Elizabeth Josephine 11/11/2020
reducing your dataset to a low dimensional dataset using the PCA
This section of the project entails reducing your dataset to a low dimensional dataset using the PCA. You will be required to perform your analysis and provide insights gained from your analysis.
You are a Data analyst at Carrefour Kenya and are currently undertaking a project that will inform the marketing department on the most relevant marketing strategies that will result in the highest no. of sales (total price including tax). Your project has been divided into four parts where you’ll explore a recent marketing dataset by performing various unsupervised learning techniques and later providing recommendations based on your insights.
- Define the question, the metric for success, the context, experimental design taken.
- Read and explore the given dataset.
- reducing your dataset to a low dimensional dataset using the PCA
The data used for this project will inform the marketing department on the most relevant marketing strategies that will result in the highest no. of sales (total price including tax)
[http://bit.ly/CarreFourDataset]
# loading libraries
library(relaimpo)## Loading required package: MASS
## Loading required package: boot
## Loading required package: survey
## Loading required package: grid
## Loading required package: Matrix
## Loading required package: survival
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## Attaching package: 'survival'
## The following object is masked from 'package:boot':
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## aml
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## Attaching package: 'survey'
## The following object is masked from 'package:graphics':
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## dotchart
## Loading required package: mitools
## This is the global version of package relaimpo.
## If you are a non-US user, a version with the interesting additional metric pmvd is available
## from Ulrike Groempings web site at prof.beuth-hochschule.de/groemping.
library(data.table)
library(ggplot2) # Data visualization
library(ggthemes) # Plot themes
library(plotly) # Interactive data visualizations##
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
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## last_plot
## The following object is masked from 'package:MASS':
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## select
## The following object is masked from 'package:stats':
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## filter
## The following object is masked from 'package:graphics':
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## layout
library(dplyr) # Data manipulation##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:data.table':
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## between, first, last
## The following object is masked from 'package:MASS':
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## select
## The following objects are masked from 'package:stats':
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## filter, lag
## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, union
library(psych) # Will be used for correlation visualization##
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
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## %+%, alpha
## The following object is masked from 'package:boot':
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## logit
# importing our data
# reading our data
df <- fread('http://bit.ly/CarreFourDataset')
df## Invoice ID Branch Customer type Gender Product line Unit price
## 1: 750-67-8428 A Member Female Health and beauty 74.69
## 2: 226-31-3081 C Normal Female Electronic accessories 15.28
## 3: 631-41-3108 A Normal Male Home and lifestyle 46.33
## 4: 123-19-1176 A Member Male Health and beauty 58.22
## 5: 373-73-7910 A Normal Male Sports and travel 86.31
## ---
## 996: 233-67-5758 C Normal Male Health and beauty 40.35
## 997: 303-96-2227 B Normal Female Home and lifestyle 97.38
## 998: 727-02-1313 A Member Male Food and beverages 31.84
## 999: 347-56-2442 A Normal Male Home and lifestyle 65.82
## 1000: 849-09-3807 A Member Female Fashion accessories 88.34
## Quantity Tax Date Time Payment cogs
## 1: 7 26.1415 1/5/2019 13:08 Ewallet 522.83
## 2: 5 3.8200 3/8/2019 10:29 Cash 76.40
## 3: 7 16.2155 3/3/2019 13:23 Credit card 324.31
## 4: 8 23.2880 1/27/2019 20:33 Ewallet 465.76
## 5: 7 30.2085 2/8/2019 10:37 Ewallet 604.17
## ---
## 996: 1 2.0175 1/29/2019 13:46 Ewallet 40.35
## 997: 10 48.6900 3/2/2019 17:16 Ewallet 973.80
## 998: 1 1.5920 2/9/2019 13:22 Cash 31.84
## 999: 1 3.2910 2/22/2019 15:33 Cash 65.82
## 1000: 7 30.9190 2/18/2019 13:28 Cash 618.38
## gross margin percentage gross income Rating Total
## 1: 4.761905 26.1415 9.1 548.9715
## 2: 4.761905 3.8200 9.6 80.2200
## 3: 4.761905 16.2155 7.4 340.5255
## 4: 4.761905 23.2880 8.4 489.0480
## 5: 4.761905 30.2085 5.3 634.3785
## ---
## 996: 4.761905 2.0175 6.2 42.3675
## 997: 4.761905 48.6900 4.4 1022.4900
## 998: 4.761905 1.5920 7.7 33.4320
## 999: 4.761905 3.2910 4.1 69.1110
## 1000: 4.761905 30.9190 6.6 649.2990
# previewing the dataset
View(df)# previewing the column names
colnames(df)## [1] "Invoice ID" "Branch"
## [3] "Customer type" "Gender"
## [5] "Product line" "Unit price"
## [7] "Quantity" "Tax"
## [9] "Date" "Time"
## [11] "Payment" "cogs"
## [13] "gross margin percentage" "gross income"
## [15] "Rating" "Total"
# previewing the dataset
class(df)## [1] "data.table" "data.frame"
# previewing the datatypes of the dataset
sapply(df, class)## Invoice ID Branch Customer type
## "character" "character" "character"
## Gender Product line Unit price
## "character" "character" "numeric"
## Quantity Tax Date
## "integer" "numeric" "character"
## Time Payment cogs
## "character" "character" "numeric"
## gross margin percentage gross income Rating
## "numeric" "numeric" "numeric"
## Total
## "numeric"
# previewing the head of the dataset
head(df, n = 5)## Invoice ID Branch Customer type Gender Product line Unit price
## 1: 750-67-8428 A Member Female Health and beauty 74.69
## 2: 226-31-3081 C Normal Female Electronic accessories 15.28
## 3: 631-41-3108 A Normal Male Home and lifestyle 46.33
## 4: 123-19-1176 A Member Male Health and beauty 58.22
## 5: 373-73-7910 A Normal Male Sports and travel 86.31
## Quantity Tax Date Time Payment cogs gross margin percentage
## 1: 7 26.1415 1/5/2019 13:08 Ewallet 522.83 4.761905
## 2: 5 3.8200 3/8/2019 10:29 Cash 76.40 4.761905
## 3: 7 16.2155 3/3/2019 13:23 Credit card 324.31 4.761905
## 4: 8 23.2880 1/27/2019 20:33 Ewallet 465.76 4.761905
## 5: 7 30.2085 2/8/2019 10:37 Ewallet 604.17 4.761905
## gross income Rating Total
## 1: 26.1415 9.1 548.9715
## 2: 3.8200 9.6 80.2200
## 3: 16.2155 7.4 340.5255
## 4: 23.2880 8.4 489.0480
## 5: 30.2085 5.3 634.3785
# previewing the tail of the dataset
tail(df, n = 5)## Invoice ID Branch Customer type Gender Product line Unit price
## 1: 233-67-5758 C Normal Male Health and beauty 40.35
## 2: 303-96-2227 B Normal Female Home and lifestyle 97.38
## 3: 727-02-1313 A Member Male Food and beverages 31.84
## 4: 347-56-2442 A Normal Male Home and lifestyle 65.82
## 5: 849-09-3807 A Member Female Fashion accessories 88.34
## Quantity Tax Date Time Payment cogs gross margin percentage
## 1: 1 2.0175 1/29/2019 13:46 Ewallet 40.35 4.761905
## 2: 10 48.6900 3/2/2019 17:16 Ewallet 973.80 4.761905
## 3: 1 1.5920 2/9/2019 13:22 Cash 31.84 4.761905
## 4: 1 3.2910 2/22/2019 15:33 Cash 65.82 4.761905
## 5: 7 30.9190 2/18/2019 13:28 Cash 618.38 4.761905
## gross income Rating Total
## 1: 2.0175 6.2 42.3675
## 2: 48.6900 4.4 1022.4900
## 3: 1.5920 7.7 33.4320
## 4: 3.2910 4.1 69.1110
## 5: 30.9190 6.6 649.2990
# checking the structure of the data
str(df)## Classes 'data.table' and 'data.frame': 1000 obs. of 16 variables:
## $ Invoice ID : chr "750-67-8428" "226-31-3081" "631-41-3108" "123-19-1176" ...
## $ Branch : chr "A" "C" "A" "A" ...
## $ Customer type : chr "Member" "Normal" "Normal" "Member" ...
## $ Gender : chr "Female" "Female" "Male" "Male" ...
## $ Product line : chr "Health and beauty" "Electronic accessories" "Home and lifestyle" "Health and beauty" ...
## $ Unit price : num 74.7 15.3 46.3 58.2 86.3 ...
## $ Quantity : int 7 5 7 8 7 7 6 10 2 3 ...
## $ Tax : num 26.14 3.82 16.22 23.29 30.21 ...
## $ Date : chr "1/5/2019" "3/8/2019" "3/3/2019" "1/27/2019" ...
## $ Time : chr "13:08" "10:29" "13:23" "20:33" ...
## $ Payment : chr "Ewallet" "Cash" "Credit card" "Ewallet" ...
## $ cogs : num 522.8 76.4 324.3 465.8 604.2 ...
## $ gross margin percentage: num 4.76 4.76 4.76 4.76 4.76 ...
## $ gross income : num 26.14 3.82 16.22 23.29 30.21 ...
## $ Rating : num 9.1 9.6 7.4 8.4 5.3 4.1 5.8 8 7.2 5.9 ...
## $ Total : num 549 80.2 340.5 489 634.4 ...
## - attr(*, ".internal.selfref")=<externalptr>
# checking the dimension/shape of the data
dim(df) # 1000 rows and 16 columns## [1] 1000 16
# checking for missing values
sum(is.na(df))# there are no missing values in the data## [1] 0
# displaying all rows from the dataset which don't contain any missing values
na.omit(df)## Invoice ID Branch Customer type Gender Product line Unit price
## 1: 750-67-8428 A Member Female Health and beauty 74.69
## 2: 226-31-3081 C Normal Female Electronic accessories 15.28
## 3: 631-41-3108 A Normal Male Home and lifestyle 46.33
## 4: 123-19-1176 A Member Male Health and beauty 58.22
## 5: 373-73-7910 A Normal Male Sports and travel 86.31
## ---
## 996: 233-67-5758 C Normal Male Health and beauty 40.35
## 997: 303-96-2227 B Normal Female Home and lifestyle 97.38
## 998: 727-02-1313 A Member Male Food and beverages 31.84
## 999: 347-56-2442 A Normal Male Home and lifestyle 65.82
## 1000: 849-09-3807 A Member Female Fashion accessories 88.34
## Quantity Tax Date Time Payment cogs
## 1: 7 26.1415 1/5/2019 13:08 Ewallet 522.83
## 2: 5 3.8200 3/8/2019 10:29 Cash 76.40
## 3: 7 16.2155 3/3/2019 13:23 Credit card 324.31
## 4: 8 23.2880 1/27/2019 20:33 Ewallet 465.76
## 5: 7 30.2085 2/8/2019 10:37 Ewallet 604.17
## ---
## 996: 1 2.0175 1/29/2019 13:46 Ewallet 40.35
## 997: 10 48.6900 3/2/2019 17:16 Ewallet 973.80
## 998: 1 1.5920 2/9/2019 13:22 Cash 31.84
## 999: 1 3.2910 2/22/2019 15:33 Cash 65.82
## 1000: 7 30.9190 2/18/2019 13:28 Cash 618.38
## gross margin percentage gross income Rating Total
## 1: 4.761905 26.1415 9.1 548.9715
## 2: 4.761905 3.8200 9.6 80.2200
## 3: 4.761905 16.2155 7.4 340.5255
## 4: 4.761905 23.2880 8.4 489.0480
## 5: 4.761905 30.2085 5.3 634.3785
## ---
## 996: 4.761905 2.0175 6.2 42.3675
## 997: 4.761905 48.6900 4.4 1022.4900
## 998: 4.761905 1.5920 7.7 33.4320
## 999: 4.761905 3.2910 4.1 69.1110
## 1000: 4.761905 30.9190 6.6 649.2990
# checking for duplicates
duplicated_rows <- df[duplicated(df),]
duplicated_rows # there are no duplicates in the data## Empty data.table (0 rows and 16 cols): Invoice ID,Branch,Customer type,Gender,Product line,Unit price...
# showing these unique items and assigning to a variable unique_items below
unique_items <- df[!duplicated(df), ]
unique_items## Invoice ID Branch Customer type Gender Product line Unit price
## 1: 750-67-8428 A Member Female Health and beauty 74.69
## 2: 226-31-3081 C Normal Female Electronic accessories 15.28
## 3: 631-41-3108 A Normal Male Home and lifestyle 46.33
## 4: 123-19-1176 A Member Male Health and beauty 58.22
## 5: 373-73-7910 A Normal Male Sports and travel 86.31
## ---
## 996: 233-67-5758 C Normal Male Health and beauty 40.35
## 997: 303-96-2227 B Normal Female Home and lifestyle 97.38
## 998: 727-02-1313 A Member Male Food and beverages 31.84
## 999: 347-56-2442 A Normal Male Home and lifestyle 65.82
## 1000: 849-09-3807 A Member Female Fashion accessories 88.34
## Quantity Tax Date Time Payment cogs
## 1: 7 26.1415 1/5/2019 13:08 Ewallet 522.83
## 2: 5 3.8200 3/8/2019 10:29 Cash 76.40
## 3: 7 16.2155 3/3/2019 13:23 Credit card 324.31
## 4: 8 23.2880 1/27/2019 20:33 Ewallet 465.76
## 5: 7 30.2085 2/8/2019 10:37 Ewallet 604.17
## ---
## 996: 1 2.0175 1/29/2019 13:46 Ewallet 40.35
## 997: 10 48.6900 3/2/2019 17:16 Ewallet 973.80
## 998: 1 1.5920 2/9/2019 13:22 Cash 31.84
## 999: 1 3.2910 2/22/2019 15:33 Cash 65.82
## 1000: 7 30.9190 2/18/2019 13:28 Cash 618.38
## gross margin percentage gross income Rating Total
## 1: 4.761905 26.1415 9.1 548.9715
## 2: 4.761905 3.8200 9.6 80.2200
## 3: 4.761905 16.2155 7.4 340.5255
## 4: 4.761905 23.2880 8.4 489.0480
## 5: 4.761905 30.2085 5.3 634.3785
## ---
## 996: 4.761905 2.0175 6.2 42.3675
## 997: 4.761905 48.6900 4.4 1022.4900
## 998: 4.761905 1.5920 7.7 33.4320
## 999: 4.761905 3.2910 4.1 69.1110
## 1000: 4.761905 30.9190 6.6 649.2990
# selecting the numerical data columns
df1 <- df %>% select_if(is.numeric)
colnames(df1)## [1] "Unit price" "Quantity"
## [3] "Tax" "cogs"
## [5] "gross margin percentage" "gross income"
## [7] "Rating" "Total"
# renaming columns for easy analysis
df1 <- df1 %>% rename(Unit_price = "Unit price")
df1 <- df1 %>% rename(gross_income = "gross income")
# selecting needed columns
df2 <- subset(df1, select = c("Unit_price", "Quantity", "Tax", "cogs", "gross_income", "Rating", "Total"))
colnames(df2)## [1] "Unit_price" "Quantity" "Tax" "cogs" "gross_income"
## [6] "Rating" "Total"
describe(df2)## vars n mean sd median trimmed mad min max
## Unit_price 1 1000 55.67 26.49 55.23 55.62 33.37 10.08 99.96
## Quantity 2 1000 5.51 2.92 5.00 5.51 2.97 1.00 10.00
## Tax 3 1000 15.38 11.71 12.09 14.00 11.13 0.51 49.65
## cogs 4 1000 307.59 234.18 241.76 279.91 222.65 10.17 993.00
## gross_income 5 1000 15.38 11.71 12.09 14.00 11.13 0.51 49.65
## Rating 6 1000 6.97 1.72 7.00 6.97 2.22 4.00 10.00
## Total 7 1000 322.97 245.89 253.85 293.91 233.78 10.68 1042.65
## range skew kurtosis se
## Unit_price 89.88 0.01 -1.22 0.84
## Quantity 9.00 0.01 -1.22 0.09
## Tax 49.14 0.89 -0.09 0.37
## cogs 982.83 0.89 -0.09 7.41
## gross_income 49.14 0.89 -0.09 0.37
## Rating 6.00 0.01 -1.16 0.05
## Total 1031.97 0.89 -0.09 7.78
str(df2)## Classes 'data.table' and 'data.frame': 1000 obs. of 7 variables:
## $ Unit_price : num 74.7 15.3 46.3 58.2 86.3 ...
## $ Quantity : int 7 5 7 8 7 7 6 10 2 3 ...
## $ Tax : num 26.14 3.82 16.22 23.29 30.21 ...
## $ cogs : num 522.8 76.4 324.3 465.8 604.2 ...
## $ gross_income: num 26.14 3.82 16.22 23.29 30.21 ...
## $ Rating : num 9.1 9.6 7.4 8.4 5.3 4.1 5.8 8 7.2 5.9 ...
## $ Total : num 549 80.2 340.5 489 634.4 ...
## - attr(*, ".internal.selfref")=<externalptr>
# We then pass df to the prcomp(). We also set two arguments, center and scale,
# to be TRUE then preview our object with summary
df3 <- prcomp(df2)
#df4=prcomp(df4)#,center=T,scale.=T)
#, center = TRUE, scale. = TRUE)
summary(df3)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 340.3819 20.53212 1.71932 1.24589 1.678e-13 7.548e-15
## Proportion of Variance 0.9963 0.00363 0.00003 0.00001 0.000e+00 0.000e+00
## Cumulative Proportion 0.9963 0.99996 0.99999 1.00000 1.000e+00 1.000e+00
## PC7
## Standard deviation 1.78e-15
## Proportion of Variance 0.00e+00
## Cumulative Proportion 1.00e+00
# Calling str() to have a look at your PCA object
str(df3)## List of 5
## $ sdev : num [1:7] 3.40e+02 2.05e+01 1.72 1.25 1.68e-13 ...
## $ rotation: num [1:7, 1:7] -0.04952 -0.00605 -0.0344 -0.68798 -0.0344 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:7] "Unit_price" "Quantity" "Tax" "cogs" ...
## .. ..$ : chr [1:7] "PC1" "PC2" "PC3" "PC4" ...
## $ center : Named num [1:7] 55.67 5.51 15.38 307.59 15.38 ...
## ..- attr(*, "names")= chr [1:7] "Unit_price" "Quantity" "Tax" "cogs" ...
## $ scale : logi FALSE
## $ x : num [1:1000, 1:7] -313 337.2 -23.8 -229.5 -431.5 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : NULL
## .. ..$ : chr [1:7] "PC1" "PC2" "PC3" "PC4" ...
## - attr(*, "class")= chr "prcomp"
# Installing our ggbiplot visualisation package
#
library(devtools)## Loading required package: usethis
Sys.setenv(R_REMOTES_NO_ERRORS_FROM_WARNINGS="true")
#install_github("vqv/ggbiplot",force=TRUE)
library(ggbiplot)## Loading required package: plyr
## ------------------------------------------------------------------------------
## You have loaded plyr after dplyr - this is likely to cause problems.
## If you need functions from both plyr and dplyr, please load plyr first, then dplyr:
## library(plyr); library(dplyr)
## ------------------------------------------------------------------------------
##
## Attaching package: 'plyr'
## The following objects are masked from 'package:dplyr':
##
## arrange, count, desc, failwith, id, mutate, rename, summarise,
## summarize
## The following objects are masked from 'package:plotly':
##
## arrange, mutate, rename, summarise
## Loading required package: scales
##
## Attaching package: 'scales'
## The following objects are masked from 'package:psych':
##
## alpha, rescale
ggbiplot(df3)
# Adding more detail to the plot, we provide arguments rownames as labels
#
ggbiplot(df3, labels=rownames(df), obs.scale = 1, var.scale = 1)