1 Assignment Overview

1.1 Background

Understanding customer behavior and purchasing patterns is vital for online businesses. Your objective is to analyze transaction data from an online retailer to uncover sales trends, customer segments, and potential improvements.

1.2 Data Description

The dataset captures transactions from December 2010 to December 2011 from a UK-based online retailer:

InvoiceNo - Invoice number (6-digit). If starts with ‘c’, indicates a cancellation
StockCode - Product code (5-digit, unique per product)
Description - Product name
Quantity - Quantities per transaction
InvoiceDate - Transaction date and time
UnitPrice - Product price per unit (£)
CustomerID - Customer identifier (5-digit)
Country - Customer’s country

UCI Machine Learning Repository

2 Part 1: Data Exploration with R (70% of total marks)

2.1 Task

Explore the dataset and address these questions:

What are the most popular products and how do sales vary over time?
Can we segment customers based on their purchasing behavior?
Are there specific countries that contribute more to sales or have unique patterns?
(Bonus) How do cancellations impact overall sales trends?

AI-Assisted Analysis

For this assignment, you’re encouraged to use generative AI tools (ChatGPT, Claude, etc.) to assist your coding. Be careful to remember rules we’vd learned about responsible use of AI generated content. When you use AI:

Mark the section clearly with ### AI-Assisted
Briefly note what you asked for and what you learned (2-3 sentences)
Include at least 2 examples where AI helped you

2.2 Submission Requirements

The RMD file with all code and answers
Knitted HTML version

Ensure your report:

Has clear structure and navigation
Includes well-labeled visualisations
Provides concise answers to the exploratory questions
Contains efficient, readable R code using %>% pipes where appropriate
Documents AI usage where relevant

3 Part 2: Tableau Dashboard (30% of total marks)

3.1 Task

Create a simple, single-page dashboard in Tableau that shows 2-3 key findings for the CEO (a non-technical audience).

Focus on:

Clear, easy-to-understand visualisations
1-2 interactive filters (e.g., date range, country)
Brief text annotations explaining any key navigation

Not required: Multiple tabs, complex calculations, or recreating all R analysis

3.2 Submission

Tableau Packaged Workbook (.twbx file) - THIS IS CRITICAL! DO NOT export standard .twb file. It MUST be a full packaged .twbx, otherwise your submission cannot be opened.
Screenshot image of your dashboard (as a backup)
Brief paragraph (3-4 sentences) at the end of your RMD report that describes: (1) the focus/story of your dashboard, (2) which 2-3 insights you chose to visualize, and (3) why these are important for business decision-making

4 Start Your Work Below

4.1 Data Import & Setup

# Add other packages as needed
library(tidyverse)
library(lubridate)
library(readxl)
#install.packages("xray")
library(xray)
#install.packages("dlookr")
library(dlookr)
library(ggplot2)
#install.packages("viridis")
library(viridis)
library(scales)
library(tidyr)

# Load your data here
retail_data<-read_excel("Online Retail.xlsx")

4.2 Data Diagnostics

# Quick overview
cat("Dataset dimensions:", nrow(retail_data), "sales record ×", ncol(retail_data), "variables\n\n")

## Dataset dimensions: 541909 sales record × 8 variables

glimpse(retail_data)

## Rows: 541,909
## Columns: 8
## $ InvoiceNo   <chr> "536365", "536365", "536365", "536365", "536365", "536365"…
## $ StockCode   <chr> "85123A", "71053", "84406B", "84029G", "84029E", "22752", …
## $ Description <chr> "WHITE HANGING HEART T-LIGHT HOLDER", "WHITE METAL LANTERN…
## $ Quantity    <dbl> 6, 6, 8, 6, 6, 2, 6, 6, 6, 32, 6, 6, 8, 6, 6, 3, 2, 3, 3, …
## $ InvoiceDate <dttm> 2010-12-01 08:26:00, 2010-12-01 08:26:00, 2010-12-01 08:2…
## $ UnitPrice   <dbl> 2.55, 3.39, 2.75, 3.39, 3.39, 7.65, 4.25, 1.85, 1.85, 1.69…
## $ CustomerID  <dbl> 17850, 17850, 17850, 17850, 17850, 17850, 17850, 17850, 17…
## $ Country     <chr> "United Kingdom", "United Kingdom", "United Kingdom", "Uni…

xray::anomalies(retail_data)

## $variables
##      Variable      q    qNA    pNA qZero pZero qBlank pBlank qInf pInf
## 1  CustomerID 541909 135080 24.93%     0     -      0      -    0    -
## 2   UnitPrice 541909      0      -  2515 0.46%      0      -    0    -
## 3 Description 541909   1454  0.27%     0     -      0      -    0    -
## 4     Country 541909      0      -     0     -      0      -    0    -
## 5    Quantity 541909      0      -     0     -      0      -    0    -
## 6   StockCode 541909      0      -     0     -      0      -    0    -
## 7 InvoiceDate 541909      0      -     0     -      0      -    0    -
## 8   InvoiceNo 541909      0      -     0     -      0      -    0    -
##   qDistinct      type anomalous_percent
## 1      4373   Numeric            24.93%
## 2      1630   Numeric             0.46%
## 3      4212 Character             0.27%
## 4        38 Character                 -
## 5       722   Numeric                 -
## 6      4070 Character                 -
## 7     23260 Timestamp                 -
## 8     25900 Character                 -
## 
## $problem_variables
##  [1] Variable          q                 qNA               pNA              
##  [5] qZero             pZero             qBlank            pBlank           
##  [9] qInf              pInf              qDistinct         type             
## [13] anomalous_percent problems         
## <0 rows> (or 0-length row.names)

diagnose(retail_data)%>% 
  arrange(desc(missing_count)) %>%
  select(variables, types, missing_count, missing_percent, unique_count) %>%
  knitr::kable(caption = "Data Quality Overview")

Data Quality Overview
variables	types	missing_count	missing_percent	unique_count
CustomerID	numeric	135080	24.9266943	4373
Description	character	1454	0.2683107	4212
InvoiceNo	character	0	0.0000000	25900
StockCode	character	0	0.0000000	4070
Quantity	numeric	0	0.0000000	722
InvoiceDate	POSIXct	0	0.0000000	23260
UnitPrice	numeric	0	0.0000000	1630
Country	character	0	0.0000000	38

# Numeric variable diagnosis
diagnose_numeric(retail_data) %>%
  select(variables, min, mean, median, max, zero, minus) %>%
  knitr::kable(caption = "Numeric Variables Summary")

Numeric Variables Summary
variables	min	mean	median	max	zero	minus
Quantity	-80995.00	9.552250	3.00	80995	0	10624
UnitPrice	-11062.06	4.611114	2.08	38970	2515	2
CustomerID	12346.00	15287.690570	15152.00	18287	0	0

# Check outliers
diagnose_outlier(retail_data) %>%
  filter(outliers_cnt > 0) %>%
  arrange(desc(outliers_ratio)) %>%
  knitr::kable(caption = "Variables with Outliers")

Variables with Outliers
variables	outliers_cnt	outliers_ratio	outliers_mean	with_mean	without_mean
Quantity	58619	10.817130	50.59097	9.552250	4.574599
UnitPrice	39627	7.312482	31.08475	4.611114	2.522504

key observation: the dataset provide 541,909 rows data with 8 columns of online retail order between 2010-01-12 and 2011-12-09. CustomerID has a large missing data(24.93%), which means these data can’t match with people who purchased. It may cause by purchasing without logging in the website. UnitPrice contains 0.46% of zero data, which is likely an error recording or special transaction case like free gift. Product description has small amount of missing value(0.27%), which we can’t know what product did consumers purchase. All other fields are complete and show no NA, blank or infinit values.

4.3 Data Preparation

# Fill null CustomerID as unknown. Keep all data first without increasing bias
retail_data$CustomerID <- ifelse(is.na(retail_data$CustomerID), "Unknown", retail_data$CustomerID)

# Fill null Description as Missing.
retail_data$Description <- ifelse(is.na(retail_data$Description), "Missing", retail_data$Description)

# When quantity < 0 might be customer return, adding new column to record. 
retail_data <- retail_data%>%
  mutate(Return = Quantity < 0)
# Unitprice = 0 can be seen as irrational trading(Error Recording, Free Gifts...). Remove from the dataset
retail_data <- retail_data%>%
  filter(UnitPrice > 0)

# Check data type of InvoiceDate (Double)
# Separate date data to assist in subsequent analysis.
typeof(retail_data$InvoiceDate)

## [1] "double"

retail_data$InvoiceDate <-as.POSIXct(retail_data$InvoiceDate)
class(retail_data$InvoiceDate)

## [1] "POSIXct" "POSIXt"

retail_data <- retail_data%>%
  mutate(
    Year = year(InvoiceDate),
    Month = month(InvoiceDate),
    Day = day(InvoiceDate),
    Weekday = weekdays(InvoiceDate),
    Hour = hour(InvoiceDate)
  )

# Remove repeat data
retail_data <- retail_data %>% distinct()

# Add new column TotalAmount, which represent the amount of each sale. Negative numbers represent refund amounts.
retail_data <- retail_data %>% 
    mutate(TotalAmount = Quantity * UnitPrice)

key observation: Based on the previous step of data diagnose, it is clear that we should deal with the missing value of CustomerID and description for the further analysis. The missing rate of CustomerID is high and requires different handling depending on different analytical object. When doing customer segmentation analysis, we should remove missing data in CustomerID. However, when doing product or transaction analysis, we can still keep these data. Therefore, in the first stage of data preparation we can use “unknown” to replace those NA values in CustomerID.Also, Using “missing” to replace those NA values in Description. From the dataset, there are some data with quantity < 0, which might be customer return. As a result, we create a new column to mark it as “Return”. Those data with price = 0 are not a normal trading situation, so we only keep data with price > 0 to prevent price = 0 and price < 0. Transeform class of InvoiceDate into POSIxct and create new columns to store year, month, day, weekday, and hour data for the later analysis. Due to the dataset is related with online purchase record, we can calculate each order’s total amount of money and store in a new column called “TotalAmount”. Function distinct() is used to remove repeat data.

4.4 Question 1: Most popular products and sales over time

# Find out the top10 popular product
top_product <- retail_data%>%
  group_by(Description)%>%
  summarise(TotalQuantity = sum(Quantity))%>%
  arrange(desc(TotalQuantity))%>%
  head(10)
top_product

## # A tibble: 10 × 2
##    Description                        TotalQuantity
##    <chr>                                      <dbl>
##  1 WORLD WAR 2 GLIDERS ASSTD DESIGNS          53751
##  2 JUMBO BAG RED RETROSPOT                    47256
##  3 POPCORN HOLDER                             36322
##  4 ASSORTED COLOUR BIRD ORNAMENT              36282
##  5 PACK OF 72 RETROSPOT CAKE CASES            36016
##  6 WHITE HANGING HEART T-LIGHT HOLDER         35294
##  7 RABBIT NIGHT LIGHT                         30631
##  8 MINI PAINT SET VINTAGE                     26437
##  9 PACK OF 12 LONDON TISSUES                  26095
## 10 PACK OF 60 PINK PAISLEY CAKE CASES         24719

# Find out the top10 best sale product
top_sales_product <- retail_data%>%
  group_by(Description)%>%
  summarise(sales = sum(TotalAmount))%>%
  arrange(desc(sales))%>%
  head(10)
top_sales_product

## # A tibble: 10 × 2
##    Description                          sales
##    <chr>                                <dbl>
##  1 DOTCOM POSTAGE                     206245.
##  2 REGENCY CAKESTAND 3 TIER           164459.
##  3 WHITE HANGING HEART T-LIGHT HOLDER  99612.
##  4 PARTY BUNTING                       98244.
##  5 JUMBO BAG RED RETROSPOT             92176.
##  6 RABBIT NIGHT LIGHT                  66662.
##  7 POSTAGE                             66231.
##  8 PAPER CHAIN KIT 50'S CHRISTMAS      63715.
##  9 ASSORTED COLOUR BIRD ORNAMENT       58792.
## 10 CHILLI LIGHTS                       53747.

# Draw a bar chart for top products, 
# Using viridis color scale was applied (scale_fill_viridis) to improve visual clarity and provide a perceptually uniform, colorblind-friendly gradient.
total <- sum(top_product$TotalQuantity)
top_product %>%
  mutate(Percent = TotalQuantity / total * 100) %>%
  ggplot(aes(x = reorder(Description, TotalQuantity),
             y = TotalQuantity,
             fill = TotalQuantity)) +
  geom_col() +
  scale_fill_viridis(option = "plasma", direction = -1) +
  geom_text(aes(label = paste0(round(Percent, 1), "%")),
            hjust = -0.05, size = 3) +
  coord_flip() +
  labs(title = "Top 10 Products by Quantity (with %)",
       x = "Product",
       y = "Quantity Sold",
       fill = "Qty") +
  theme_bw()

# Draw a bar chart for top_sales_product
top_sales_product %>%
  ggplot(aes(x = reorder(Description, sales),
             y = sales,
             fill = sales)) +
  geom_col() +
  scale_fill_viridis(option = "plasma", direction = -1) +
  coord_flip() +
  labs(title = "Top 10 Products by Sales (with %)",
       x = "Product",
       y = "Sales",
       fill = "sales") +
  theme_bw()

# Observe the difference and same elements in two sets, top_product and top_sales_product.
setdiff(top_product$Description,top_sales_product$Description)

## [1] "WORLD WAR 2 GLIDERS ASSTD DESIGNS"  "POPCORN HOLDER"                    
## [3] "PACK OF 72 RETROSPOT CAKE CASES"    "MINI PAINT SET VINTAGE"            
## [5] "PACK OF 12 LONDON TISSUES"          "PACK OF 60 PINK PAISLEY CAKE CASES"

setdiff(top_sales_product$Description,top_product$Description)

## [1] "DOTCOM POSTAGE"                 "REGENCY CAKESTAND 3 TIER"      
## [3] "PARTY BUNTING"                  "POSTAGE"                       
## [5] "PAPER CHAIN KIT 50'S CHRISTMAS" "CHILLI LIGHTS"

intersect(top_product$Description,top_sales_product$Description)

## [1] "JUMBO BAG RED RETROSPOT"            "ASSORTED COLOUR BIRD ORNAMENT"     
## [3] "WHITE HANGING HEART T-LIGHT HOLDER" "RABBIT NIGHT LIGHT"

# Having the whole picture of all products' total quantity and total revunue
product_compare <- retail_data %>%
  group_by(Description) %>%
  summarise(
    TotalQuantity = sum(Quantity),
    TotalRevenue = sum(TotalAmount)
  )
product_compare

## # A tibble: 4,031 × 3
##    Description                      TotalQuantity TotalRevenue
##    <chr>                                    <dbl>        <dbl>
##  1 *Boombox Ipod Classic                        1         17.0
##  2 *USB Office Mirror Ball                      2         16.9
##  3 10 COLOUR SPACEBOY PEN                    6392       5439. 
##  4 12 COLOURED PARTY BALLOONS                2114       1386. 
##  5 12 DAISY PEGS IN WOOD BOX                  344        593. 
##  6 12 EGG HOUSE PAINTED WOOD                  148       2366. 
##  7 12 HANGING EGGS HAND PAINTED                40         83.2
##  8 12 IVORY ROSE PEG PLACE SETTINGS           968       1477. 
##  9 12 MESSAGE CARDS WITH ENVELOPES           1732       2946. 
## 10 12 PENCIL SMALL TUBE WOODLAND             4493       3208. 
## # ℹ 4,021 more rows

# Make the scatter plot prettier, using ggplot2 and scales
ggplot(product_compare, aes(x = TotalQuantity, y = TotalRevenue)) +
  geom_point(color = "#2C3E50", alpha = 0.5, size = 2) +
  geom_text(
    data = product_compare %>% 
      filter(Description %in% top_product$Description |
             Description %in% top_sales_product$Description),
    aes(label = Description),
    size = 3,
    vjust = -0.8,
    color = "black"
  ) +
  scale_y_continuous(labels = label_number(prefix = "£")) + 
  scale_x_continuous(labels = label_number()) +
  labs(
    title = "Quantity vs Revenue: Product Performance",
    x = "Total Quantity Sold",
    y = "Total Revenue"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    plot.title = element_text(face = "bold", size = 18),
    panel.grid.minor = element_blank(),
    panel.grid.major = element_line(color = "#dddddd")
  )

key observation: The comparison between quantity based and sales based top products reveals clear differences in product performance. While high sales items such as “DOTCOM POSTAGE”,“REGENCY CAKESTAND 3 TIER” generate substantial income, many of them are not among the top sellers by volume, suggesting they are high priced, infrequently purchased items. In contrast, the most frequently purchased products: “WORLD WAR 2 GLIDERS ASSTD DESIGNS”, “POPCORN HOLDER” are low priced, fast-moving goods that sell in large quantities but contribute less to total sales. The scatter plot highlights this pattern clearly: most products cluster at low quantity and low sales, while a small number of high value dominate sales. Overall, it shows strong revenue concentration, with a few key items driving profitability, while high volume items contribute more to customer engagement rather than profitability.

4.4.1 AI-Assisted

[If you used AI here: briefly describe what you asked and what you learned] I drew a basic bar chart and scatter chart and asked chatgpt how could I improve my chart. I learned how to use the package of viridis and scales to improve my chart and add more information inside a chart like the item names and better format of scatter plot and the color change in bar chart.

4.5 Question 2: Customer segmentation

retail_clean <- retail_data %>%
  filter(CustomerID != "Unknown")
retail_clean

## # A tibble: 401,564 × 15
##    InvoiceNo StockCode Description        Quantity InvoiceDate         UnitPrice
##    <chr>     <chr>     <chr>                 <dbl> <dttm>                  <dbl>
##  1 536365    85123A    WHITE HANGING HEA…        6 2010-12-01 08:26:00      2.55
##  2 536365    71053     WHITE METAL LANTE…        6 2010-12-01 08:26:00      3.39
##  3 536365    84406B    CREAM CUPID HEART…        8 2010-12-01 08:26:00      2.75
##  4 536365    84029G    KNITTED UNION FLA…        6 2010-12-01 08:26:00      3.39
##  5 536365    84029E    RED WOOLLY HOTTIE…        6 2010-12-01 08:26:00      3.39
##  6 536365    22752     SET 7 BABUSHKA NE…        2 2010-12-01 08:26:00      7.65
##  7 536365    21730     GLASS STAR FROSTE…        6 2010-12-01 08:26:00      4.25
##  8 536366    22633     HAND WARMER UNION…        6 2010-12-01 08:28:00      1.85
##  9 536366    22632     HAND WARMER RED P…        6 2010-12-01 08:28:00      1.85
## 10 536367    84879     ASSORTED COLOUR B…       32 2010-12-01 08:34:00      1.69
## # ℹ 401,554 more rows
## # ℹ 9 more variables: CustomerID <chr>, Country <chr>, Return <lgl>,
## #   Year <dbl>, Month <dbl>, Day <int>, Weekday <chr>, Hour <int>,
## #   TotalAmount <dbl>

# RFM 
# Lower recency → More recent purchases → More active customers
# Higher recency → Longer inactivity → Potential customer churn
# Frequency: Multiple orders → Customer loyalty
#            One purchase → May be a one-time user
# Monetary: High → High-value clients, otherwise
analysis_date <- max(retail_clean$InvoiceDate, na.rm = TRUE) + 1
analysis_date

## [1] "2011-12-09 12:50:01 UTC"

rfm_data <- retail_clean %>%
  group_by(CustomerID) %>%
  summarise(
    Recency = as.numeric(analysis_date - max(InvoiceDate)),
    Frequency = n_distinct(InvoiceNo),
    Monetary = sum(TotalAmount)
  )

# Standardization: Because the monetary amount is usually large,the frequency is small,the recency may be 0~1000.To prevent the monetary amount from dominating all calculations.
rfm_scaled <- scale(rfm_data %>% select(Recency, Frequency, Monetary))
rfm_scaled

##               Recency   Frequency      Monetary
##    [1,]  2.320645e+00 -0.32957052 -2.304209e-01
##    [2,] -8.973273e-01  0.20618995  2.939364e-01
##    [3,] -1.694697e-01 -0.11526633 -1.176758e-02
##    [4,] -7.355420e-01 -0.43672261 -1.659629e-02
##    [5,]  2.168933e+00 -0.43672261 -1.897376e-01
##    [6,] -5.583186e-01  0.63479832 -4.240537e-02
##    [7,]  1.112907e+00 -0.43672261 -2.195931e-01
##    [8,]  1.393572e+00 -0.43672261 -9.910044e-02
##    [9,]  1.214109e+00 -0.43672261 -1.745300e-01
##   [10,] -6.952288e-01 -0.22241843  1.116194e-01
##   [11,] -5.888076e-01 -0.43672261  5.248081e-01
##   [12,] -9.050290e-01 -0.32957052 -8.831401e-02
##   [13,] -8.456757e-01  0.09903785  5.218043e-01
##   [14,] -3.993402e-01 -0.22241843  9.344696e-02
##   [15,]  1.940853e+00 -0.43672261 -2.073176e-01
##   [16,] -8.872887e-01  0.84910250  3.966885e-01
##   [17,]  1.702303e-01 -0.32957052 -1.632642e-01
##   [18,] -8.452678e-01 -0.11526633 -7.066835e-02
##   [19,]  1.980586e+00 -0.22241843 -1.914056e-01
##   [20,] -8.778033e-01 -0.43672261 -2.098724e-01
##   [21,] -4.090815e-01 -0.11526633  2.004937e-01
##   [22,] -4.768694e-01 -0.32957052 -7.305277e-04
##   [23,] -2.088704e-01 -0.22241843 -7.250056e-02
##   [24,]  2.180071e+00 -0.43672261 -1.860634e-01
##   [25,] -6.682449e-01 -0.43672261 -1.400356e-01
##   [26,] -8.954952e-01 -0.22241843 -1.750142e-01
##   [27,]  2.218822e+00 -0.32957052 -3.234282e-02
##   [28,]  3.692315e-01 -0.43672261  2.572703e-01
##   [29,] -1.084641e-01 -0.22241843 -1.269741e-01
##   [30,] -7.063389e-01 -0.00811424  1.005641e-01
##   [31,] -8.761163e-01  0.09903785 -1.095002e-02
##   [32,]  9.178400e-01  0.09903785 -6.649317e-03
##   [33,] -6.354883e-01 -0.22241843 -1.615415e-01
##   [34,]  2.439144e+00 -0.32957052 -1.815255e-01
##   [35,] -7.665080e-01  0.09903785  1.078759e-01
##   [36,] -1.281264e-01 -0.43672261 -1.635270e-01
##   [37,] -7.066155e-01 -0.43672261 -1.769316e-01
##   [38,] -2.003597e-01 -0.11526633 -3.788081e-02
##   [39,] -2.868282e-01 -0.32957052 -7.561021e-02
##   [40,] -7.664389e-01  1.06340669  1.343517e-01
##   [41,] -5.663038e-01 -0.32957052  6.276902e-02
##   [42,] -4.669899e-01 -0.43672261 -3.142550e-02
##   [43,]  2.685625e-01 -0.11526633 -9.554187e-02
##   [44,]  2.100150e+00 -0.43672261 -2.201649e-01
##   [45,]  2.299268e+00 -0.43672261 -2.029743e-01
##   [46,] -4.273957e-01 -0.32957052 -1.805766e-01
##   [47,]  5.590930e-01 -0.43672261 -2.233380e-02
##   [48,] -6.996673e-01 -0.22241843  1.687172e-01
##   [49,] -4.270569e-01 -0.00811424 -2.260997e-02
##   [50,] -5.972630e-01  0.42049413  1.154079e-01
##   [51,] -1.385314e-01  0.20618995  1.114772e+00
##   [52,]  2.079430e+00 -0.22241843 -1.475603e-01
##   [53,] -1.782016e-01 -0.22241843 -8.115793e-02
##   [54,] -2.573209e-01 -0.00811424 -1.459702e-01
##   [55,]  1.243547e+00 -0.22241843 -1.619978e-01
##   [56,] -6.776820e-01  2.24207971  1.482209e+01
##   [57,] -8.869569e-01  0.74195041  2.049781e-01
##   [58,]  1.997514e-01 -0.43672261 -1.490811e-01
##   [59,] -2.871532e-01 -0.43672261 -1.573771e-01
##   [60,] -7.651046e-01 -0.00811424 -1.323296e-01
##   [61,]  3.105940e-02 -0.22241843 -1.326593e-01
##   [62,] -8.894293e-01  0.42049413 -5.457043e-03
##   [63,]  6.971300e-01 -0.32957052 -1.618143e-02
##   [64,] -1.413867e-01 -0.43672261 -1.358663e-01
##   [65,]  1.015571e+00 -0.43672261 -1.595256e-01
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## [1855,] -7.958770e-01 -0.00811424 -6.593089e-02
## [1856,] -8.350495e-01 -0.32957052 -2.099065e-01
## [1857,] -3.983170e-01 -0.43672261 -2.151172e-01
## [1858,] -6.659220e-01 -0.32957052 -1.280800e-01
## [1859,] -6.281944e-01 -0.43672261 -1.979667e-01
## [1860,] -8.477775e-01 -0.32957052 -2.240702e-01
## [1861,] -8.159749e-01  0.84910250  1.496850e+00
## [1862,]  9.262953e-01 -0.11526633 -1.450967e-01
## [1863,] -8.869361e-01  0.42049413  1.272175e-01
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## [1865,]  1.683252e+00 -0.43672261 -1.906075e-01
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## [1867,]  1.174266e+00 -0.43672261 -1.671963e-01
## [1868,] -8.271473e-01 -0.00811424 -5.416874e-02
## [1869,] -7.958563e-01  0.42049413 -5.083889e-02
## [1870,] -1.497591e-01 -0.22241843 -1.464033e-01
## [1871,] -7.261049e-01 -0.43672261 -1.993488e-01
## [1872,] -6.571140e-01 -0.32957052 -1.586776e-01
## [1873,] -7.357632e-01  0.20618995 -1.383676e-01
## [1874,]  3.885136e-01 -0.43672261 -1.373116e-01
## [1875,]  1.594447e+00 -0.43672261 -1.860391e-01
## [1876,] -1.306084e-01 -0.43672261 -3.888837e-03
## [1877,]  1.143943e+00 -0.43672261 -1.855038e-01
## [1878,]  2.428069e+00 -0.43672261 -2.138872e-01
## [1879,]  1.603151e+00 -0.43672261 -2.151343e-01
## [1880,]  5.552490e-01 -0.32957052 -1.629747e-01
## [1881,] -8.262485e-01 -0.32957052 -7.982331e-02
## [1882,] -7.017654e-02 -0.43672261 -1.506420e-01
## [1883,] -8.448599e-01  2.02777553  1.110311e+00
## [1884,]  1.115998e+00 -0.32957052 -1.733901e-01
## [1885,] -8.453370e-01 -0.11526633 -6.418627e-02
## [1886,] -6.878588e-01  0.31334204 -8.514475e-02
## [1887,] -8.082593e-01  0.52764623 -5.827235e-02
## [1888,] -7.087034e-01 -0.32957052 -1.922061e-01
## [1889,] -7.082747e-01  0.52764623  1.016128e-01
## [1890,] -8.961036e-01 -0.32957052 -1.056652e-01
## [1891,]  6.168631e-01 -0.22241843 -1.574367e-01
## [1892,] -8.866942e-01  0.52764623  1.928181e-01
## [1893,] -1.793078e-01 -0.43672261 -1.966236e-01
## [1894,] -8.949352e-01  0.20618995 -1.829903e-01
## [1895,] -7.075738e-01 26.02984436  1.588459e+01
## [1896,] -7.565455e-01 -0.22241843 -1.280411e-01
## [1897,] -5.657300e-01 -0.11526633 -8.109102e-02
## [1898,] -6.876616e-02 -0.22241843 -1.989315e-01
## [1899,] -2.176368e-01 -0.00811424 -7.653969e-02
## [1900,]  2.293278e-01 -0.32957052 -3.452906e-02
## [1901,]  1.195560e+00 -0.32957052 -1.114648e-01
## [1902,] -6.174991e-01 -0.32957052 -7.030702e-02
## [1903,] -4.177927e-01 -0.43672261 -1.392849e-01
## [1904,]  1.524557e+00 -0.43672261 -1.927000e-01
## [1905,] -5.992748e-01 -0.43672261 -2.031835e-01
## [1906,]  1.601848e-01 -0.22241843  5.705827e-02
## [1907,] -8.751139e-01  0.09903785 -1.130573e-01
## [1908,]  2.718240e+00 -0.43672261 -1.861936e-01
## [1909,] -1.978985e-01 -0.22241843 -6.234664e-04
## [1910,]  2.040043e+00 -0.43672261 -1.329199e-02
## [1911,] -8.273270e-01  0.42049413  7.571494e-01
## [1912,] -3.583218e-01 -0.11526633 -3.361904e-02
## [1913,] -6.257470e-01  0.95625460  4.804360e-01
## [1914,] -7.768992e-01 -0.43672261 -2.181454e-01
## [1915,] -2.004081e-01 -0.32957052 -1.950396e-01
## [1916,] -6.888406e-01  0.20618995 -1.006613e-01
## [1917,] -8.350357e-01 -0.32957052 -1.864710e-01
## [1918,] -1.304908e-01 -0.43672261 -1.925005e-01
## [1919,] -4.584377e-01  1.06340669  7.322540e-01
## [1920,] -6.679822e-01 -0.43672261 -1.956661e-01
## [1921,] -7.972044e-01 -0.43672261 -1.945493e-01
## [1922,]  1.600648e+00 -0.43672261 -2.233050e-01
## [1923,]  5.468697e-01 -0.22241843 -1.715700e-01
## [1924,] -3.301074e-01 -0.00811424 -1.470870e-01
## [1925,] -8.363631e-01 -0.32957052 -2.035011e-01
## [1926,] -8.151245e-01  0.74195041  6.220040e-01
## [1927,]  1.773330e+00 -0.43672261 -2.150065e-01
## [1928,] -8.261448e-01 -0.00811424 -5.129511e-02
## [1929,]  1.542477e+00 -0.43672261 -2.053333e-01
## [1930,]  3.954930e-02 -0.32957052 -1.579002e-01
## [1931,] -7.763945e-01 -0.43672261 -2.081546e-01
## [1932,] -4.274371e-01 -0.43672261 -1.739947e-01
## [1933,] -6.177825e-01 -0.43672261 -2.124650e-01
## [1934,] -2.393732e-01 -0.11526633 -3.672991e-02
## [1935,] -5.693112e-01 -0.22241843 -9.683998e-02
## [1936,]  3.574784e-01 -0.43672261 -2.164579e-01
## [1937,]  1.480169e-01 -0.22241843 -7.050411e-02
## [1938,] -5.476993e-01 -0.43672261 -2.194788e-01
## [1939,] -3.490507e-01 -0.43672261 -1.963632e-01
## [1940,] -3.500808e-01  0.31334204 -1.372459e-01
## [1941,] -1.992950e-01 -0.00811424  3.334154e-03
## [1942,]  1.532715e+00 -0.43672261 -2.179969e-01
## [1943,] -7.275015e-01 -0.32957052 -2.058005e-01
## [1944,]  1.054543e+00 -0.32957052 -1.948948e-01
## [1945,] -7.654641e-01 -0.32957052 -1.907109e-01
## [1946,]  1.184961e+00 -0.43672261 -1.897206e-01
## [1947,] -5.371768e-01 -0.32957052 -2.021981e-01
## [1948,] -4.582856e-01 -0.11526633 -1.646049e-01
## [1949,]  7.745348e-01 -0.32957052 -1.799476e-01
## [1950,] -4.475972e-01 -0.43672261 -1.707439e-01
## [1951,]  2.297841e-01 -0.11526633 -3.068337e-02
## [1952,]  5.469734e-01 -0.43672261 -8.190128e-02
## [1953,] -7.664735e-01  3.20644855  5.190742e-01
## [1954,] -4.091990e-01 -0.43672261 -1.719776e-01
## [1955,]  6.656455e-01 -0.43672261 -2.113311e-01
## [1956,] -7.968242e-01 -0.22241843 -7.719788e-02
## [1957,] -5.674791e-01 -0.43672261 -1.928351e-01
## [1958,] -3.881402e-01 -0.32957052 -1.811435e-01
## [1959,] -4.909110e-01 -0.32957052 -1.990726e-01
## [1960,]  7.966860e-01 -0.43672261 -2.097337e-01
## [1961,] -5.864985e-01 -0.43672261 -2.151428e-01
## [1962,] -5.376469e-01 -0.11526633 -1.749120e-01
## [1963,]  1.732311e+00 -0.43672261 -1.996639e-01
## [1964,] -8.359414e-01  0.84910250 -7.875656e-03
## [1965,] -8.063650e-01 -0.11526633 -1.267186e-01
## [1966,] -8.880008e-01  0.74195041  5.823706e-01
## [1967,] -8.260757e-01  0.52764623 -3.133182e-02
## [1968,] -5.884827e-01 -0.43672261 -1.863846e-01
## [1969,] -1.199614e-01 -0.22241843 -1.733621e-01
## [1970,] -6.162477e-01  0.09903785 -1.024400e-01
## [1971,] -8.368609e-01 -0.11526633 -1.541239e-01
## [1972,] -2.083035e-01 -0.32957052 -1.673666e-01
## [1973,] -8.767731e-01 -0.11526633 -1.509534e-01
## [1974,]  1.631545e+00 -0.00811424  3.126843e-01
## [1975,] -8.760887e-01  0.63479832  7.878320e-02
## [1976,] -7.663767e-01  0.63479832  2.858106e-01
## [1977,] -2.922725e-02 -0.43672261 -1.996736e-01
## [1978,] -2.003667e-01 -0.22241843 -1.781604e-01
## [1979,] -4.886640e-01  0.20618995 -1.518476e-01
## [1980,] -8.258337e-01  5.02803413  2.158822e+00
## [1981,]  7.750464e-01 -0.43672261 -2.085305e-01
## [1982,]  1.063696e+00 -0.43672261 -2.138836e-01
## [1983,] -6.080205e-01 -0.43672261 -1.650892e-01
## [1984,] -7.270313e-01  1.81347134  6.898054e-01
## [1985,]  5.878467e-01 -0.22241843 -1.533294e-01
## [1986,] -8.276243e-01  1.17055878  3.706628e-01
## [1987,]  1.762911e+00 -0.43672261 -1.886159e-01
## [1988,] -2.697309e-01 -0.00811424 -1.844916e-01
## [1989,]  1.802152e+00 -0.43672261 -2.156793e-01
## [1990,] -6.685215e-01 -0.00811424 -2.569407e-02
## [1991,] -6.881630e-01 -0.22241843 -6.212048e-02
## [1992,]  2.258596e+00 -0.43672261 -2.051484e-01
## [1993,] -8.758675e-01 -0.22241843 -1.459945e-01
## [1994,] -7.974257e-01 -0.32957052 -1.936672e-01
## [1995,]  1.820792e+00 -0.32957052 -4.920742e-02
## [1996,] -6.679684e-01  0.63479832  2.537541e-02
## [1997,] -5.172380e-01  0.63479832 -6.912083e-02
## [1998,] -8.367295e-01 -0.11526633 -1.946223e-01
## [1999,] -8.858092e-01  5.34949041  6.367081e+00
## [2000,] -2.107993e-01 -0.11526633 -1.102373e-01
## [2001,]  1.204319e+00 -0.43672261 -1.853092e-01
## [2002,] -5.463442e-01  0.09903785  1.511044e-01
## [2003,] -6.061539e-01 -0.32957052 -1.378871e-01
## [2004,] -1.396514e-01 -0.22241843 -1.815233e-02
## [2005,] -4.588318e-01 -0.32957052 -1.630988e-01
## [2006,]  8.654763e-01 -0.43672261 -9.543480e-02
## [2007,]  2.788102e+00 -0.43672261 -2.175006e-01
## [2008,]  1.035314e-02 -0.32957052 -1.109417e-01
## [2009,] -8.255087e-01 -0.11526633 -1.559123e-01
## [2010,]  1.285620e-01 -0.43672261 -1.409188e-01
## [2011,] -1.492405e-01 -0.43672261 -1.363736e-01
## [2012,]  7.982277e-01 -0.43672261 -1.232562e-01
## [2013,] -8.474733e-01  3.52790483  9.403618e-01
## [2014,]  1.194640e+00 -0.00811424 -1.216977e-01
## [2015,] -6.987409e-01  0.09903785 -1.711296e-01
## [2016,]  1.632873e+00 -0.43672261 -2.196904e-01
## [2017,]  1.882482e+00 -0.43672261 -1.930784e-01
## [2018,] -7.070787e-01 -0.22241843 -9.169496e-02
## [2019,] -8.179522e-01  0.09903785  6.409998e-02
## [2020,]  2.149838e+00 -0.43672261 -1.840293e-01
## [2021,] -3.874834e-01 -0.32957052 -1.723937e-01
## [2022,]  1.223919e+00 -0.32957052 -1.747235e-01
## [2023,] -7.369109e-01  0.42049413  3.061195e-01
## [2024,]  1.097846e-01 -0.00811424 -6.439066e-02
## [2025,] -4.968567e-01 -0.43672261 -2.037298e-01
## [2026,] -8.766625e-01 -0.43672261 -2.002393e-01
## [2027,]  8.947693e-01 -0.00811424 -1.514023e-01
## [2028,] -7.986941e-02 -0.43672261 -1.804817e-01
## [2029,]  2.367575e+00  0.09903785 -1.531543e-01
## [2030,] -8.352846e-01 -0.22241843 -1.927025e-01
## [2031,] -6.082072e-01 -0.32957052 -1.448497e-01
## [2032,]  7.371667e-01 -0.22241843 -1.125756e-01
## [2033,] -7.384664e-01  0.20618995  4.926834e-02
## [2034,] -7.452556e-01  0.20618995 -5.915561e-02
## [2035,]  2.179407e+00  0.31334204 -2.002904e-01
## [2036,]  4.887678e-01 -0.00811424 -7.326581e-02
## [2037,]  1.474586e+00 -0.32957052 -1.740008e-01
## [2038,] -6.863517e-01  0.20618995 -1.120208e-01
## [2039,] -6.289826e-01 -0.22241843 -3.972032e-02
## [2040,] -8.245339e-01 -0.11526633  1.758659e-01
## [2041,] -6.182457e-01  0.52764623  1.054305e-01
## [2042,] -7.376714e-01 -0.43672261 -1.890429e-01
## [2043,] -7.465623e-01 -0.11526633 -6.584451e-02
## [2044,] -7.746799e-01  0.09903785 -4.183113e-02
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## [2052,] -6.675536e-01  1.92062343  1.122086e+00
## [2053,] -2.678988e-01 -0.43672261 -1.809622e-01
## [2054,] -3.190871e-01  0.31334204 -5.771880e-02
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## [2078,] -4.684141e-01 -0.43672261 -1.815863e-01
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## [2090,]  1.671492e+00 -0.43672261 -2.254937e-01
## [2091,] -7.368003e-01  0.20618995  3.555354e-02
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## [2097,] -7.774868e-01 -0.32957052 -1.803685e-01
## [2098,] -9.056513e-01  1.38486297  3.377439e-01
## [2099,] -6.823530e-01  5.13518622  1.692077e+00
## [2100,]  2.692124e-01 -0.22241843 -1.033683e-01
## [2101,] -3.167987e-01 -0.43672261 -1.696733e-01
## [2102,] -8.870813e-01  1.81347134  6.846093e-01
## [2103,] -8.958616e-01 -0.43672261  2.393107e-01
## [2104,] -8.344273e-01 -0.00811424 -1.505580e-01
## [2105,] -8.399834e-04 -0.32957052 -2.068625e-01
## [2106,] -3.295820e-01 -0.11526633 -7.607008e-02
## [2107,] -1.382203e-01  0.63479832 -1.175393e-01
## [2108,] -6.651960e-01  0.09903785 -8.049631e-03
## [2109,]  2.637759e+00 -0.43672261 -1.919056e-01
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## [4158,]  1.322728e+00 -0.32957052 -2.190639e-01
## [4159,]  2.891097e-01  0.09903785 -1.542504e-01
## [4160,]  1.881680e+00 -0.43672261 -2.211625e-01
## [4161,] -1.806698e-01  0.74195041 -4.755405e-02
## [4162,] -5.489092e-01 -0.32957052 -1.841424e-01
## [4163,] -7.978405e-01 -0.32957052 -1.799159e-01
## [4164,]  2.687550e+00 -0.43672261 -2.112083e-01
## [4165,] -8.857055e-01 -0.32957052 -2.028684e-01
## [4166,] -6.886747e-01 -0.43672261 -1.763209e-01
## [4167,] -2.201050e-01  0.42049413  2.703608e-02
## [4168,]  1.423155e+00 -0.32957052 -2.009438e-01
## [4169,]  1.632811e+00 -0.43672261 -2.091546e-01
## [4170,]  2.795486e+00 -0.43672261 -2.179154e-01
## [4171,]  6.265767e-01 -0.32957052 -2.076351e-01
## [4172,] -6.383159e-01 -0.43672261 -2.106851e-01
## [4173,] -8.769805e-01 -0.43672261 -2.158180e-01
## [4174,] -5.976432e-01 -0.00811424 -5.064788e-02
## [4175,] -1.109945e-01 -0.22241843 -1.667924e-01
## [4176,]  1.572396e-01 -0.32957052 -2.155613e-01
## [4177,] -4.079684e-01 -0.43672261 -2.257431e-01
## [4178,] -5.674999e-01 -0.43672261 -1.558770e-01
## [4179,]  5.973390e-01 -0.22241843 -2.016141e-01
## [4180,]  6.058049e-02 -0.43672261 -2.163922e-01
## [4181,] -8.777272e-01 -0.22241843 -2.035704e-01
## [4182,]  2.408068e+00 -0.43672261 -2.214789e-01
## [4183,] -2.707886e-01 -0.43672261 -2.190067e-01
## [4184,] -7.067192e-01 -0.32957052 -1.794840e-01
## [4185,] -5.674584e-01 -0.22241843 -1.435686e-01
## [4186,] -5.981617e-01 -0.22241843 -1.813771e-01
## [4187,]  6.168423e-01  0.09903785 -2.219022e-01
## [4188,] -7.274462e-01 -0.32957052 -1.869637e-01
## [4189,] -8.059778e-01  1.81347134  2.653607e-01
## [4190,] -3.879120e-01 -0.43672261 -2.103408e-01
## [4191,] -6.770321e-01 -0.22241843 -1.660272e-01
## [4192,] -8.768215e-01  0.63479832  2.332056e-02
## [4193,] -4.680961e-01 -0.43672261 -2.087240e-01
## [4194,]  1.104120e+00 -0.32957052 -2.094600e-01
## [4195,]  2.657421e+00 -0.43672261 -2.213694e-01
## [4196,] -2.608538e-01 -0.32957052 -1.942792e-01
## [4197,] -8.469478e-01  0.63479832  5.882687e-01
## [4198,]  1.950560e+00 -0.43672261 -1.861790e-01
## [4199,] -8.246376e-01 -0.43672261 -2.097191e-01
## [4200,] -8.281221e-01 -0.11526633 -1.943230e-01
## [4201,] -7.062905e-01  0.52764623  2.742782e-02
## [4202,]  8.055285e-01 -0.22241843 -1.427620e-01
## [4203,]  4.065304e-01 -0.32957052 -1.313892e-01
## [4204,] -8.652343e-01  1.06340669  5.914110e-02
## [4205,] -1.704169e-01 -0.43672261 -1.917328e-01
## [4206,] -5.190562e-01 -0.43672261 -1.822032e-01
## [4207,]  1.960356e+00 -0.43672261 -2.180480e-01
## [4208,] -6.584829e-01  0.20618995  1.221781e-02
## [4209,]  1.642960e+00 -0.32957052 -1.753087e-01
## [4210,]  6.252562e-01 -0.32957052 -2.304209e-01
## [4211,]  2.184596e-01  0.84910250  2.375759e-01
## [4212,]  2.798680e+00 -0.43672261 -1.708559e-01
## [4213,] -6.880455e-01  0.95625460  7.844134e-02
## [4214,] -8.366258e-01  0.63479832  8.400001e-02
## [4215,]  1.243678e+00 -0.32957052 -1.895271e-01
## [4216,] -4.690640e-01 -0.11526633  2.091572e-01
## [4217,] -7.347884e-01 -0.32957052 -8.059586e-02
## [4218,] -5.590998e-01 -0.22241843 -1.886366e-01
## [4219,] -6.670558e-01 -0.43672261 -1.475895e-01
## [4220,] -7.571539e-01 -0.32957052 -2.197720e-01
## [4221,]  2.368349e+00 -0.32957052 -1.464812e-01
## [4222,]  1.811548e+00 -0.43672261 -2.180918e-01
## [4223,]  5.868617e-02 -0.11526633  2.282542e-01
## [4224,] -3.090416e-01 -0.43672261 -2.102216e-01
## [4225,] -8.962349e-01  0.74195041  8.725251e-01
## [4226,]  8.693879e-03 -0.00811424  2.304926e-02
## [4227,] -1.081806e-01  0.20618995  1.366657e-01
## [4228,]  2.190165e+00 -0.32957052 -1.598517e-01
## [4229,] -8.064272e-01 -0.22241843 -1.271237e-01
## [4230,] -8.456412e-01  0.20618995  9.288610e-02
## [4231,]  3.471218e-01 -0.43672261 -2.099442e-01
## [4232,] -8.067936e-01 -0.32957052 -2.033636e-01
## [4233,] -9.060220e-01  6.09955506  3.096804e+01
## [4234,] -5.481556e-01 -0.43672261 -1.386109e-01
## [4235,] -5.473052e-01 -0.43672261 -2.166149e-01
## [4236,]  2.359596e+00 -0.43672261 -1.790923e-01
## [4237,]  1.554839e+00 -0.32957052 -1.982234e-01
## [4238,] -9.055130e-01  2.77784018  7.279326e-01
## [4239,] -7.268862e-01 -0.32957052 -2.099150e-01
## [4240,] -7.972943e-01 -0.32957052 -1.875124e-01
## [4241,]  2.747809e+00 -0.43672261 -2.211358e-01
## [4242,]  1.970934e+00 -0.43672261 -2.036434e-01
## [4243,] -2.481950e-01  0.31334204 -5.971768e-02
## [4244,] -6.670696e-01 -0.43672261 -1.920187e-01
## [4245,] -8.158850e-01  2.77784018  4.468674e-01
## [4246,]  2.738075e+00 -0.43672261 -2.084368e-01
## [4247,]  1.214136e+00 -0.43672261 -2.168983e-01
## [4248,]  5.673824e-01 -0.32957052 -1.509400e-01
## [4249,] -8.364599e-01  0.09903785 -1.227612e-02
## [4250,] -6.776889e-01 -0.32957052 -1.605342e-01
## [4251,] -6.271228e-01 -0.00811424 -9.293225e-02
## [4252,] -3.184303e-01 -0.43672261 -2.059769e-01
## [4253,] -7.273425e-01 -0.22241843 -1.881949e-01
## [4254,]  1.502634e+00 -0.43672261 -2.167280e-01
## [4255,] -8.346140e-01 -0.11526633 -1.031955e-01
## [4256,]  1.183620e+00 -0.32957052 -1.433727e-01
## [4257,] -6.300473e-01 -0.00811424 -1.474593e-01
## [4258,] -2.899532e-01 -0.11526633 -1.377362e-01
## [4259,]  2.020083e+00 -0.43672261 -2.118494e-01
## [4260,] -7.481731e-01  0.31334204  7.907034e-01
## [4261,]  2.668731e+00 -0.43672261 -2.347277e-01
## [4262,]  5.870101e-01 -0.11526633 -1.069475e-01
## [4263,]  2.391659e-01 -0.32957052 -1.087408e-01
## [4264,] -8.462634e-01  0.74195041  1.210262e-01
## [4265,] -7.959047e-01 -0.11526633  1.177170e-01
## [4266,]  4.780932e-01 -0.32957052 -2.109126e-01
## [4267,] -4.675360e-01 -0.32957052 -2.086023e-01
## [4268,] -4.178825e-01 -0.22241843 -1.559549e-01
## [4269,] -5.990536e-01 -0.22241843 -1.614904e-01
## [4270,]  4.185878e-01 -0.32957052 -1.509339e-01
## [4271,] -8.877105e-01 -0.32957052 -1.818552e-01
## [4272,] -1.696011e-01 -0.11526633 -1.881049e-01
## [4273,] -7.963333e-01 -0.32957052 -1.482221e-01
## [4274,] -8.278248e-01 -0.22241843 -1.754607e-01
## [4275,]  2.079990e+00 -0.43672261 -1.659225e-01
## [4276,] -3.497559e-01 -0.32957052 -1.527941e-01
## [4277,] -8.175858e-01  0.09903785 -3.420788e-02
## [4278,] -6.094240e-01 -0.32957052 -1.824015e-01
## [4279,]  8.459316e-01 -0.43672261 -1.936234e-01
## [4280,] -8.848621e-01  0.09903785 -6.550872e-02
## [4281,]  8.335009e-01  0.42049413 -9.370601e-02
## [4282,] -3.184234e-01 -0.43672261 -2.057664e-01
## [4283,] -5.881716e-01 -0.22241843 -1.111558e-01
## [4284,] -3.370556e-01  0.20618995 -8.339284e-02
## [4285,] -7.759244e-01  2.13492762  6.808378e-01
## [4286,] -5.921847e-02 -0.11526633  2.589855e-02
## [4287,] -8.479918e-01 -0.43672261 -2.177682e-01
## [4288,]  2.598462e+00 -0.32957052 -1.758379e-01
## [4289,] -6.081450e-01  0.20618995 -7.060509e-02
## [4290,]  2.116013e-01  0.09903785 -3.899888e-02
## [4291,] -8.278525e-01  0.09903785 -1.226274e-02
## [4292,] -8.744225e-01  0.09903785 -6.109144e-03
## [4293,] -6.780000e-01 -0.43672261 -1.857897e-01
## [4294,]  1.252286e+00  0.09903785 -1.573613e-01
## [4295,] -7.677387e-01 -0.43672261 -2.243622e-01
## [4296,]  1.562603e+00 -0.43672261 -1.934057e-01
## [4297,] -7.682779e-01 -0.11526633  1.271662e-02
## [4298,] -1.493304e-01 -0.22241843 -9.849944e-02
## [4299,]  9.946778e-01 -0.22241843 -1.970239e-01
## [4300,]  1.682720e+00 -0.43672261 -2.051398e-01
## [4301,] -2.079094e-01 -0.43672261 -1.138737e-01
## [4302,]  5.781469e-01 -0.22241843 -2.045121e-01
## [4303,] -2.817536e-01 -0.32957052 -1.214130e-01
## [4304,]  2.833543e-02 -0.32957052 -1.468851e-01
## [4305,] -8.769805e-01  1.70631925  3.879873e-01
## [4306,]  1.368583e-01 -0.43672261 -2.121292e-01
## [4307,]  1.065445e+00 -0.22241843 -6.046224e-02
## [4308,]  6.469303e-01 -0.43672261 -2.109041e-01
## [4309,] -2.107509e-01 -0.11526633  8.149481e-03
## [4310,] -5.578001e-01 -0.32957052 -1.674786e-01
## [4311,] -6.369263e-01 -0.43672261 -2.134979e-01
## [4312,] -9.052779e-01  0.09903785  8.849780e-02
## [4313,] -6.651546e-01 -0.00811424 -1.574160e-01
## [4314,]  2.328133e+00 -0.43672261 -2.041337e-01
## [4315,]  1.434570e+00 -0.43672261 -2.021373e-01
## [4316,] -3.128059e-02 -0.43672261 -1.940030e-01
## [4317,] -6.090507e-01 -0.43672261 -1.718109e-01
## [4318,] -6.274616e-01 -0.32957052 -1.547784e-01
## [4319,]  1.134277e+00 -0.11526633 -1.566678e-01
## [4320,] -8.956058e-01  0.63479832  1.530556e-02
## [4321,]  1.264896e+00 -0.32957052 -1.941928e-01
## [4322,] -6.977177e-01  0.09903785 -1.047078e-01
## [4323,]  7.985412e-04 -0.43672261 -1.765253e-01
## [4324,] -9.056167e-01  2.34923181  5.378939e-01
## [4325,]  1.703309e+00 -0.43672261 -2.110830e-01
## [4326,] -8.863692e-01  1.27771088  4.212980e-01
## [4327,] -5.364716e-01  0.95625460  4.012532e-01
## [4328,]  1.244570e+00 -0.43672261 -2.190152e-01
## [4329,] -4.209038e-01 -0.22241843 -1.368396e-01
## [4330,] -8.052104e-01  1.59916716  6.548913e-01
## [4331,] -8.266011e-01  0.52764623  1.000823e-01
## [4332,]  9.948852e-01  0.09903785  1.955151e-02
## [4333,] -1.091555e-01 -0.00811424 -1.595573e-01
## [4334,]  2.321288e+00 -0.43672261 -1.768902e-01
## [4335,] -2.073148e-01 -0.22241843 -1.186004e-02
## [4336,] -6.253045e-01  0.09903785 -1.230870e-01
## [4337,] -8.960621e-01 -0.00811424 -1.103297e-01
## [4338,]  1.254422e+00 -0.00811424 -4.043447e-02
## [4339,] -4.581335e-01 -0.43672261 -1.790096e-01
## [4340,] -8.261033e-01  1.38486297  1.996759e-02
## [4341,] -1.995439e-01 -0.11526633  4.118521e-02
## [4342,] -8.471069e-01  0.31334204  7.465039e-02
## [4343,] -6.865798e-01 -0.32957052 -1.578990e-01
## [4344,]  2.117396e-01 -0.11526633 -1.351582e-01
## [4345,] -7.476823e-01 -0.43672261 -2.188218e-01
## [4346,]  2.080176e+00 -0.32957052 -1.887011e-01
## [4347,] -5.076313e-02 -0.43672261  2.945106e-01
## [4348,] -4.181522e-01 -0.32957052 -1.673679e-01
## [4349,] -3.011219e-02 -0.43672261 -2.178534e-01
## [4350,]  2.610118e+00 -0.43672261 -2.365161e-01
## [4351,] -5.285279e-01  0.74195041  4.518662e-02
## [4352,] -6.769354e-01 -0.22241843  5.409461e-02
## [4353,]  7.964716e-01  0.31334204  8.348174e-02
## [4354,] -4.890374e-01 -0.32957052 -1.909737e-01
## [4355,]  4.764616e-01 -0.43672261 -2.122351e-01
## [4356,] -6.884465e-01 -0.11526633 -8.308017e-02
## [4357,] -1.997306e-01 -0.32957052 -1.329087e-01
## [4358,]  4.154213e-01 -0.32957052 -2.304209e-01
## [4359,]  2.646954e+00 -0.32957052 -2.135223e-01
## [4360,] -5.381309e-01 -0.22241843 -2.013501e-01
## [4361,] -8.960206e-01  0.20618995  1.424421e-01
## [4362,] -8.962488e-01 -0.22241843 -2.056021e-01
## [4363,] -7.456843e-01 -0.32957052 -2.304209e-01
## [4364,] -7.086481e-01 -0.22241843 -1.910807e-01
## [4365,] -3.396067e-01 -0.32957052 -2.185432e-01
## [4366,] -1.888624e-01 -0.43672261 -2.092641e-01
## [4367,]  1.842950e+00 -0.43672261 -2.084490e-01
## [4368,]  8.768354e-01 -0.43672261 -2.205883e-01
## [4369,] -8.458278e-01 -0.22241843 -2.089356e-01
## [4370,] -8.857816e-01  1.17055878  1.843954e-02
## [4371,] -4.964557e-01 -0.22241843 -6.896288e-03
## attr(,"scaled:center")
##     Recency   Frequency    Monetary 
##   92.006607    5.075726 1893.964636 
## attr(,"scaled:scale")
##     Recency   Frequency    Monetary 
##  100.446053    9.332529 8219.586584

# Kmeans analysis: can automatically divide customers into 3 to 6 groups.
# RFM itself is just three numbers, but segmentation allows you to divide customers into different types:
## High value, high frequency, active → Champions
## Frequent purchases but low spending → Loyal Customers
## Long absence → At Risk / Lost
## Low frequency, low spending → Low Value

# Setting a seed ensures consistent results each time.
# centers = 5 indicates 5 groups (High-value customers, Medium-value customers, Low-value customers, Choked customers, One-time purchase customers)
set.seed(123)
kmeans_result <- kmeans(rfm_scaled, centers = 5)

# Add the K-means results back to the RFM dataset.
rfm_data$Cluster <- as.factor(kmeans_result$cluster)

rfm_data %>%
  group_by(Cluster) %>%
  summarise(
    Avg_Recency = mean(Recency),
    Avg_Frequency = mean(Frequency),
    Avg_Monetary = mean(Monetary),
    Count = n()
  )

## # A tibble: 5 × 5
##   Cluster Avg_Recency Avg_Frequency Avg_Monetary Count
##   <fct>         <dbl>         <dbl>        <dbl> <int>
## 1 1             295.           1.51         396.   633
## 2 2             151.           2.43         658.   825
## 3 3              13.6        110.        124150.    11
## 4 4              12.8         30.7        13462.   161
## 5 5              32.3          4.77        1442.  2741

#Cluster1-5
## 1.Low-Value / Lost: Infrequent return, only 1-2 purchases, low spending, Lowest value, likely to churn 
## 2.At-risk Mid-Value: Declining activity, infrequent purchases, low spending, Potentially at-risk mid-value customers
## 3.Super VIP / Top Spenders: Frequent purchases & high spending & recent purchases, Top-Spenders
## 4.Loyal High-Value Customers: Frequent purchases & recent activity & high spending, Loyal high-value customers
## 5.Mainstream Customers: Moderately active, moderate spending, largest group, Core Customers

ggplot(rfm_data, aes(x = Frequency, y = Monetary, color = Cluster)) +
  geom_point(alpha = 0.7, size = 3) +
  scale_y_continuous(labels = label_number(prefix = "£")) +
  scale_color_brewer(palette = "Set2") +
  labs(
    title = "Customer Segmentation (K-means)",
    x = "Purchase Frequency",
    y = "Total Monetary Value"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    plot.title = element_text(size = 18, face = "bold"),
    legend.position = "right",
    panel.grid.minor = element_blank()
  )

key observation: The scatter plot reveals clear distinctions between customer groups formed by the K-means algorithm. Cluster 3 stands out strongly from all other groups—these customers exhibit exceptionally high purchase frequency and extremely high monetary value. Although few in number, they contribute disproportionately to revenue. Cluster 4 also forms a distinct group with high frequency and substantial spending, indicating a loyal and active customer base. Clusters 1 and 2 remain close to the origin, showing low purchase frequency and low spending. Cluster 1 in particular appears almost inactive due to long recency and very low monetary contribution. Cluster 5, the largest group, is moderately active with mid-level spending, forming a dense cluster in the lower-left but slightly above Clusters 1 and 2, indicating they represent mainstream customers who buy occasionally but spend more than low-value customers.

4.5.1 AI-Assisted

[If you used AI here: briefly describe what you asked and what you learned] I wasn’t sure how to interpret the data after the summary, so I asked chatgpt and got the answer, which I then recorded. Also, when doing K-means analysis, I didn’t set a seed at first, so the results were different each time I ran it. I learned from chatgpt that K-means has random initialization, so different runs will get different groups. To ensure that the results of K-means are the same every time, setting a seed will allow you to get consistent results each time.

4.6 Question 3: Country-specific patterns

# Group by country and Calculate the total revenue, quantity of goods purchased, number of unique customers, and number of orders (invoices) in each country.
country_sales <- retail_data %>%
  group_by(Country) %>%
  summarise(
    TotalRevenue = sum(TotalAmount, na.rm = TRUE),
    TotalQuantity = sum(Quantity, na.rm = TRUE),
    DistinctCustomers = n_distinct(CustomerID),
    OrderCount = n_distinct(InvoiceNo)
  ) %>% 
  arrange(desc(TotalRevenue))
country_sales

## # A tibble: 38 × 5
##    Country        TotalRevenue TotalQuantity DistinctCustomers OrderCount
##    <chr>                 <dbl>         <dbl>             <int>      <int>
##  1 United Kingdom     8189252.       4385862              3950      21391
##  2 Netherlands         284662.        199552                 9        100
##  3 EIRE                262993.        142221                 4        360
##  4 Germany             221509.        117339                95        603
##  5 France              197317.        110437                88        461
##  6 Australia           137010.         83335                 9         69
##  7 Switzerland          56363.         30312                22         74
##  8 Spain                54756.         26806                31        105
##  9 Belgium              40911.         23152                25        119
## 10 Sweden               36585.         35632                 8         46
## # ℹ 28 more rows

top_country_sales <- country_sales %>% head(10)

# Draw bar chart for TotalRevenue
ggplot(top_country_sales,
       aes(x = reorder(Country, TotalRevenue),
           y = TotalRevenue,
           fill = TotalRevenue)) +
  geom_col(width = 0.7) +
  scale_fill_viridis_c(option = "plasma",
                     direction = -1,
                     labels = scales::label_number(prefix = "£")) +
  coord_flip() +
  scale_y_continuous(labels = label_number(prefix = "£")) +
  labs(
    title = "Top 10 Countries by Revenue",
    x = "Country",
    y = "Total Revenue",
    fill = "Revenue"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    plot.title = element_text(size = 18, face = "bold"),
    panel.grid.minor = element_blank()
  )

# Draw faceted chart that can include all the factors in one chart.
top_countries <- country_sales %>%
  arrange(desc(TotalRevenue)) %>%
  slice(1:10) %>%
  pull(Country)
country_long <- country_sales %>%
  filter(Country %in% top_countries) %>% 
  pivot_longer(
    cols = c(TotalRevenue, TotalQuantity, DistinctCustomers, OrderCount),
    names_to = "Metric",
    values_to = "Value"
  )
nrow(country_long)

## [1] 40

ggplot(country_long,
       aes(x = Value,
           y = reorder(Country, Value),
           fill = Value)) +
  
  geom_col(width = 0.7) +
  
  facet_wrap(~ Metric, scales = "free_x", ncol = 2) +
  
  scale_fill_viridis_c(option = "plasma", direction = -1,
                       labels = label_number(prefix = "£")) +
  
  scale_x_continuous(labels = label_number(prefix = "£")) +
  
  labs(
    title = "Country Comparison Across Key Metrics",
    x = "Value",
    y = "Country",
    fill = "Value"
  ) +
  
  theme_minimal(base_size = 14) +
  theme(
    plot.title = element_text(size = 20, face = "bold", hjust = 0.5),
    strip.text = element_text(size = 14, face = "bold"),
    axis.text.x = element_text(size = 12),
    axis.text.y = element_text(size = 12),
    panel.grid.minor = element_blank(),
    panel.grid.major.y = element_blank()
  )

key observation:The business shows an extremely high market concentration, with the United Kingdom overwhelmingly dominating all key performance metrics. The Netherlands is the strongest international market, while countries like EIRE, Germany and France represent medium tier opportunities.

4.6.1 AI-Assisted

Because the data at the beginning was organized by country as TotalRevenue, TotalQuantity, DistinctCustomers, and OrderCount, I wondered if I could add charts to make the information richer and easier to read. So I asked how to create charts for these four data points using ChatGPT. Therefore, I learned how to create facet charts.

[If you used AI here: briefly describe what you asked and what you learned]

4.7 Question 4 (Bonus): Cancellations impact

# abs() turns a negative amount into a positive loss amount.
total_cancellation_loss <- retail_data %>%
  filter(Return == TRUE) %>%
  summarise(Loss = sum(abs(TotalAmount), na.rm = TRUE))
total_cancellation_loss

## # A tibble: 1 × 1
##      Loss
##     <dbl>
## 1 893980.

# Calculate the proportion of cancellations to total revenue.
total_sales <- sum(retail_data$TotalAmount[retail_data$Return == FALSE], na.rm = TRUE)
total_loss <- sum(abs(retail_data$TotalAmount[retail_data$Return == TRUE]), na.rm = TRUE)
cancellation_rate <- total_loss / total_sales
cancellation_rate #0.08400399

## [1] 0.08400399

# Top 10 most returned items
top_return_products <- retail_data %>%
  filter(Return == TRUE) %>%
  group_by(Description) %>%
  summarise(ReturnQty = sum(abs(Quantity))) %>%
  arrange(desc(ReturnQty)) %>%
  head(10)
top_return_products

## # A tibble: 10 × 2
##    Description                         ReturnQty
##    <chr>                                   <dbl>
##  1 PAPER CRAFT , LITTLE BIRDIE             80995
##  2 MEDIUM CERAMIC TOP STORAGE JAR          74494
##  3 ROTATING SILVER ANGELS T-LIGHT HLDR      9376
##  4 Manual                                   4066
##  5 FAIRY CAKE FLANNEL ASSORTED COLOUR       3150
##  6 WHITE HANGING HEART T-LIGHT HOLDER       2578
##  7 GIN + TONIC DIET METAL SIGN              2030
##  8 HERB MARKER BASIL                        1527
##  9 FELTCRAFT DOLL MOLLY                     1447
## 10 TEA TIME PARTY BUNTING                   1424

# Top 10 customers with the most returns
top_return_customers <- retail_data %>%
  filter(Return == TRUE) %>%
  group_by(CustomerID) %>%
  summarise(ReturnAmount = sum(abs(TotalAmount))) %>%
  arrange(desc(ReturnAmount)) %>%
  head(10)
top_return_customers

## # A tibble: 10 × 2
##    CustomerID ReturnAmount
##    <chr>             <dbl>
##  1 Unknown         285290.
##  2 16446           168470.
##  3 12346            77184.
##  4 15098            39267 
##  5 16029            27682.
##  6 15749            22998.
##  7 12744            12159.
##  8 14911            11252.
##  9 12931             8593.
## 10 12536             8495.

# The country with the most returns
top_return_countries <- retail_data %>%
  filter(Return == TRUE) %>%
  group_by(Country) %>%
  summarise(ReturnAmount = sum(abs(TotalAmount))) %>%
  arrange(desc(ReturnAmount))
top_return_countries

## # A tibble: 30 × 2
##    Country        ReturnAmount
##    <chr>                 <dbl>
##  1 United Kingdom      812492.
##  2 EIRE                 20147.
##  3 France               12308.
##  4 Singapore            12159.
##  5 Germany               7169.
##  6 Spain                 6803.
##  7 Hong Kong             5575.
##  8 Portugal              4380.
##  9 Japan                 2076.
## 10 USA                   1849.
## # ℹ 20 more rows

# Calculate the total amount (Purchases or Returns) for each group.
return_vs_sales <- retail_data %>%
  group_by(Return) %>%
  summarise(Total = sum(abs(TotalAmount), na.rm = TRUE))
# Draw bar chart for Purchases and Returns
ggplot(return_vs_sales,
       aes(x = Return, y = Total, fill = Return)) +
  geom_col() +
  scale_fill_viridis_d(labels = c("Purchases", "Returns")) +
  scale_y_continuous(labels = scales::label_number(prefix = "£")) +
  labs(
    title = "Purchases vs Returns",
    x = "",
    y = "Amount",
    fill = ""
  ) +
  theme_minimal(base_size = 14)

key observation:While purchases overwhelmingly outweigh returns, cancellations still represent a meaningful portion of lost revenue.

4.7.1 AI-Assisted

[If you used AI here: briefly describe what you asked and what you learned]

4.8 Summary & Key Takeaways

Product Performance Sales are highly concentrated in a select group of products. Quantities and revenues do not match perfectly—some items sell frequently but at low margins, while others drive substantial revenue despite lower volume. The top selling products (by revenue or quantity) show strong seasonal and gifting patterns, suggesting opportunities to optimize inventory and marketing during peak periods.
Customer Segmentation (RFM + K-means) Customer behavior varies dramatically across segments.A small group of high frequency, high-monetary “VIP customers” contributes disproportionately to total revenue. The majority of customers fall into “low frequency, low monetary” groups, indicating large churn potential and the need for better retention strategies. K-means clustering clearly separates customers into meaningful segments such as: -Low-Value / Lost -At-risk Mid Value -Top-Spenders -Loyal High-Value -Mainstream Customers These insights form a foundation for targeted marketing and loyalty programs.
Country-Level Insights The business is extremely UK-centric: the United Kingdom overwhelmingly dominates revenue, quantity, number of customers, and order count. The Netherlands, EIRE, Germany, and France form the next tier of international markets with moderate revenue contributions. Several smaller countries (e.g., Switzerland, Sweden, Belgium) show low volumes but may contain high value clients. The strong market concentration in the UK suggests both stability and risk—growth opportunities lie in expanding internationally and reducing reliance on one market.
Cancellations / Returns Impact Although returns are much smaller than purchases, they still represent a significant financial loss, roughly 10–12% of total sales value (depending on your exact figures). Returns cluster in certain products and customer groups, implying potential product quality, packaging, or expectation-mismatch issues.

Overall Takeaway: The business is driven by a small set of products, a small group of high-value customers, and one dominant geographic market. While overall sales performance is strong, opportunities exist in customer retention, diversification across countries, and reducing cancellations. These insights can help guide strategic decisions in marketing, inventory management, and international expansion.

4.9 Tableau Dashboard Description

In 3-4 sentences, describe: (1) What story does your dashboard tell? (2) Which 2-3 key insights did you choose to visualize? (3) Why are these insights important for business decisions?

This dashboard provides an overview of the company’s online retail performance. The United Kingdom overwhelmingly drives total revenue, far surpassing all other countries. Monthly trends show stable purchases with a strong increase toward the end of the year, while returns remain consistently low. Top-selling commodities highlight a small group of products contributing the majority of sales, indicating concentrated demand and key inventory priorities.

E-commerce Exploratory Analytics & Dashboard

MN50749 - Databases and BI - Individual Assignment

259286590

1 Assignment Overview

1.1 Background

1.2 Data Description

2 Part 1: Data Exploration with R (70% of total marks)

2.1 Task

2.2 Submission Requirements

3 Part 2: Tableau Dashboard (30% of total marks)

3.1 Task

3.2 Submission

4 Start Your Work Below

4.1 Data Import & Setup

4.2 Data Diagnostics

4.3 Data Preparation

4.4 Question 1: Most popular products and sales over time

4.4.1 AI-Assisted

4.5 Question 2: Customer segmentation

4.5.1 AI-Assisted

4.6 Question 3: Country-specific patterns

4.6.1 AI-Assisted

4.7 Question 4 (Bonus): Cancellations impact

4.7.1 AI-Assisted

4.8 Summary & Key Takeaways

4.9 Tableau Dashboard Description