61 Mean : 7.76 Mean : 7.906 Mean : 7.993
## 3rd Qu.:10.00 3rd Qu.:10.00 3rd Qu.:10.000 3rd Qu.:10.500
## Max. :47.00 Max. :49.00 Max. :46.000 Max. :46.000
##
## W35 W36 W37 W38
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.000
## Median : 3.000 Median : 3.000 Median : 3.000 Median : 3.000
## Mean : 7.998 Mean : 8.015 Mean : 8.074 Mean : 8.252
## 3rd Qu.:10.000 3rd Qu.:10.000 3rd Qu.:11.000 3rd Qu.:11.000
## Max. :46.000 Max. :55.000 Max. :47.000 Max. :52.000
##
## W39 W40 W41 W42
## Min. : 0.000 Min. : 0.000 Min. : 0.00 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 0.00 1st Qu.: 0.000
## Median : 3.000 Median : 4.000 Median : 3.00 Median : 4.000
## Mean : 7.965 Mean : 8.182 Mean : 8.24 Mean : 8.395
## 3rd Qu.:10.000 3rd Qu.:10.000 3rd Qu.:11.00 3rd Qu.:10.000
## Max. :47.000 Max. :48.000 Max. :50.00 Max. :52.000
##
## W43 W44 W45 W46
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 1.00
## Median : 4.000 Median : 4.000 Median : 4.000 Median : 4.00
## Mean : 8.318 Mean : 8.434 Mean : 8.556 Mean : 8.72
## 3rd Qu.:11.000 3rd Qu.:11.000 3rd Qu.:11.000 3rd Qu.:11.00
## Max. :50.000 Max. :46.000 Max. :46.000 Max. :55.00
##
## W47 W48 W49 W50
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 1.000 1st Qu.: 1.000
## Median : 4.000 Median : 4.000 Median : 4.000 Median : 5.000
## Mean : 8.671 Mean : 8.674 Mean : 8.895 Mean : 8.862
## 3rd Qu.:12.000 3rd Qu.:12.000 3rd Qu.:12.000 3rd Qu.:13.000
## Max. :49.000 Max. :50.000 Max. :52.000 Max. :57.000
##
## W51 MIN MAX Normalized.0
## Min. : 0.000 Min. : 0.000 Min. : 1.00 Min. :0.0000
## 1st Qu.: 1.000 1st Qu.: 0.000 1st Qu.: 3.00 1st Qu.:0.0000
## Median : 5.000 Median : 0.000 Median : 9.00 Median :0.2500
## Mean : 8.889 Mean : 3.781 Mean :16.31 Mean :0.2894
## 3rd Qu.:14.000 3rd Qu.: 4.000 3rd Qu.:21.00 3rd Qu.:0.5000
## Max. :73.000 Max. :24.000 Max. :73.00 Max. :1.0000
##
## Normalized.1 Normalized.2 Normalized.3 Normalized.4
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.2800 Median :0.2900 Median :0.2900 Median :0.3100
## Mean :0.2991 Mean :0.3067 Mean :0.3199 Mean :0.3269
## 3rd Qu.:0.5000 3rd Qu.:0.5000 3rd Qu.:0.5350 3rd Qu.:0.5500
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
##
## Normalized.5 Normalized.6 Normalized.7 Normalized.8
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.3000 Median :0.3100 Median :0.3300 Median :0.3200
## Mean :0.3194 Mean :0.3328 Mean :0.3266 Mean :0.3243
## 3rd Qu.:0.5200 3rd Qu.:0.5300 3rd Qu.:0.5400 3rd Qu.:0.5350
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
##
## Normalized.9 Normalized.10 Normalized.11 Normalized.12
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.3300 Median :0.3100 Median :0.3100 Median :0.3300
## Mean :0.3268 Mean :0.3311 Mean :0.3315 Mean :0.3389
## 3rd Qu.:0.5300 3rd Qu.:0.5400 3rd Qu.:0.5500 3rd Qu.:0.5600
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
##
## Normalized.13 Normalized.14 Normalized.15 Normalized.16
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.3300 Median :0.3600 Median :0.3300 Median :0.3300
## Mean :0.3316 Mean :0.3558 Mean :0.3448 Mean :0.3359
## 3rd Qu.:0.5300 3rd Qu.:0.5600 3rd Qu.:0.5800 3rd Qu.:0.5600
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
##
## Normalized.17 Normalized.18 Normalized.19 Normalized.20
## Min. :0.0000 Min. :0.000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.3300 Median :0.350 Median :0.3100 Median :0.3300
## Mean :0.3453 Mean :0.355 Mean :0.3302 Mean :0.3403
## 3rd Qu.:0.5600 3rd Qu.:0.560 3rd Qu.:0.5400 3rd Qu.:0.5600
## Max. :1.0000 Max. :1.000 Max. :1.0000 Max. :1.0000
##
## Normalized.21 Normalized.22 Normalized.23 Normalized.24
## Min. :0.0000 Min. :0.000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.1300
## Median :0.3600 Median :0.360 Median :0.3800 Median :0.4400
## Mean :0.3536 Mean :0.366 Mean :0.3706 Mean :0.4177
## 3rd Qu.:0.5500 3rd Qu.:0.580 3rd Qu.:0.5800 3rd Qu.:0.6350
## Max. :1.0000 Max. :1.000 Max. :1.0000 Max. :1.0000
##
## Normalized.25 Normalized.26 Normalized.27 Normalized.28
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0600 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.3500 Median :0.1800 Median :0.200 Median :0.2100
## Mean :0.3896 Mean :0.2076 Mean :0.223 Mean :0.2296
## 3rd Qu.:0.6000 3rd Qu.:0.3300 3rd Qu.:0.365 3rd Qu.:0.3600
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
##
## Normalized.29 Normalized.30 Normalized.31 Normalized.32
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.1900 Median :0.2100 Median :0.2200 Median :0.2200
## Mean :0.2244 Mean :0.2405 Mean :0.2504 Mean :0.2483
## 3rd Qu.:0.3800 3rd Qu.:0.3900 3rd Qu.:0.4000 3rd Qu.:0.4000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
##
## Normalized.33 Normalized.34 Normalized.35 Normalized.36
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.2300 Median :0.2500 Median :0.2500 Median :0.2400
## Mean :0.2594 Mean :0.2623 Mean :0.2689 Mean :0.2702
## 3rd Qu.:0.4150 3rd Qu.:0.4300 3rd Qu.:0.4500 3rd Qu.:0.4200
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
##
## Normalized.37 Normalized.38 Normalized.39 Normalized.40
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.2500 Median :0.2500 Median :0.250 Median :0.2500
## Mean :0.2731 Mean :0.2775 Mean :0.265 Mean :0.2864
## 3rd Qu.:0.4400 3rd Qu.:0.4500 3rd Qu.:0.430 3rd Qu.:0.4700
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
##
## Normalized.41 Normalized.42 Normalized.43 Normalized.44
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.2600 Median :0.2800 Median :0.2700 Median :0.3000
## Mean :0.2794 Mean :0.2991 Mean :0.2876 Mean :0.3048
## 3rd Qu.:0.4400 3rd Qu.:0.4900 3rd Qu.:0.4500 3rd Qu.:0.5000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
##
## Normalized.45 Normalized.46 Normalized.47 Normalized.48
## Min. :0.000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.020 1st Qu.:0.0850 1st Qu.:0.0000 1st Qu.:0.1050
## Median :0.310 Median :0.3300 Median :0.3100 Median :0.3300
## Mean :0.316 Mean :0.3348 Mean :0.3146 Mean :0.3382
## 3rd Qu.:0.500 3rd Qu.:0.5000 3rd Qu.:0.5000 3rd Qu.:0.5000
## Max. :1.000 Max. :1.0000 Max. :1.0000 Max. :1.0000
##
## Normalized.49 Normalized.50 Normalized.51
## Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.1000 1st Qu.:0.110 1st Qu.:0.0900
## Median :0.3300 Median :0.350 Median :0.4300
## Mean :0.3589 Mean :0.373 Mean :0.4279
## 3rd Qu.:0.5500 3rd Qu.:0.560 3rd Qu.:0.6700
## Max. :1.0000 Max. :1.000 Max. :1.0000
## #811 observations and 107 variables
#52-Column Weekly Sales Transaction
#52-Column Normalized Weekly Sales TransactionView(Sales_Transaction)#Exploratory data analysis
describe(Sales_Transaction)## vars n mean sd median trimmed mad min max range
## Product_Code* 1 811 406.00 234.26 406.00 406.00 300.97 1 811 810
## W0 2 811 8.90 12.07 3.00 6.46 4.45 0 54 54
## W1 3 811 9.13 12.56 3.00 6.52 4.45 0 53 53
## W2 4 811 9.39 13.05 3.00 6.62 4.45 0 56 56
## W3 5 811 9.72 13.55 4.00 6.86 5.93 0 59 59
## W4 6 811 9.57 13.10 4.00 6.87 5.93 0 61 61
## W5 7 811 9.47 12.82 3.00 6.84 4.45 0 52 52
## W6 8 811 9.72 13.35 4.00 6.93 5.93 0 56 56
## W7 9 811 9.59 13.05 4.00 6.84 5.93 0 62 62
## W8 10 811 9.78 13.55 4.00 6.94 5.93 0 63 63
## W9 11 811 9.68 13.14 4.00 7.02 5.93 0 52 52
## W10 12 811 9.79 13.58 4.00 6.91 5.93 0 56 56
## W11 13 811 9.68 13.01 4.00 7.07 5.93 0 57 57
## W12 14 811 9.83 13.37 3.00 7.10 4.45 0 61 61
## W13 15 811 9.69 13.21 4.00 6.99 5.93 0 55 55
## W14 16 811 9.91 13.39 4.00 7.13 5.93 0 57 57
## W15 17 811 10.05 13.74 4.00 7.19 5.93 0 59 59
## W16 18 811 10.03 13.89 4.00 7.13 5.93 0 62 62
## W17 19 811 9.91 13.36 4.00 7.22 5.93 0 67 67
## W18 20 811 10.01 13.56 4.00 7.18 5.93 0 57 57
## W19 21 811 9.64 13.13 4.00 6.95 5.93 0 56 56
## W20 22 811 9.85 13.47 4.00 7.10 5.93 0 64 64
## W21 23 811 9.71 12.83 4.00 7.17 5.93 0 58 58
## W22 24 811 9.90 13.00 4.00 7.36 5.93 0 51 51
## W23 25 811 9.86 12.62 4.00 7.47 5.93 0 72 72
## W24 26 811 10.17 12.30 5.00 8.04 7.41 0 64 64
## W25 27 811 8.89 10.02 5.00 7.35 7.41 0 64 64
## W26 28 811 6.95 9.45 3.00 4.98 4.45 0 46 46
## W27 29 811 7.19 9.73 3.00 5.18 4.45 0 47 47
## W28 30 811 7.38 10.19 3.00 5.24 4.45 0 44 44
## W29 31 811 7.34 10.16 3.00 5.17 4.45 0 42 42
## W30 32 811 7.61 10.60 3.00 5.33 4.45 0 48 48
## W31 33 811 7.61 10.39 3.00 5.41 4.45 0 47 47
## W32 34 811 7.76 10.71 3.00 5.50 4.45 0 49 49
## W33 35 811 7.91 10.84 3.00 5.62 4.45 0 46 46
## W34 36 811 7.99 10.82 3.00 5.74 4.45 0 46 46
## W35 37 811 8.00 10.77 3.00 5.76 4.45 0 46 46
## W36 38 811 8.01 10.95 3.00 5.70 4.45 0 55 55
## W37 39 811 8.07 10.85 3.00 5.81 4.45 0 47 47
## W38 40 811 8.25 11.27 3.00 5.86 4.45 0 52 52
## W39 41 811 7.97 10.76 3.00 5.70 4.45 0 47 47
## W40 42 811 8.18 11.08 4.00 5.86 5.93 0 48 48
## W41 43 811 8.24 11.14 3.00 5.94 4.45 0 50 50
## W42 44 811 8.39 11.35 4.00 6.03 5.93 0 52 52
## W43 45 811 8.32 11.25 4.00 5.96 5.93 0 50 50
## W44 46 811 8.43 11.22 4.00 6.12 5.93 0 46 46
## W45 47 811 8.56 11.38 4.00 6.19 5.93 0 46 46
## W46 48 811 8.72 11.62 4.00 6.31 5.93 0 55 55
## W47 49 811 8.67 11.44 4.00 6.34 5.93 0 49 49
## W48 50 811 8.67 11.22 4.00 6.45 5.93 0 50 50
## W49 51 811 8.90 10.94 4.00 6.88 5.93 0 52 52
## W50 52 811 8.86 10.49 5.00 7.04 7.41 0 57 57
## W51 53 811 8.89 9.56 5.00 7.48 7.41 0 73 73
## MIN 54 811 3.78 6.40 0.00 2.29 0.00 0 24 24
## MAX 55 811 16.31 17.15 9.00 13.50 10.38 1 73 72
## Normalized.0 56 811 0.29 0.27 0.25 0.26 0.37 0 1 1
## Normalized.1 57 811 0.30 0.28 0.28 0.27 0.42 0 1 1
## Normalized.2 58 811 0.31 0.28 0.29 0.28 0.43 0 1 1
## Normalized.3 59 811 0.32 0.30 0.29 0.29 0.43 0 1 1
## Normalized.4 60 811 0.33 0.30 0.31 0.30 0.46 0 1 1
## Normalized.5 61 811 0.32 0.29 0.30 0.29 0.43 0 1 1
## Normalized.6 62 811 0.33 0.30 0.31 0.30 0.46 0 1 1
## Normalized.7 63 811 0.33 0.30 0.33 0.30 0.44 0 1 1
## Normalized.8 64 811 0.32 0.29 0.32 0.30 0.44 0 1 1
## Normalized.9 65 811 0.33 0.29 0.33 0.30 0.40 0 1 1
## Normalized.10 66 811 0.33 0.30 0.31 0.30 0.46 0 1 1
## Normalized.11 67 811 0.33 0.30 0.31 0.30 0.46 0 1 1
## Normalized.12 68 811 0.34 0.30 0.33 0.31 0.43 0 1 1
## Normalized.13 69 811 0.33 0.29 0.33 0.31 0.40 0 1 1
## Normalized.14 70 811 0.36 0.30 0.36 0.33 0.39 0 1 1
## Normalized.15 71 811 0.34 0.31 0.33 0.32 0.49 0 1 1
## Normalized.16 72 811 0.34 0.30 0.33 0.31 0.43 0 1 1
## Normalized.17 73 811 0.35 0.30 0.33 0.32 0.44 0 1 1
## Normalized.18 74 811 0.35 0.30 0.35 0.33 0.39 0 1 1
## Normalized.19 75 811 0.33 0.30 0.31 0.30 0.44 0 1 1
## Normalized.20 76 811 0.34 0.30 0.33 0.31 0.43 0 1 1
## Normalized.21 77 811 0.35 0.29 0.36 0.33 0.36 0 1 1
## Normalized.22 78 811 0.37 0.30 0.36 0.34 0.39 0 1 1
## Normalized.23 79 811 0.37 0.30 0.38 0.35 0.37 0 1 1
## Normalized.24 80 811 0.42 0.32 0.44 0.40 0.36 0 1 1
## Normalized.25 81 811 0.39 0.32 0.35 0.36 0.40 0 1 1
## Normalized.26 82 811 0.21 0.21 0.18 0.18 0.27 0 1 1
## Normalized.27 83 811 0.22 0.23 0.20 0.19 0.30 0 1 1
## Normalized.28 84 811 0.23 0.23 0.21 0.20 0.31 0 1 1
## Normalized.29 85 811 0.22 0.23 0.19 0.19 0.28 0 1 1
## Normalized.30 86 811 0.24 0.24 0.21 0.21 0.31 0 1 1
## Normalized.31 87 811 0.25 0.25 0.22 0.22 0.33 0 1 1
## Normalized.32 88 811 0.25 0.24 0.22 0.22 0.33 0 1 1
## Normalized.33 89 811 0.26 0.25 0.23 0.23 0.34 0 1 1
## Normalized.34 90 811 0.26 0.25 0.25 0.23 0.37 0 1 1
## Normalized.35 91 811 0.27 0.25 0.25 0.24 0.37 0 1 1
## Normalized.36 92 811 0.27 0.26 0.24 0.24 0.34 0 1 1
## Normalized.37 93 811 0.27 0.25 0.25 0.25 0.37 0 1 1
## Normalized.38 94 811 0.28 0.25 0.25 0.25 0.37 0 1 1
## Normalized.39 95 811 0.26 0.25 0.25 0.24 0.37 0 1 1
## Normalized.40 96 811 0.29 0.26 0.25 0.26 0.37 0 1 1
## Normalized.41 97 811 0.28 0.25 0.26 0.25 0.36 0 1 1
## Normalized.42 98 811 0.30 0.27 0.28 0.27 0.33 0 1 1
## Normalized.43 99 811 0.29 0.26 0.27 0.26 0.34 0 1 1
## Normalized.44 100 811 0.30 0.26 0.30 0.28 0.30 0 1 1
## Normalized.45 101 811 0.32 0.26 0.31 0.29 0.28 0 1 1
## Normalized.46 102 811 0.33 0.28 0.33 0.31 0.30 0 1 1
## Normalized.47 103 811 0.31 0.27 0.31 0.29 0.30 0 1 1
## Normalized.48 104 811 0.34 0.28 0.33 0.31 0.28 0 1 1
## Normalized.49 105 811 0.36 0.29 0.33 0.33 0.33 0 1 1
## Normalized.50 106 811 0.37 0.30 0.35 0.35 0.33 0 1 1
## Normalized.51 107 811 0.43 0.34 0.43 0.41 0.44 0 1 1
## skew kurtosis se
## Product_Code* 0.00 -1.20 8.23
## W0 1.49 1.13 0.42
## W1 1.54 1.26 0.44
## W2 1.58 1.38 0.46
## W3 1.57 1.32 0.48
## W4 1.56 1.41 0.46
## W5 1.51 1.18 0.45
## W6 1.56 1.35 0.47
## W7 1.58 1.52 0.46
## W8 1.58 1.42 0.48
## W9 1.49 0.99 0.46
## W10 1.57 1.34 0.48
## W11 1.48 1.12 0.46
## W12 1.52 1.21 0.47
## W13 1.51 1.12 0.46
## W14 1.56 1.35 0.47
## W15 1.53 1.24 0.48
## W16 1.57 1.40 0.49
## W17 1.52 1.35 0.47
## W18 1.57 1.42 0.48
## W19 1.53 1.30 0.46
## W20 1.55 1.36 0.47
## W21 1.46 1.03 0.45
## W22 1.45 0.99 0.46
## W23 1.48 1.42 0.44
## W24 1.31 0.85 0.43
## W25 1.26 1.31 0.35
## W26 1.65 1.92 0.33
## W27 1.57 1.51 0.34
## W28 1.62 1.62 0.36
## W29 1.60 1.51 0.36
## W30 1.67 1.86 0.37
## W31 1.65 1.82 0.36
## W32 1.64 1.78 0.38
## W33 1.61 1.51 0.38
## W34 1.56 1.35 0.38
## W35 1.56 1.36 0.38
## W36 1.68 2.03 0.38
## W37 1.58 1.45 0.38
## W38 1.63 1.67 0.40
## W39 1.59 1.49 0.38
## W40 1.60 1.49 0.39
## W41 1.59 1.53 0.39
## W42 1.62 1.62 0.40
## W43 1.61 1.57 0.40
## W44 1.55 1.31 0.39
## W45 1.56 1.26 0.40
## W46 1.62 1.59 0.41
## W47 1.55 1.36 0.40
## W48 1.51 1.25 0.39
## W49 1.39 0.89 0.38
## W50 1.33 0.91 0.37
## W51 1.34 2.39 0.34
## MIN 1.71 1.47 0.22
## MAX 1.23 0.29 0.60
## Normalized.0 0.57 -0.53 0.01
## Normalized.1 0.60 -0.55 0.01
## Normalized.2 0.54 -0.75 0.01
## Normalized.3 0.49 -0.87 0.01
## Normalized.4 0.50 -0.76 0.01
## Normalized.5 0.54 -0.68 0.01
## Normalized.6 0.51 -0.75 0.01
## Normalized.7 0.49 -0.79 0.01
## Normalized.8 0.47 -0.79 0.01
## Normalized.9 0.47 -0.77 0.01
## Normalized.10 0.50 -0.80 0.01
## Normalized.11 0.51 -0.82 0.01
## Normalized.12 0.43 -0.90 0.01
## Normalized.13 0.43 -0.80 0.01
## Normalized.14 0.37 -0.86 0.01
## Normalized.15 0.45 -0.95 0.01
## Normalized.16 0.47 -0.82 0.01
## Normalized.17 0.39 -0.92 0.01
## Normalized.18 0.37 -0.82 0.01
## Normalized.19 0.50 -0.74 0.01
## Normalized.20 0.45 -0.85 0.01
## Normalized.21 0.33 -0.85 0.01
## Normalized.22 0.35 -0.86 0.01
## Normalized.23 0.31 -0.89 0.01
## Normalized.24 0.19 -0.98 0.01
## Normalized.25 0.41 -0.93 0.01
## Normalized.26 1.05 1.00 0.01
## Normalized.27 0.98 0.76 0.01
## Normalized.28 0.93 0.47 0.01
## Normalized.29 0.98 0.68 0.01
## Normalized.30 0.92 0.60 0.01
## Normalized.31 0.94 0.40 0.01
## Normalized.32 0.83 0.28 0.01
## Normalized.33 0.84 0.24 0.01
## Normalized.34 0.73 -0.05 0.01
## Normalized.35 0.66 -0.24 0.01
## Normalized.36 0.88 0.27 0.01
## Normalized.37 0.68 -0.06 0.01
## Normalized.38 0.73 0.05 0.01
## Normalized.39 0.74 0.05 0.01
## Normalized.40 0.71 -0.12 0.01
## Normalized.41 0.72 -0.02 0.01
## Normalized.42 0.70 -0.06 0.01
## Normalized.43 0.67 -0.07 0.01
## Normalized.44 0.61 -0.20 0.01
## Normalized.45 0.57 -0.20 0.01
## Normalized.46 0.59 -0.25 0.01
## Normalized.47 0.52 -0.40 0.01
## Normalized.48 0.58 -0.24 0.01
## Normalized.49 0.47 -0.52 0.01
## Normalized.50 0.40 -0.71 0.01
## Normalized.51 0.25 -1.17 0.01# we can see the mean, median, min, and max for each product for each week.#exlporatory data analysis
#since the data is wide format, which is not easy to apply ggplot, so I can the wide format to long format
Sales<-gather(data = Sales_Transaction[1:53], key = Week, value = Sales, -Product_Code)
hist(Sales$Sales, main = "Sales",col = "yellow",xlab = "Number of Sales", ylab = "Count Number of Sales")
#It is seen that there are big number of products with a very small amount of sales, and the data skewed toward the left as well. #based on the EDA, the data is very skewed, the price of each product is not given, I will only focus on the top 5 product with highest sales by adding the sales of 52 weeks.
Sales1<-Sales_Transaction[1:53]
df<-na.omit(Sales1)
df1<-cbind(df, Total_Sales=rowSums(df[2:53]))df1 %>% arrange(-Total_Sales) ## Product_Code W0 W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 W14 W15 W16
## 1 P409 42 48 38 43 35 39 36 38 49 46 44 25 43 38 34 48 52
## 2 P34 47 42 24 55 42 23 41 51 45 29 51 40 28 48 35 40 38
## 3 P178 35 34 40 36 45 37 43 47 34 39 33 41 47 40 47 53 44
## 4 P135 38 32 36 37 42 33 56 37 39 31 43 45 39 55 43 45 47
## 5 P43 28 43 40 43 54 33 39 30 38 38 56 34 37 32 44 47 45
## 6 P190 54 41 51 45 51 46 31 37 38 35 43 36 41 54 47 30 47
## 7 P179 44 43 35 36 39 42 31 44 37 38 33 35 37 34 51 50 43
## 8 P173 34 25 42 47 37 40 30 44 37 38 41 38 42 40 44 41 54
## 9 P92 26 36 56 40 31 44 37 40 38 43 41 38 36 39 45 59 48
## 10 P137 37 41 43 41 40 47 54 30 43 40 33 45 35 43 41 44 34
## 11 P38 37 36 43 52 61 50 35 52 49 46 53 57 35 33 42 41 31
## 12 P174 37 42 30 43 48 44 47 27 43 41 34 53 33 35 40 52 47
## 13 P24 36 42 27 33 40 48 38 39 41 39 44 35 53 52 43 45 41
## 14 P16 30 27 27 43 29 32 49 41 49 38 42 30 43 43 54 48 34
## 15 P40 41 27 27 51 37 38 48 40 39 40 47 31 48 43 37 45 47
## 16 P54 41 42 37 40 29 52 43 40 41 38 33 52 37 43 47 33 34
## 17 P136 39 37 39 52 38 28 51 39 42 37 35 47 32 32 45 36 34
## 18 P193 36 22 32 45 35 44 39 41 33 43 49 41 45 45 43 35 46
## 19 P37 36 39 43 42 38 37 31 26 36 29 31 36 46 25 51 44 42
## 20 P191 48 36 42 35 44 39 37 45 42 40 40 42 57 46 38 35 31
## 21 P180 40 38 34 43 43 34 41 31 55 34 51 37 40 44 38 53 55
## 22 P101 26 51 45 47 40 36 38 28 38 45 52 37 49 36 37 40 52
## 23 P36 41 32 39 45 38 40 39 39 27 48 47 35 61 34 37 47 30
## 24 P66 35 41 45 34 50 40 41 39 36 45 48 27 35 34 44 27 48
## 25 P134 32 41 50 35 36 35 41 33 32 34 38 29 42 52 57 31 34
## 26 P75 34 45 37 27 40 22 28 44 38 45 52 41 45 44 45 28 33
## 27 P129 21 36 44 47 26 33 30 27 37 34 41 45 41 36 37 43 44
## 28 P128 36 43 28 39 41 37 41 45 43 40 46 40 40 33 35 31 35
## 29 P175 30 40 48 28 30 34 40 53 43 37 29 38 38 36 36 46 37
## 30 P63 37 39 54 44 30 36 48 39 40 34 50 40 40 41 55 34 42
## 31 P132 39 36 45 41 43 37 38 39 32 45 48 32 36 40 37 28 30
## 32 P41 35 27 26 43 44 38 40 38 47 48 32 37 35 36 50 41 50
## 33 P72 26 34 39 41 39 38 52 40 28 34 43 32 36 45 43 39 48
## 34 P83 46 40 34 38 36 45 48 37 63 37 30 37 44 31 41 37 46
## 35 P112 31 36 32 51 39 33 35 46 57 34 39 30 32 27 41 27 50
## 36 P15 19 45 47 42 29 44 43 36 25 52 39 42 43 42 43 51 40
## 37 P35 34 37 26 27 49 48 36 34 28 41 41 35 29 42 41 31 38
## 38 P27 44 34 33 39 34 30 47 27 45 39 47 39 35 47 29 45 52
## 39 P48 29 51 40 33 43 28 29 41 35 45 43 41 30 32 51 50 45
## 40 P172 32 48 44 40 31 40 30 45 40 29 45 32 37 36 43 36 34
## 41 P96 31 35 36 44 36 38 36 39 47 39 24 29 46 38 34 26 36
## 42 P186 36 34 37 36 41 33 51 43 21 44 35 50 39 37 26 41 48
## 43 P49 37 28 42 38 37 35 42 36 30 48 28 39 32 44 36 41 35
## 44 P168 34 29 34 59 27 39 34 49 35 45 39 28 43 40 37 33 42
## 45 P184 30 37 38 30 32 32 52 33 47 44 38 45 38 47 44 52 40
## 46 P618 40 35 49 31 34 45 40 42 42 41 42 34 37 39 37 29 51
## 47 P133 30 48 29 38 40 42 47 42 33 38 47 32 40 30 42 42 42
## 48 P185 32 28 36 40 40 50 43 40 38 35 43 41 29 34 37 33 25
## 49 P17 49 40 40 28 40 47 44 45 39 33 39 37 33 52 29 45 34
## 50 P130 19 53 43 41 39 46 45 31 50 46 39 35 38 29 37 28 32
## 51 P39 31 21 28 39 53 39 25 31 43 40 41 43 47 35 36 34 35
## 52 P84 29 26 31 39 28 44 32 42 41 42 46 35 42 35 56 34 62
## 53 P69 26 43 46 39 41 31 41 35 44 26 48 46 35 38 39 36 38
## 54 P131 29 32 32 35 49 38 34 43 39 31 45 38 40 40 42 45 34
## 55 P47 40 42 27 28 33 29 33 58 37 34 37 19 41 37 47 36 30
## 56 P58 32 34 38 41 24 29 34 47 41 42 28 35 26 32 36 41 35
## 57 P140 28 36 41 46 34 38 38 28 34 27 28 39 45 19 32 44 33
## 58 P167 33 45 42 41 32 45 43 45 45 36 48 46 33 42 34 37 41
## 59 P120 37 35 27 30 31 42 30 37 37 39 32 31 38 38 35 47 52
## 60 P57 38 26 37 43 51 39 42 27 36 45 27 39 37 41 28 45 39
## 61 P119 30 40 46 33 28 41 34 33 44 49 37 29 42 31 45 43 37
## 62 P177 25 38 37 48 34 40 30 29 39 40 36 35 30 44 43 46 29
## 63 P46 27 46 31 38 40 40 53 43 45 32 37 32 38 39 28 43 50
## 64 P52 40 44 37 48 28 40 35 32 41 36 44 39 31 32 43 39 46
## 65 P60 37 41 46 27 51 28 38 40 37 34 34 26 39 33 32 37 45
## 66 P176 38 44 41 26 28 36 29 38 45 32 45 53 44 31 35 37 35
## 67 P170 29 37 32 43 30 27 28 22 37 42 32 36 31 34 28 48 35
## 68 P139 32 36 32 38 47 31 48 27 41 36 31 34 47 39 38 38 47
## 69 P90 42 34 40 39 47 31 43 40 47 35 38 37 44 27 30 47 39
## 70 P73 35 30 36 46 34 29 34 41 56 33 44 36 36 44 37 39 22
## 71 P181 32 44 31 38 37 36 30 42 49 46 26 31 39 47 43 50 35
## 72 P86 37 33 33 32 36 26 45 37 43 36 36 46 32 46 29 39 30
## 73 P56 31 28 41 36 45 25 42 47 36 42 42 37 45 38 40 31 34
## 74 P621 31 33 29 38 36 27 38 62 39 39 38 34 33 36 35 35 52
## 75 P196 43 34 39 32 45 35 43 44 36 39 37 27 38 34 32 30 47
## 76 P28 34 32 36 41 31 31 32 29 43 33 37 44 37 27 36 38 24
## 77 P143 31 35 29 42 31 35 28 41 49 41 36 27 39 43 33 47 43
## 78 P622 29 33 39 40 40 37 37 37 26 42 34 32 25 36 46 41 35
## 79 P44 34 27 28 36 50 28 31 33 34 27 29 33 30 45 35 42 45
## 80 P67 36 30 38 44 47 37 38 31 47 37 42 34 33 42 33 42 30
## 81 P548 32 28 39 36 47 40 35 39 40 37 38 31 29 41 41 34 33
## 82 P30 46 36 45 34 35 36 43 28 26 33 46 42 41 42 37 38 40
## 83 P19 26 31 45 36 31 28 28 34 42 40 43 35 30 33 40 45 48
## 84 P192 24 33 30 35 36 43 43 31 31 39 26 33 39 39 29 43 40
## 85 P76 27 34 43 45 28 35 26 34 38 45 26 49 51 41 34 38 41
## 86 P18 40 38 39 38 39 33 28 44 36 36 23 38 38 41 43 27 38
## 87 P79 37 34 45 41 37 23 41 40 41 38 37 37 42 30 43 35 30
## 88 P262 25 31 33 23 38 34 31 31 38 34 28 25 29 31 33 53 41
## 89 P188 33 34 36 52 42 49 39 30 43 20 25 49 35 34 39 35 52
## 90 P189 32 34 46 30 39 51 28 25 30 32 38 23 41 29 39 38 35
## 91 P141 27 45 40 34 31 35 37 40 40 37 34 25 29 30 42 35 37
## 92 P89 24 26 44 31 37 37 38 30 35 49 49 41 45 41 31 27 32
## 93 P623 38 27 36 36 35 39 33 29 41 31 37 37 30 35 25 28 42
## 94 P619 38 31 31 41 41 36 37 27 40 34 45 33 22 37 43 32 52
## 95 P61 25 30 32 47 45 50 40 35 33 33 35 43 41 32 38 40 30
## 96 P42 42 27 40 27 32 42 31 37 22 38 33 39 37 45 48 31 45
## 97 P70 31 39 50 31 37 30 37 44 35 33 26 32 41 35 35 47 43
## 98 P138 36 44 22 35 34 34 38 34 26 36 33 28 43 38 19 40 41
## 99 P142 23 29 40 43 34 30 42 43 35 35 43 37 25 42 42 39 43
## 100 P78 39 40 31 39 44 34 31 32 47 36 44 34 31 39 32 44 44
## 101 P617 36 33 40 46 39 39 26 44 34 34 43 46 36 28 27 44 32
## 102 P45 40 29 39 34 37 23 33 26 34 41 33 29 54 37 37 27 33
## 103 P64 34 37 29 42 31 36 36 43 29 30 48 34 38 33 28 45 41
## 104 P85 39 34 28 38 33 37 52 28 31 27 35 41 43 36 28 40 29
## 105 P208 30 26 36 33 33 30 33 28 19 26 43 36 31 33 41 29 33
## 106 P97 29 37 36 40 33 29 27 49 38 43 35 37 46 44 30 41 28
## 107 P87 30 38 35 39 37 42 40 35 40 41 34 39 37 40 28 38 31
## 108 P102 34 41 22 32 36 27 44 33 22 38 33 33 39 31 28 37 44
## 109 P55 34 30 42 42 29 24 36 42 42 29 42 47 26 30 32 37 40
## 110 P182 42 28 34 28 26 35 29 36 44 37 47 29 43 37 36 31 39
## 111 P549 35 29 40 32 33 30 36 42 40 44 40 38 34 34 36 38 31
## 112 P88 41 28 32 30 33 41 42 35 45 38 28 43 38 37 32 35 34
## 113 P169 38 31 22 43 29 25 46 32 38 39 32 32 31 37 29 36 37
## 114 P183 25 37 42 50 18 32 38 37 33 30 37 20 41 40 39 38 34
## 115 P194 35 37 31 23 37 42 38 34 33 37 34 43 37 32 43 42 41
## 116 P113 22 26 31 37 32 25 28 33 40 27 38 40 31 32 29 34 34
## 117 P25 26 28 33 32 20 33 42 29 24 32 45 41 35 39 32 36 31
## 118 P80 38 29 32 40 29 36 47 24 36 31 39 35 40 37 51 46 21
## 119 P620 31 27 37 29 34 39 28 28 30 32 38 37 39 30 40 32 42
## 120 P187 31 38 47 36 36 27 28 19 40 38 28 31 34 38 36 30 33
## 121 P557 28 23 35 34 33 27 33 27 25 32 40 28 34 24 31 23 27
## 122 P511 25 23 30 33 20 27 31 26 21 42 22 30 33 27 28 32 31
## 123 P615 17 16 19 20 19 19 29 35 15 27 24 24 34 29 24 29 24
## 124 P533 28 33 21 37 20 28 29 23 27 23 23 24 29 37 41 26 29
## 125 P613 18 26 12 17 23 15 18 19 33 31 21 32 21 17 29 20 20
## 126 P261 20 36 17 19 16 23 28 19 22 19 21 18 27 24 24 24 26
## 127 P270 26 16 23 19 29 21 16 14 29 13 20 22 16 26 19 26 23
## 128 P10 22 19 19 29 20 16 26 20 24 20 31 22 23 19 15 19 22
## 129 P516 24 18 15 21 20 19 21 25 21 13 31 20 23 18 16 18 15
## 130 P519 30 26 16 16 23 30 21 18 27 23 16 24 22 27 8 26 27
## 131 P405 23 12 16 22 18 18 17 11 28 10 25 24 22 25 12 17 16
## 132 P512 17 17 16 16 27 18 17 17 16 20 21 14 19 10 18 26 20
## 133 P268 18 18 18 14 18 24 15 13 17 18 14 21 29 20 19 20 24
## 134 P286 17 19 13 15 16 23 18 16 15 19 14 22 18 18 24 26 33
## 135 P407 22 23 10 19 16 26 19 16 23 23 23 17 31 19 18 17 16
## 136 P554 24 15 32 28 22 21 19 23 17 17 31 23 18 12 22 22 21
## 137 P535 15 26 11 15 19 15 16 19 19 23 24 24 19 26 19 16 20
## 138 P566 24 26 22 24 20 13 17 21 18 18 21 30 22 24 15 22 28
## 139 P486 16 30 25 11 23 19 27 15 30 23 19 22 16 17 19 20 30
## 140 P263 18 12 20 21 12 24 13 13 23 18 19 19 16 12 23 14 16
## 141 P51 19 14 17 27 14 18 18 18 14 18 19 17 28 25 21 16 24
## 142 P284 26 17 17 22 23 24 26 15 18 19 16 14 20 29 17 21 17
## 143 P491 19 20 27 23 19 30 23 23 13 12 14 28 11 15 24 15 25
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## W51 Total_Sales
## 1 73 2220
## 2 26 1932
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## 811 0 1#total sales over 52 weeks less than 20
df1%>% arrange(Total_Sales) %>% filter(Total_Sales<=20) %>%count()## # A tibble: 1 x 1
## n
## <int>
## 1 199#select top 5 Total_Sales products
p409<-subset(df1, Product_Code=="P409")
p34<-subset(df1,Product_Code=="P34")
p178<-subset(df1,Product_Code=="P178")
p135<-subset(df1,Product_Code=="P135")
p43<-subset(df1,Product_Code=="P43")#transpose the data for time series
p409_t<-t(p409[2:53])
p34_t<-t(p34[2:53])
p178_t<-t(p178[2:53])
p135_t<-t(p135[2:53])
p43_t<-t(p43[2:53])#Time series of p409
ts_p409<-ts(p409_t,start=c(2018,1),frequency=52)
autoplot(ts_p409)+xlab("Time")+ylab("sales") +ggtitle("P409 Time Series")
autoplot(ts_p409,series="mean")+
autolayer(ma(ts_p409,5), series="5-MA")+ggtitle("P409 MA")## Warning: Removed 4 rows containing missing values (geom_path).
#Estimate the Trend-Cycle with Seasonal Data
autoplot(ts_p409,series = "Holdings")+
autolayer(ma(ts_p409,12),series="12-MA")+
xlab("Time")+ylab("Sales")+
ggtitle("Trend-Cycle with Seasonal Data")## Warning: Removed 12 rows containing missing values (geom_path).
#Time series of p34
ts_p34<-ts(p34_t,start=c(2018,1),frequency=52)
autoplot(ts_p34)+xlab("Time")+ylab("sales")+ggtitle("P34 Time Series")
autoplot(ts_p34,series="mean")+
autolayer(ma(ts_p34,5), series="5-MA")+ggtitle("P34 MA")## Warning: Removed 4 rows containing missing values (geom_path).
#Estimate the Trend-Cycle with Seasonal Data
autoplot(ts_p34,series = "Holdings")+
autolayer(ma(ts_p34,12),series="12-MA")+
xlab("Time")+ylab("Sales")+
ggtitle("Trend-Cycle with Seasonal Data")## Warning: Removed 12 rows containing missing values (geom_path).
#Time series of p178
ts_p178<-ts(p178_t,start=c(2018,1),frequency=52)
autoplot(ts_p178)+xlab("Time")+ylab("sales")+ggtitle("P178 Time Series")
autoplot(ts_p178,series="mean")+
autolayer(ma(ts_p178,5), series="5-MA")+ggtitle("P178 MA")## Warning: Removed 4 rows containing missing values (geom_path).
#Estimate the Trend-Cycle with Seasonal Data
autoplot(ts_p178,series = "Holdings")+
autolayer(ma(ts_p178,12),series="12-MA")+
xlab("Time")+ylab("Sales")+
ggtitle("Trend-Cycle with Seasonal Data")## Warning: Removed 12 rows containing missing values (geom_path).
#Time series of p135
ts_p135<-ts(p135_t,start=c(2018,1),frequency=52)
autoplot(ts_p135)+xlab("Time")+ylab("sales")+ggtitle("P135 Time Series")
autoplot(ts_p135,series="mean")+
autolayer(ma(ts_p135,5), series="5-MA")+ggtitle("P135 MA")## Warning: Removed 4 rows containing missing values (geom_path).
#Estimate the Trend-Cycle with Seasonal Data
autoplot(ts_p135,series = "Holdings")+
autolayer(ma(ts_p135,12),series="12-MA")+
xlab("Time")+ylab("Sales")+
ggtitle("Trend-Cycle with Seasonal Data")## Warning: Removed 12 rows containing missing values (geom_path).
#Time series of p43
ts_p43<-ts(p43_t,start=c(2018,1),frequency=52)
autoplot(ts_p43)+xlab("Time")+ylab("sales")+ggtitle("P43 Time Series")
autoplot(ts_p43,series="mean")+
autolayer(ma(ts_p43,5), series="5-MA")+ggtitle("P43 MA")## Warning: Removed 4 rows containing missing values (geom_path).
#Estimate the Trend-Cycle with Seasonal Data
autoplot(ts_p43,series = "Holdings")+
autolayer(ma(ts_p43,12),series="12-MA")+
xlab("Time")+ylab("Sales")+
ggtitle("Trend-Cycle with Seasonal Data")## Warning: Removed 12 rows containing missing values (geom_path).
#since this is an one-year dataset, it's hard to see the trend or seasonality. The rapid increase or decrease can be caused by festivals. In addition, most of the decomposition methods are not applicable because the data lack seasonality. Also, weekly data is difficult to work with because the seasonal period (the number of weeks in a year) is both large and non-integer. The average number of weeks in a year is 52.18. Most of the methods we have considered require the seasonal period to be an integer. Even if we approximate it by 52, most of the methods will not handle such a large seasonal period efficiently.
# In this case, I only use moving average method to show the trend of top 5 sales products.#product P409
#Seasonal Naive Method
naive_p409<-snaive(ts_p409,4)
autoplot(naive_p409) + autolayer(naive_p409,series = "snaive")
#Simple exponential smoothing
ses_p409<-ses(ts_p409,h=4)
autoplot(ses_p409)+
autolayer(fitted(ses_p409),series="Fitted")+
ylab("Sales")+ xlab("Week")
#Holt's linear trend method
holt_p409<-holt(ts_p409,h=4)
autoplot(holt_p409)+
autolayer(holt_p409,series="Holt's method",PI=FALSE)
#Damped Holt's Trend Method
damp_p409<-holt(ts_p409,damped = TRUE,h=4)
autoplot(damp_p409)+
autolayer(damp_p409$fitted)
#ETS method
ets_p409<-ets(ts_p409)
autoplot(forecast(ets_p409,h=4))+ggtitle("P409 ETS")
#ARIMA Models
arima_p409<-auto.arima(ts_p409,seasonal = FALSE)
arima_p409%>% forecast(h=4) %>% autoplot(include=80)+
ylab("Sales")+ xlab("Week")+ggtitle("P409 Arima")
ggAcf(ts_p409)
ggPacf(ts_p409)
checkresiduals(ets_p409)
##
## Ljung-Box test
##
## data: Residuals from ETS(M,N,N)
## Q* = 11.714, df = 8.4, p-value = 0.1894
##
## Model df: 2. Total lags used: 10.4checkresiduals(arima_p409)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,0,0) with non-zero mean
## Q* = 13.541, df = 8.4, p-value = 0.1113
##
## Model df: 2. Total lags used: 10.4accuracy(ets_p409)## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.8212682 10.57843 7.725092 -3.44772 19.74376 NaN 0.04469462accuracy(arima_p409)## ME RMSE MAE MPE MAPE MASE
## Training set 0.01617023 10.29233 7.781377 -6.132657 19.99894 NaN
## ACF1
## Training set -0.04291878#product P34
#Seasonal Naive Method
naive_p34<-snaive(ts_p34,4)
autoplot(naive_p34) + autolayer(naive_p34,series = "snaive")
#Simple exponential smoothing
ses_p34<-ses(ts_p34,h=4)
autoplot(ses_p34)+
autolayer(fitted(ses_p34),series="Fitted")+
ylab("Sales")+ xlab("Week")
#Holt's linear trend method
holt_p34<-holt(ts_p34,h=4)
autoplot(holt_p34)+
autolayer(holt_p34,series="Holt's method",PI=FALSE)
#Damped Holt's Trend Method
damp_p34<-holt(ts_p34,damped = TRUE,h=4)
autoplot(damp_p34)+
autolayer(damp_p34$fitted)
#ETS method
ets_p34<-ets(ts_p34)
autoplot(forecast(ets_p34,h=4))
#ARIMA Models
arima_p34<-auto.arima(ts_p34,seasonal = FALSE)
arima_p34%>% forecast(h=4) %>% autoplot(include=80)+
ylab("Sales")+ xlab("Week")
ggAcf(ts_p34)
ggPacf(ts_p34)
summary(arima_p34)## Series: ts_p34
## ARIMA(3,1,2)
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## -0.9397 -0.5901 -0.2055 -0.0596 -0.5850
## s.e. 0.3688 0.2525 0.2577 0.3408 0.2344
##
## sigma^2 estimated as 55.82: log likelihood=-173.4
## AIC=358.8 AICc=360.71 BIC=370.39
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.582173 7.02675 5.616037 -5.177022 16.33428 NaN
## ACF1
## Training set -0.004282835checkresiduals(arima_p34)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(3,1,2)
## Q* = 7.9037, df = 5.4, p-value = 0.1932
##
## Model df: 5. Total lags used: 10.4checkresiduals(ets_p34)
##
## Ljung-Box test
##
## data: Residuals from ETS(M,N,N)
## Q* = 19.527, df = 8.4, p-value = 0.01536
##
## Model df: 2. Total lags used: 10.4checkresiduals(arima_p34)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(3,1,2)
## Q* = 7.9037, df = 5.4, p-value = 0.1932
##
## Model df: 5. Total lags used: 10.4accuracy(ets_p34)## ME RMSE MAE MPE MAPE MASE
## Training set -1.100599 7.789164 5.909122 -7.572166 17.78021 NaN
## ACF1
## Training set -0.1352629accuracy(arima_p34)## ME RMSE MAE MPE MAPE MASE
## Training set -0.582173 7.02675 5.616037 -5.177022 16.33428 NaN
## ACF1
## Training set -0.004282835#product P178
#Seasonal Naive Method
naive_p178<-snaive(ts_p178,4)
autoplot(naive_p178) + autolayer(naive_p178,series = "snaive")
#Simple exponential smoothing
ses_p178<-ses(ts_p178,h=4)
autoplot(ses_p178)+
autolayer(fitted(ses_p178),series="Fitted")+
ylab("Sales")+ xlab("Week")
#Holt's linear trend method
holt_p178<-holt(ts_p178,h=4)
autoplot(holt_p178)+
autolayer(holt_p178,series="Holt's method",PI=FALSE)
#Damped Holt's Trend Method
damp_p178<-holt(ts_p178,damped = TRUE,h=4)
autoplot(damp_p178)+
autolayer(damp_p178$fitted)
#ETS method
ets_p178<-ets(ts_p178)
autoplot(forecast(ets_p178,h=4))
#ARIMA Models
arima_p178<-auto.arima(ts_p178,seasonal = FALSE)
arima_p178%>% forecast(h=4) %>% autoplot(include=80)+
ylab("Sales")+ xlab("Week")
ggAcf(ts_p178)
ggPacf(ts_p178)
checkresiduals(arima_p178)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,1)
## Q* = 4.456, df = 9.4, p-value = 0.8993
##
## Model df: 1. Total lags used: 10.4checkresiduals(ets_p178)
##
## Ljung-Box test
##
## data: Residuals from ETS(A,N,N)
## Q* = 4.4406, df = 8.4, p-value = 0.8438
##
## Model df: 2. Total lags used: 10.4checkresiduals(arima_p178)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,1)
## Q* = 4.456, df = 9.4, p-value = 0.8993
##
## Model df: 1. Total lags used: 10.4accuracy(ets_p178)## ME RMSE MAE MPE MAPE MASE
## Training set -0.4285944 7.278231 5.643992 -5.073001 16.56116 NaN
## ACF1
## Training set -0.01996414accuracy(arima_p178)## ME RMSE MAE MPE MAPE MASE
## Training set -0.2971663 7.28012 5.583733 -4.662119 16.3296 NaN
## ACF1
## Training set -0.03425538#product P135
#Seasonal Naive Method
naive_p135<-snaive(ts_p135,4)
autoplot(naive_p135) + autolayer(naive_p135,series = "snaive")
#Simple exponential smoothing
ses_p135<-ses(ts_p135,h=4)
autoplot(ses_p135)+
autolayer(fitted(ses_p135),series="Fitted")+
ylab("Sales")+ xlab("Week")
#Holt's linear trend method
holt_p135<-holt(ts_p135,h=4)
autoplot(holt_p135)+
autolayer(holt_p135,series="Holt's method",PI=FALSE)
#Damped Holt's Trend Method
damp_p135<-holt(ts_p135,damped = TRUE,h=4)
autoplot(damp_p135)+
autolayer(damp_p135$fitted)
#ETS method
ets_p135<-ets(ts_p135)
autoplot(forecast(ets_p135,h=4))
#ARIMA Models
arima_p135<-auto.arima(ts_p135,seasonal = FALSE)
arima_p135%>% forecast(h=4) %>% autoplot(include=80)+
ylab("Sales")+ xlab("Week")
ggAcf(ts_p135)
ggPacf(ts_p135)
summary(arima_p135)## Series: ts_p135
## ARIMA(0,1,1)
##
## Coefficients:
## ma1
## -0.7394
## s.e. 0.1240
##
## sigma^2 estimated as 56.83: log likelihood=-175.28
## AIC=354.56 AICc=354.81 BIC=358.42
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.5842343 7.392498 5.773752 -6.020816 17.57901 NaN
## ACF1
## Training set -0.05516129checkresiduals(arima_p135)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,1)
## Q* = 9.1443, df = 9.4, p-value = 0.462
##
## Model df: 1. Total lags used: 10.4checkresiduals(ets_p135)
##
## Ljung-Box test
##
## data: Residuals from ETS(A,N,N)
## Q* = 8.5352, df = 8.4, p-value = 0.4223
##
## Model df: 2. Total lags used: 10.4checkresiduals(arima_p135)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,1)
## Q* = 9.1443, df = 9.4, p-value = 0.462
##
## Model df: 1. Total lags used: 10.4accuracy(ets_p135)## ME RMSE MAE MPE MAPE MASE
## Training set -0.6751885 7.389274 5.741731 -6.331545 17.5548 NaN
## ACF1
## Training set -0.03564441accuracy(arima_p135)## ME RMSE MAE MPE MAPE MASE
## Training set -0.5842343 7.392498 5.773752 -6.020816 17.57901 NaN
## ACF1
## Training set -0.05516129#product P43
#Seasonal Naive Method
naive_p43<-snaive(ts_p43,4)
autoplot(naive_p43) + autolayer(naive_p43,series = "snaive")
#Simple exponential smoothing
ses_p43<-ses(ts_p43,h=4)
autoplot(ses_p43)+
autolayer(fitted(ses_p43),series="Fitted")+
ylab("Sales")+ xlab("Week")
#Holt's linear trend method
holt_p43<-holt(ts_p43,h=4)
autoplot(holt_p43)+
autolayer(holt_p43,series="Holt's method",PI=FALSE)
#Damped Holt's Trend Method
damp_p43<-holt(ts_p43,damped = TRUE,h=4)
autoplot(damp_p43)+
autolayer(damp_p43$fitted)
#ETS method
ets_p43<-ets(ts_p43)
autoplot(forecast(ets_p43,h=4))
#ARIMA Models
arima_p43<-auto.arima(ts_p43,seasonal = FALSE)
arima_p43%>% forecast(h=4) %>% autoplot(include=80)+
ylab("Sales")+ xlab("Week")
ggAcf(ts_p43)
ggPacf(ts_p43)
checkresiduals(ets_p43)
##
## Ljung-Box test
##
## data: Residuals from ETS(M,N,N)
## Q* = 11.824, df = 8.4, p-value = 0.1836
##
## Model df: 2. Total lags used: 10.4checkresiduals(arima_p43)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,1,1)
## Q* = 6.3172, df = 8.4, p-value = 0.6519
##
## Model df: 2. Total lags used: 10.4accuracy(ets_p43)## ME RMSE MAE MPE MAPE MASE
## Training set -0.4379003 8.04433 6.976893 -5.388537 20.01099 NaN
## ACF1
## Training set 0.02390699accuracy(arima_p43)## ME RMSE MAE MPE MAPE MASE
## Training set -0.08635984 8.03272 6.833405 -4.336936 19.45645 NaN
## ACF1
## Training set 0.0176316R Markdown
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