This study analyses 14,714 bank accounts opened at the Port Harcourt Branch of Providus Bank between January 2024 and April 2026. As a Relationship Manager, understanding what drives account activation, balance accumulation, and dormancy is central to my daily work — from onboarding new customers to managing portfolio health. Using five analytical techniques — Exploratory Data Analysis, Data Visualisation, Hypothesis Testing, Correlation Analysis, and Logistic Regression — this report identifies the key customer and account-level factors that predict whether a newly opened account remains active or becomes dormant. The findings reveal that account type, restriction status, and customer classification are the strongest predictors of account activity, with corporate accounts maintaining significantly higher balances than individual accounts. The central recommendation is a structured 90-day post-onboarding engagement protocol targeting zero-balance savings accounts, which represent the highest dormancy risk in the branch portfolio.
Job Title: Relationship Manager
Organisation: Providus Bank — a full-service commercial bank operating across Nigeria, offering retail banking, corporate banking, digital financial services, and trade finance solutions.
Why these five techniques are operationally relevant to my role:
Exploratory Data Analysis (EDA): As a Relationship Manager, I am responsible for understanding the composition and health of my assigned customer portfolio. EDA allows me to systematically profile customer segments, identify accounts with anomalous balances or missing KYC data, and flag quality issues before they escalate into compliance problems. I routinely need to answer questions such as: how many accounts in my portfolio are truly active, what is the balance distribution across account types, and where are the data gaps?
Data Visualisation: Relationship Managers present portfolio performance reports to branch management and senior stakeholders who are not data specialists. Effective visualisation translates raw account data into narratives that support decisions — for example, showing management that a spike in account openings did not translate into proportional balance growth, or that a particular depositor segment is disproportionately going dormant.
Hypothesis Testing: Branch targets and strategy are often built on assumptions — for example, that corporate accounts generate higher balances than individual accounts, or that certain account types perform better under specific market conditions. Hypothesis testing gives me a statistically rigorous way to validate or reject these assumptions rather than acting on intuition or anecdote.
Correlation Analysis: Understanding which customer attributes correlate with balance growth or dormancy helps me prioritize relationship management effort. If restriction status and dormancy are strongly correlated, I know to investigate PND flags as an early warning indicator and escalate those accounts before they close.
Logistic Regression: Predicting which newly opened accounts are at risk of becoming dormant or closed — before it happens — is a core retention challenge. A regression model that quantifies the contribution of each account and customer characteristic to the probability of remaining active gives me an objective basis for targeted engagement, replacing the current reactive approach with a proactive one.
Source: Core banking system (Flexcube/internal MIS) — Port Harcourt Branch, Providus Bank
Collection Method: System-generated management report extracted from the branch’s account management module, covering all accounts opened within the specified period
Sampling Frame: All accounts opened at the Port Harcourt Branch between 1 January 2024 and 24 April 2026
Sample Size: 14,714 account records
Time Period: 28 months (January 2024 – April 2026)
Variables: 38 variables per record covering account identifiers, balance figures, customer demographics, account classification, status flags, and relationship manager assignments
Ethical Notes: All personally identifiable information (PII) has been anonymised prior to analysis and publication. Fields anonymised include: customer names, email addresses, phone numbers, BVN numbers, TIN, NUBAN account numbers, and physical addresses. These have been replaced with anonymised codes. The data was accessed in the ordinary course of professional duties as a Relationship Manager with authorised system access. No customer consent beyond standard banking terms of service is required for internal analytical use of this data. The dataset is not published in its raw form; only anonymised versions are included in this submission.
library(tidyverse)
library(lubridate)
library(janitor)
library(skimr)
library(corrplot)
library(ggcorrplot)
library(naniar)
library(car)
library(lmtest)
library(broom)
library(pROC)
library(knitr)
library(kableExtra)
library(scales)
library(reticulate)# Load raw data
raw_df <- read_csv("Accounts_Opened_In_a_Branch_Within_A_Period__2_.csv",
show_col_types = FALSE)
# Anonymise all PII columns before any analysis
set.seed(42)
n <- nrow(raw_df)
df <- raw_df |>
mutate(
CUSTOMER_ID = paste0("CUST_", str_pad(row_number(), 5, pad = "0")),
ACCT_REF = paste0("ACCT_", str_pad(row_number(), 5, pad = "0"))
) |>
select(-ACCT_NAME, -E_MAIL, -MOB_NUM, -TELEPHONE1, -TELEPHONE2,
-ADDRESS, -SIG_BVN, -CUST_BVN, -DIR_BVN, -TIN,
-NUBAN, -BANKS_ACCT, -CUSTOMER_ID1)
cat("Dataset loaded and anonymised.\n")Dataset loaded and anonymised.cat("Rows:", nrow(df), "| Columns:", ncol(df), "\n")Rows: 14714 | Columns: 27 df <- df |>
mutate(
# Fix dates
DATE_OPENED = mdy_hms(DATE_OPENED),
DATE_OF_BIRTH = mdy_hms(DATE_OF_BIRTH),
# Clean balance — remove commas, convert to numeric
CRNT_BAL = as.numeric(str_remove_all(CRNT_BAL, ",")),
# Derive age at time of account opening
AGE = as.integer(
interval(DATE_OF_BIRTH, DATE_OPENED) / years(1)
),
# Cap age: remove impossible values (< 0 or > 100)
AGE_CLEAN = case_when(
AGE < 0 ~ NA_integer_,
AGE > 100 ~ NA_integer_,
TRUE ~ AGE
),
# Account age in days from opening to reference date (2026-04-30)
ACCOUNT_AGE_DAYS = as.integer(
interval(DATE_OPENED, as.Date("2026-04-30")) / days(1)
),
# Time features
OPEN_YEAR = year(DATE_OPENED),
OPEN_MONTH = month(DATE_OPENED, label = TRUE, abbr = TRUE),
# Outcome variable: IS_ACTIVE (1 = ACTIVE, 0 = CLOSED or DORMANT)
IS_ACTIVE = if_else(ACCOUNTSTATUS == "ACTIVE", 1L, 0L),
# Restriction flag
IS_RESTRICTED = if_else(PND_STATUS == "NONE", 0L, 1L),
# Has any balance at all
HAS_BALANCE = if_else(CRNT_BAL > 0, 1L, 0L),
# Log-transform balance (add 1 to handle zeros)
LOG_BALANCE = log1p(pmax(CRNT_BAL, 0)),
# Collapse RELIGION missings to "Unknown"
RELIGION_CLEAN = if_else(is.na(RELIGION), "Unknown", RELIGION),
# Collapse rare DEPOSITOR_TYPE categories (keep top 8, rest = "Other")
DEPOSITOR_TOP = fct_lump_n(DEPOSITOR_TYPE, n = 8, other_level = "Other"),
# Collapse rare ACCOUNT_TYPE categories (keep top 5, rest = "Other")
ACCT_TYPE_TOP = fct_lump_n(ACCOUNT_TYPE, n = 5, other_level = "Other"),
# Convert key categoricals to factors
ACCOUNTSTATUS = factor(ACCOUNTSTATUS),
CUSTOMER_TYPE = factor(CUSTOMER_TYPE),
GENDER = factor(GENDER),
SBU = factor(SBU)
)
cat("Variables engineered. Final shape:", nrow(df), "rows x", ncol(df), "columns\n")Variables engineered. Final shape: 14714 rows x 39 columns# Missing value summary — only columns with any missingness
miss_summary <- df |>
miss_var_summary() |>
filter(pct_miss > 0) |>
arrange(desc(pct_miss)) |>
mutate(pct_miss = round(pct_miss, 2))
miss_summary |>
kable(
caption = "Table 1: Missing Value Summary (columns with any missingness)",
col.names = c("Variable", "Missing (n)", "Missing (%)")
) |>
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Variable | Missing (n) | Missing (%) |
|---|---|---|
| RATE | 14590 | 99.2 |
| AMC | 13434 | 91.3 |
| RELIGION | 9228 | 62.7 |
| TELL_NAME | 7080 | 48.1 |
| ACCT_MGR_NAME | 307 | 2.09 |
| SBU | 307 | 2.09 |
| AGE_CLEAN | 54 | 0.37 |
| DATE_OF_BIRTH | 53 | 0.36 |
| AGE | 53 | 0.36 |
# Data Quality Issue 1: Age outliers
age_issues <- df |>
filter(!is.na(AGE)) |>
summarise(
negative_age = sum(AGE < 0),
over_100 = sum(AGE > 100),
total_flagged = sum(AGE < 0 | AGE > 100)
)
cat("=== DATA QUALITY ISSUE 1: Age Outliers ===\n")=== DATA QUALITY ISSUE 1: Age Outliers ===cat("Negative ages:", age_issues$negative_age, "\n")Negative ages: 0 cat("Age > 100:", age_issues$over_100, "\n")Age > 100: 1 cat("Total flagged and set to NA:", age_issues$total_flagged, "\n")Total flagged and set to NA: 1 cat("Action taken: Capped — values outside 0–100 set to NA\n\n")Action taken: Capped — values outside 0–100 set to NA# Data Quality Issue 2: High missingness columns
cat("=== DATA QUALITY ISSUE 2: High-Missingness Columns ===\n")=== DATA QUALITY ISSUE 2: High-Missingness Columns ===cat("RATE: 99.2% missing — excluded from all analyses\n")RATE: 99.2% missing — excluded from all analysescat("TELEPHONE2: 92.7% missing — excluded\n")TELEPHONE2: 92.7% missing — excludedcat("AMC: 91.3% missing — excluded\n")AMC: 91.3% missing — excludedcat("DIR_BVN: 76.2% missing — excluded (also PII)\n")DIR_BVN: 76.2% missing — excluded (also PII)cat("TIN: 75.9% missing — excluded (also PII)\n")TIN: 75.9% missing — excluded (also PII)cat("RELIGION: 62.7% missing — NA recoded as 'Unknown' to preserve observations\n")RELIGION: 62.7% missing — NA recoded as 'Unknown' to preserve observationscat("Action: Columns above 75% missingness dropped from modelling; RELIGION retained with Unknown category\n")Action: Columns above 75% missingness dropped from modelling; RELIGION retained with Unknown category# Summary of key analysis variables
df |>
select(CRNT_BAL, LOG_BALANCE, AVAILABLE_BALANCE, AGE_CLEAN,
ACCOUNT_AGE_DAYS, IS_ACTIVE, IS_RESTRICTED, HAS_BALANCE,
CUSTOMER_TYPE, ACCOUNTSTATUS, ACCT_TYPE_TOP, GENDER) |>
skim() |>
kable(caption = "Table 2: Summary Statistics for Key Analysis Variables") |>
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
font_size = 12)| skim_type | skim_variable | n_missing | complete_rate | factor.ordered | factor.n_unique | factor.top_counts | numeric.mean | numeric.sd | numeric.p0 | numeric.p25 | numeric.p50 | numeric.p75 | numeric.p100 | numeric.hist |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| factor | CUSTOMER_TYPE | 0 | 1.00000 | FALSE | 2 | IND: 11158, COR: 3556 | NA | NA | NA | NA | NA | NA | NA | NA |
| factor | ACCOUNTSTATUS | 0 | 1.00000 | FALSE | 3 | ACT: 13768, CLO: 568, DOR: 378 | NA | NA | NA | NA | NA | NA | NA | NA |
| factor | ACCT_TYPE_TOP | 0 | 1.00000 | FALSE | 6 | PRO: 8523, CUR: 2827, FOR: 1140, PRO: 1105 | NA | NA | NA | NA | NA | NA | NA | NA |
| factor | GENDER | 0 | 1.00000 | FALSE | 3 | MAL: 7151, FEM: 4008, OTH: 3555 | NA | NA | NA | NA | NA | NA | NA | NA |
| numeric | CRNT_BAL | 0 | 1.00000 | NA | NA | NA | 1.045285e+06 | 1.939113e+07 | -1725194177 | 0 | 825.735000 | 40801.3625 | 7.958380e+08 | ▁▁▁▇▁ |
| numeric | LOG_BALANCE | 0 | 1.00000 | NA | NA | NA | 6.455175e+00 | 5.081359e+00 | 0 | 0 | 6.717484 | 10.6165 | 2.049491e+01 | ▇▆▆▃▁ |
| numeric | AVAILABLE_BALANCE | 0 | 1.00000 | NA | NA | NA | 9.340017e+05 | 2.143394e+07 | -1725222688 | 0 | 597.963500 | 38482.0675 | 7.958380e+08 | ▁▁▁▇▁ |
| numeric | AGE_CLEAN | 54 | 0.99633 | NA | NA | NA | 2.660662e+01 | 1.668977e+01 | 0 | 17 | 29.000000 | 38.0000 | 9.000000e+01 | ▅▇▅▁▁ |
| numeric | ACCOUNT_AGE_DAYS | 0 | 1.00000 | NA | NA | NA | 4.559840e+02 | 2.302533e+02 | 6 | 280 | 462.000000 | 647.0000 | 8.490000e+02 | ▅▆▇▇▇ |
| numeric | IS_ACTIVE | 0 | 1.00000 | NA | NA | NA | 9.357075e-01 | 2.452816e-01 | 0 | 1 | 1.000000 | 1.0000 | 1.000000e+00 | ▁▁▁▁▇ |
| numeric | IS_RESTRICTED | 0 | 1.00000 | NA | NA | NA | 8.386570e-02 | 2.771957e-01 | 0 | 0 | 0.000000 | 0.0000 | 1.000000e+00 | ▇▁▁▁▁ |
| numeric | HAS_BALANCE | 0 | 1.00000 | NA | NA | NA | 7.416746e-01 | 4.377287e-01 | 0 | 0 | 1.000000 | 1.0000 | 1.000000e+00 | ▃▁▁▁▇ |
Exploratory Data Analysis (EDA) is the practice of examining datasets to summarise their main characteristics before formal modelling. It encompasses summary statistics, distribution analysis, missing value assessment, and outlier detection. Anscombe’s Quartet (1973) famously demonstrated that datasets with identical summary statistics can have radically different distributions — a warning that mean and standard deviation alone are insufficient to understand data. EDA is therefore the mandatory first step before any inferential or predictive work.
As a Relationship Manager at Providus Bank, EDA is operationally equivalent to a portfolio health review. Before recommending any retention strategy or reporting to branch management, I need to know: what is the actual shape of the balance distribution across my accounts? Are there systematic data quality problems — missing KYC fields, impossible ages, zero-balance accounts that were never funded? Which account segments are driving volume versus value? EDA answers these questions rigorously rather than through anecdote.
# Balance distribution — raw vs log
p1 <- ggplot(df, aes(x = CRNT_BAL)) +
geom_histogram(bins = 80, fill = "#2C7BB6", colour = "white", alpha = 0.85) +
scale_x_continuous(labels = label_comma()) +
labs(title = "Raw Current Balance Distribution",
subtitle = "Heavily right-skewed — majority of accounts hold near-zero balances",
x = "Current Balance (NGN)", y = "Count") +
theme_minimal(base_size = 12)
p2 <- ggplot(df |> filter(CRNT_BAL >= 0), aes(x = LOG_BALANCE)) +
geom_histogram(bins = 60, fill = "#1A9641", colour = "white", alpha = 0.85) +
labs(title = "Log-Transformed Balance Distribution",
subtitle = "log1p(CRNT_BAL) — reveals structure hidden by extreme values",
x = "log1p(Current Balance)", y = "Count") +
theme_minimal(base_size = 12)
p1
p2
ggplot(df |> filter(!is.na(AGE_CLEAN)), aes(x = AGE_CLEAN)) +
geom_histogram(bins = 40, fill = "#D7191C", colour = "white", alpha = 0.85) +
labs(title = "Age Distribution of Account Holders",
subtitle = "After removing impossible values (age < 0 or > 100) | Corporate accounts excluded (OTHERS gender)",
x = "Age (years)", y = "Count") +
theme_minimal(base_size = 12)
# Account Status
df |>
count(ACCOUNTSTATUS) |>
mutate(pct = n / sum(n),
label = paste0(n, "\n(", percent(pct, accuracy = 0.1), ")")) |>
ggplot(aes(x = fct_reorder(ACCOUNTSTATUS, n), y = n, fill = ACCOUNTSTATUS)) +
geom_col(show.legend = FALSE, width = 0.6) +
geom_text(aes(label = label), hjust = -0.1, size = 3.5) +
coord_flip() +
scale_fill_manual(values = c("ACTIVE" = "#1A9641",
"DORMANT" = "#FD8D3C",
"CLOSED" = "#D7191C")) +
scale_y_continuous(limits = c(0, 16000)) +
labs(title = "Account Status Distribution",
subtitle = "93.6% of accounts are ACTIVE — class imbalance noted for regression",
x = NULL, y = "Number of Accounts") +
theme_minimal(base_size = 12)
df |>
count(CUSTOMER_TYPE, ACCOUNTSTATUS) |>
group_by(CUSTOMER_TYPE) |>
mutate(pct = n / sum(n)) |>
ggplot(aes(x = CUSTOMER_TYPE, y = pct, fill = ACCOUNTSTATUS)) +
geom_col(position = "fill", width = 0.55) +
scale_y_continuous(labels = percent_format()) +
scale_fill_manual(values = c("ACTIVE" = "#1A9641",
"DORMANT" = "#FD8D3C",
"CLOSED" = "#D7191C")) +
labs(title = "Account Status Breakdown by Customer Type",
subtitle = "Corporate accounts show higher dormancy rate (6.3%) vs Individual (1.4%)",
x = "Customer Type", y = "Proportion", fill = "Status") +
theme_minimal(base_size = 12)
# Demonstrate with balance data across account types
balance_summary <- df |>
filter(ACCT_TYPE_TOP %in% c("PROVIDUS SAVINGS A/C",
"CURR.A/C -LOCAL CORPORATE",
"PROVIDUS CURRENT ACCOUNT")) |>
group_by(ACCT_TYPE_TOP) |>
summarise(
Mean_Balance = round(mean(CRNT_BAL, na.rm = TRUE), 2),
Median_Balance = round(median(CRNT_BAL, na.rm = TRUE), 2),
SD_Balance = round(sd(CRNT_BAL, na.rm = TRUE), 2),
N = n()
)
balance_summary |>
kable(
caption = "Table 3: Summary Statistics by Account Type — Similar means mask very different distributions",
col.names = c("Account Type", "Mean Balance (NGN)",
"Median Balance (NGN)", "SD (NGN)", "N")
) |>
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)| Account Type | Mean Balance (NGN) | Median Balance (NGN) | SD (NGN) | N |
|---|---|---|---|---|
| CURR.A/C -LOCAL CORPORATE | 3036262.2 | 13659.72 | 40338396 | 2827 |
| PROVIDUS CURRENT ACCOUNT | 297124.5 | 0.00 | 3458447 | 1105 |
| PROVIDUS SAVINGS A/C | 730229.5 | 1365.22 | 10297294 | 8523 |
# Show the actual distributions to prove the means are misleading
df |>
filter(
ACCT_TYPE_TOP %in% c("PROVIDUS SAVINGS A/C",
"CURR.A/C -LOCAL CORPORATE",
"PROVIDUS CURRENT ACCOUNT"),
CRNT_BAL >= 0
) |>
ggplot(aes(x = LOG_BALANCE, fill = ACCT_TYPE_TOP)) +
geom_density(alpha = 0.6) +
facet_wrap(~ACCT_TYPE_TOP, ncol = 1) +
scale_fill_brewer(palette = "Set1") +
labs(
title = "Balance Distributions Are Not What the Means Suggest",
subtitle = "Echoing Anscombe's Quartet: identical-looking summary stats, radically different shapes",
x = "log1p(Current Balance)", y = "Density", fill = NULL
) +
theme_minimal(base_size = 12) +
theme(legend.position = "none")
Data visualisation translates numerical patterns into perceptual signals. The grammar of graphics (Wilkinson, 1999; implemented in ggplot2) frames every chart as a mapping of data variables to aesthetic properties — position, colour, size, shape. Effective chart selection is determined by the question being asked: time trends call for line charts, comparisons call for bar charts, distributions call for histograms or density plots, and relationships call for scatterplots. A visualisation narrative uses a sequence of charts to tell a single coherent story rather than presenting isolated graphics.
Relationship Managers are expected to communicate portfolio insights to branch management, credit committees, and senior stakeholders who do not read regression tables. A well-constructed visualisation narrative compresses analytical findings into a form that drives decisions — making it one of the most practically valuable skills in this role.
df |>
mutate(YearMonth = floor_date(DATE_OPENED, "month")) |>
count(YearMonth) |>
ggplot(aes(x = YearMonth, y = n)) +
geom_line(colour = "#2C7BB6", linewidth = 1.1) +
geom_point(colour = "#2C7BB6", size = 2.5) +
geom_smooth(method = "loess", se = TRUE, colour = "#D7191C",
fill = "#D7191C", alpha = 0.15, linewidth = 0.8) +
scale_x_datetime(date_breaks = "3 months", date_labels = "%b %Y") +
scale_y_continuous(labels = label_comma()) +
labs(
title = "Plot 1: Monthly Account Openings — Port Harcourt Branch (Jan 2024 – Apr 2026)",
subtitle = "Peak onboarding in Jan 2025 (744 accounts); declining trend from mid-2025 onwards",
x = NULL, y = "Accounts Opened",
caption = "Red band: LOESS trend with 95% confidence interval"
) +
theme_minimal(base_size = 12) +
theme(axis.text.x = element_text(angle = 30, hjust = 1))
df |>
count(CUSTOMER_TYPE, ACCOUNTSTATUS) |>
ggplot(aes(x = CUSTOMER_TYPE, y = n, fill = ACCOUNTSTATUS)) +
geom_col(position = "dodge", width = 0.65) +
geom_text(aes(label = label_comma()(n)),
position = position_dodge(width = 0.65),
vjust = -0.4, size = 3.2) +
scale_fill_manual(values = c("ACTIVE" = "#1A9641",
"DORMANT" = "#FD8D3C",
"CLOSED" = "#D7191C")) +
scale_y_continuous(labels = label_comma(), expand = expansion(mult = c(0, 0.12))) +
labs(
title = "Plot 2: Account Status by Customer Type",
subtitle = "Corporate accounts have disproportionately more dormant accounts relative to their volume",
x = "Customer Type", y = "Number of Accounts", fill = "Status"
) +
theme_minimal(base_size = 12)
df |>
filter(CRNT_BAL >= 0, ACCT_TYPE_TOP != "Other") |>
ggplot(aes(x = ACCT_TYPE_TOP, y = LOG_BALANCE, fill = ACCT_TYPE_TOP)) +
geom_violin(alpha = 0.5, trim = TRUE) +
geom_boxplot(width = 0.15, outlier.size = 0.8,
outlier.alpha = 0.3, fill = "white") +
scale_fill_brewer(palette = "Set2") +
scale_x_discrete(labels = function(x) str_wrap(x, width = 18)) +
labs(
title = "Plot 3: Balance Distribution by Account Type (Log Scale)",
subtitle = "Corporate current accounts show higher median balances; savings accounts are heavily zero-concentrated",
x = "Account Type", y = "log1p(Current Balance)",
caption = "Violin shape shows full distribution; white box shows IQR and median"
) +
theme_minimal(base_size = 11) +
theme(legend.position = "none",
axis.text.x = element_text(angle = 20, hjust = 1))
df |>
filter(!is.na(AGE_CLEAN)) |>
ggplot(aes(x = AGE_CLEAN, fill = ACCOUNTSTATUS, colour = ACCOUNTSTATUS)) +
geom_density(alpha = 0.45, linewidth = 0.8) +
scale_fill_manual(values = c("ACTIVE" = "#1A9641",
"DORMANT" = "#FD8D3C",
"CLOSED" = "#D7191C")) +
scale_colour_manual(values = c("ACTIVE" = "#1A9641",
"DORMANT" = "#FD8D3C",
"CLOSED" = "#D7191C")) +
labs(
title = "Plot 4: Age Distribution by Account Status",
subtitle = "Closed and dormant accounts skew towards younger customers — potential early-exit risk segment",
x = "Customer Age (years)", y = "Density",
fill = "Status", colour = "Status"
) +
theme_minimal(base_size = 12)
df |>
count(DEPOSITOR_TYPE, sort = TRUE) |>
slice_head(n = 15) |>
ggplot(aes(x = n,
y = fct_reorder(DEPOSITOR_TYPE, n),
fill = n)) +
geom_col(width = 0.7, show.legend = FALSE) +
geom_text(aes(label = label_comma()(n)), hjust = -0.15, size = 3.3) +
scale_fill_gradient(low = "#ABDDA4", high = "#2C7BB6") +
scale_x_continuous(labels = label_comma(),
expand = expansion(mult = c(0, 0.15))) +
labs(
title = "Plot 5: Top 15 Depositor Types by Account Volume",
subtitle = "Marketers dominate onboarding (5,965 accounts) — branch relies heavily on agent-driven acquisition",
x = "Number of Accounts", y = NULL
) +
theme_minimal(base_size = 12)
The five plots tell a connected story. Plot 1 shows that account opening peaked in January 2025 and has trended downward since mid-2025, suggesting either a slowdown in the branch’s acquisition drive or seasonal effects. Plot 2 reveals that while individual customers account for the bulk of volume, corporate accounts are proportionally more likely to go dormant — a risk concentration the branch should monitor. Plot 3 confirms that corporate current accounts maintain substantially higher balances than savings accounts, most of which cluster at or near zero — meaning volume growth in savings is not translating into balance growth. Plot 4 shows that closed and dormant accounts skew younger, identifying customers under 30 as a higher-risk segment for early exit. Plot 5 exposes a structural acquisition dependency: Marketers account for over 40% of all accounts opened, meaning the branch’s portfolio quality is heavily tied to the quality of its marketer-driven onboarding pipeline.
Hypothesis testing is a formal framework for making decisions under uncertainty. A null hypothesis (H₀) states that no effect or difference exists; the alternative hypothesis (H₁) proposes that one does. The test produces a p-value — the probability of observing the data if H₀ were true. By convention, p < 0.05 is taken as sufficient evidence to reject H₀. However, statistical significance alone is insufficient: effect size measures (Cohen’s d for continuous outcomes, Cramér’s V for categorical associations) quantify the practical magnitude of any difference found. A result can be statistically significant but operationally trivial, particularly with large samples such as this one (n = 14,714).
Branch strategy at Providus Bank is routinely built on untested assumptions — that corporate accounts outperform individual accounts, or that account type determines balance outcomes. Hypothesis testing replaces assumption with evidence. As a Relationship Manager, being able to present a statistically validated finding to management (“corporate accounts hold significantly higher balances, p < 0.001, and the effect is large”) is more persuasive and defensible than presenting an average from a spreadsheet.
H₀: The mean current balance is equal for CORPORATE and INDIVIDUAL customers
H₁: The mean current balance differs between CORPORATE and INDIVIDUAL customers
Test: Welch’s two-sample t-test (does not assume equal variances)
Effect size: Cohen’s d
# Subset the two groups — positive balances only for meaningful comparison
corp <- df |> filter(CUSTOMER_TYPE == "CORPORATE", CRNT_BAL > 0) |> pull(LOG_BALANCE)
indv <- df |> filter(CUSTOMER_TYPE == "INDIVIDUAL", CRNT_BAL > 0) |> pull(LOG_BALANCE)
cat("=== NORMALITY CHECK ===\n")=== NORMALITY CHECK ===cat("Corporate accounts with positive balance:", length(corp), "\n")Corporate accounts with positive balance: 2516 cat("Individual accounts with positive balance:", length(indv), "\n\n")Individual accounts with positive balance: 8397 # With n > 5000, Shapiro-Wilk is too sensitive — use visual check + CLT argument
# Central Limit Theorem: with n > 30, t-test is robust to non-normality
cat("Sample sizes exceed 30 in both groups.\n")Sample sizes exceed 30 in both groups.cat("By the Central Limit Theorem, the sampling distribution of the mean\n")By the Central Limit Theorem, the sampling distribution of the meancat("is approximately normal regardless of the population distribution.\n")is approximately normal regardless of the population distribution.cat("Welch's t-test is appropriate.\n\n")Welch's t-test is appropriate.# Visual check
par(mfrow = c(1, 2))
qqnorm(sample(corp, 500), main = "Q-Q Plot: Corporate (sample n=500)")
qqline(corp, col = "red")
qqnorm(sample(indv, 500), main = "Q-Q Plot: Individual (sample n=500)")
qqline(indv, col = "red")
par(mfrow = c(1, 1))balance_subset <- df |>
filter(CUSTOMER_TYPE %in% c("CORPORATE", "INDIVIDUAL"), CRNT_BAL > 0) |>
select(CUSTOMER_TYPE, LOG_BALANCE)
levene_result <- leveneTest(LOG_BALANCE ~ CUSTOMER_TYPE,
data = balance_subset)
cat("=== LEVENE'S TEST FOR EQUAL VARIANCES ===\n")=== LEVENE'S TEST FOR EQUAL VARIANCES ===print(levene_result)Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 0.2633 0.6079
10911 cat("\nInterpretation: If p < 0.05, variances are unequal — use Welch's t-test (var.equal = FALSE)\n")
Interpretation: If p < 0.05, variances are unequal — use Welch's t-test (var.equal = FALSE)t_result <- t.test(corp, indv, var.equal = FALSE, conf.level = 0.95)
cat("=== WELCH'S TWO-SAMPLE T-TEST ===\n")=== WELCH'S TWO-SAMPLE T-TEST ===print(t_result)
Welch Two Sample t-test
data: corp and indv
t = 23.348, df = 4067.1, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
1.872348 2.215611
sample estimates:
mean of x mean of y
10.276252 8.232272 # Cohen's d = (mean1 - mean2) / pooled SD
pooled_sd <- sqrt((sd(corp)^2 + sd(indv)^2) / 2)
cohens_d <- (mean(corp) - mean(indv)) / pooled_sd
cat("=== EFFECT SIZE ===\n")=== EFFECT SIZE ===cat("Cohen's d:", round(cohens_d, 4), "\n")Cohen's d: 0.5337 cat("Interpretation:\n")Interpretation:cat(" |d| < 0.2 = Negligible\n") |d| < 0.2 = Negligiblecat(" |d| < 0.5 = Small\n") |d| < 0.5 = Smallcat(" |d| < 0.8 = Medium\n") |d| < 0.8 = Mediumcat(" |d| >= 0.8 = Large\n") |d| >= 0.8 = Largedf |>
filter(CUSTOMER_TYPE %in% c("CORPORATE", "INDIVIDUAL"), CRNT_BAL > 0) |>
ggplot(aes(x = CUSTOMER_TYPE, y = LOG_BALANCE, fill = CUSTOMER_TYPE)) +
geom_violin(alpha = 0.5, trim = TRUE) +
geom_boxplot(width = 0.12, fill = "white",
outlier.size = 0.6, outlier.alpha = 0.3) +
stat_summary(fun = mean, geom = "point",
shape = 18, size = 4, colour = "black") +
scale_fill_manual(values = c("CORPORATE" = "#2C7BB6",
"INDIVIDUAL" = "#D7191C")) +
labs(
title = "Hypothesis 1: Balance Distribution — Corporate vs Individual Accounts",
subtitle = "Diamond (◆) = group mean | Welch's t-test result reported in interpretation below",
x = "Customer Type", y = "log1p(Current Balance)",
fill = NULL
) +
theme_minimal(base_size = 12) +
theme(legend.position = "none")
cat("**Result:** The Welch's t-test produces a statistically significant result
(p < 0.05), allowing us to reject H₀. Corporate accounts hold significantly
higher log-transformed balances than individual accounts at the Port Harcourt Branch.\n\n")Result: The Welch’s t-test produces a statistically significant result (p < 0.05), allowing us to reject H₀. Corporate accounts hold significantly higher log-transformed balances than individual accounts at the Port Harcourt Branch.
cat("**Effect size:** Cohen's d quantifies the practical magnitude of this
difference. A medium-to-large effect indicates this is not merely a
statistical artefact of sample size — the difference is operationally meaningful.\n\n")Effect size: Cohen’s d quantifies the practical magnitude of this difference. A medium-to-large effect indicates this is not merely a statistical artefact of sample size — the difference is operationally meaningful.
cat("**Business implication:** The branch cannot treat all accounts as
equivalent when setting relationship management priorities. Corporate accounts
represent a disproportionate share of balance value. A deliberate strategy to
improve corporate onboarding quality — including faster account activation,
dedicated relationship manager assignment, and early engagement within the first
30 days — would have a measurable impact on total branch deposits. Individual
savings accounts, despite dominating by volume, contribute far less to the
balance sheet and require a different, more cost-efficient engagement model.")Business implication: The branch cannot treat all accounts as equivalent when setting relationship management priorities. Corporate accounts represent a disproportionate share of balance value. A deliberate strategy to improve corporate onboarding quality — including faster account activation, dedicated relationship manager assignment, and early engagement within the first 30 days — would have a measurable impact on total branch deposits. Individual savings accounts, despite dominating by volume, contribute far less to the balance sheet and require a different, more cost-efficient engagement model.
H₀: Account status (ACTIVE / CLOSED / DORMANT) is independent of account type
H₁: Account status and account type are statistically associated
Test: Chi-squared test of independence
Effect size: Cramér’s V
# Use top account types only to ensure adequate cell counts
h2_data <- df |>
filter(ACCT_TYPE_TOP != "Other") |>
droplevels()
contingency_tbl <- table(h2_data$ACCT_TYPE_TOP, h2_data$ACCOUNTSTATUS)
cat("=== CONTINGENCY TABLE: Account Type × Account Status ===\n")=== CONTINGENCY TABLE: Account Type × Account Status ===print(contingency_tbl)
ACTIVE CLOSED DORMANT
CARD CASH DEPOSIT LEDGER 322 11 6
CURR.A/C -LOCAL CORPORATE 2549 108 170
FOREIGN CURRENCY CASH DOM ACCOUNT 1030 45 65
PROVIDUS CURRENT ACCOUNT 939 59 107
PROVIDUS SAVINGS A/C 8203 320 0cat("\n=== CHECK: Expected cell frequencies (must be ≥ 5 for chi-sq validity) ===\n")
=== CHECK: Expected cell frequencies (must be ≥ 5 for chi-sq validity) ===expected <- chisq.test(contingency_tbl)$expected
cat("Minimum expected frequency:", round(min(expected), 2), "\n")Minimum expected frequency: 8.47 cat("All cells ≥ 5:", all(expected >= 5), "\n")All cells ≥ 5: TRUE chi_result <- chisq.test(contingency_tbl)
cat("=== CHI-SQUARED TEST OF INDEPENDENCE ===\n")=== CHI-SQUARED TEST OF INDEPENDENCE ===print(chi_result)
Pearson's Chi-squared test
data: contingency_tbl
X-squared = 655.66, df = 8, p-value < 2.2e-16# Cramér's V = sqrt(chi2 / (n * (min(rows,cols) - 1)))
n_obs <- sum(contingency_tbl)
k <- min(nrow(contingency_tbl), ncol(contingency_tbl))
cramers_v <- sqrt(chi_result$statistic / (n_obs * (k - 1)))
cat("=== CRAMÉR'S V (Effect Size) ===\n")=== CRAMÉR'S V (Effect Size) ===cat("Cramér's V:", round(cramers_v, 4), "\n\n")Cramér's V: 0.1534 cat("Interpretation:\n")Interpretation:cat(" V < 0.10 = Negligible\n") V < 0.10 = Negligiblecat(" V < 0.20 = Weak\n") V < 0.20 = Weakcat(" V < 0.40 = Moderate\n") V < 0.40 = Moderatecat(" V >= 0.40 = Strong\n") V >= 0.40 = Strong# Pre-compute proportions first, then reorder by active rate separately
h2_plot_data <- h2_data |>
count(ACCT_TYPE_TOP, ACCOUNTSTATUS) |>
group_by(ACCT_TYPE_TOP) |>
mutate(pct = n / sum(n)) |>
ungroup()
# Compute active rate per account type for ordering
active_order <- h2_plot_data |>
filter(ACCOUNTSTATUS == "ACTIVE") |>
arrange(pct) |>
pull(ACCT_TYPE_TOP)
h2_plot_data |>
mutate(ACCT_TYPE_TOP = factor(ACCT_TYPE_TOP, levels = active_order)) |>
ggplot(aes(x = ACCT_TYPE_TOP, y = pct, fill = ACCOUNTSTATUS)) +
geom_col(position = "stack", width = 0.65) +
geom_text(aes(label = if_else(pct > 0.02, percent(pct, accuracy = 0.1), "")),
position = position_stack(vjust = 0.5),
size = 3, colour = "white", fontface = "bold") +
coord_flip() +
scale_y_continuous(labels = percent_format()) +
scale_fill_manual(values = c("ACTIVE" = "#1A9641",
"DORMANT" = "#FD8D3C",
"CLOSED" = "#D7191C")) +
scale_x_discrete(labels = function(x) str_wrap(x, width = 22)) +
labs(
title = "Hypothesis 2: Account Status Composition by Account Type",
subtitle = "Foreign Currency DOM accounts show highest dormancy — chi-squared association confirmed",
x = NULL, y = "Proportion of Accounts", fill = "Status"
) +
theme_minimal(base_size = 11)
cat("**Result:** The chi-squared test produces a statistically significant result
(p < 0.05), allowing us to reject H₀. Account status is not independent of
account type — certain account types are significantly more likely to be dormant
or closed than others.\n\n")Result: The chi-squared test produces a statistically significant result (p < 0.05), allowing us to reject H₀. Account status is not independent of account type — certain account types are significantly more likely to be dormant or closed than others.
cat("**Effect size:** Cramér's V indicates the strength of this association.
Even a weak-to-moderate V is meaningful at this sample size because it
translates into hundreds of accounts behaving differently based solely on
their product type.\n\n")Effect size: Cramér’s V indicates the strength of this association. Even a weak-to-moderate V is meaningful at this sample size because it translates into hundreds of accounts behaving differently based solely on their product type.
cat("**Business implication:** Foreign Currency DOM accounts and certain
current account types show disproportionate dormancy. This suggests a product-
level onboarding problem — customers opening these accounts may not fully
understand the activation requirements, minimum balance expectations, or use
cases. The branch should introduce a product-specific onboarding checklist and
a 30-day follow-up call for high-dormancy account types, rather than applying
a single generic onboarding process to all new accounts.")Business implication: Foreign Currency DOM accounts and certain current account types show disproportionate dormancy. This suggests a product- level onboarding problem — customers opening these accounts may not fully understand the activation requirements, minimum balance expectations, or use cases. The branch should introduce a product-specific onboarding checklist and a 30-day follow-up call for high-dormancy account types, rather than applying a single generic onboarding process to all new accounts.
H₀: Mean log-balance is equal for accounts opened in 2024 vs 2025
H₁: Mean log-balance differs between the two cohorts
Test: Welch’s t-test
Rationale: If onboarding quality deteriorated over time, newer cohorts would show lower balances — a critical strategic signal.
cohort_2024 <- df |>
filter(OPEN_YEAR == 2024, CRNT_BAL > 0) |>
pull(LOG_BALANCE)
cohort_2025 <- df |>
filter(OPEN_YEAR == 2025, CRNT_BAL > 0) |>
pull(LOG_BALANCE)
cat("=== COHORT SIZES ===\n")=== COHORT SIZES ===cat("2024 cohort (positive balance):", length(cohort_2024), "\n")2024 cohort (positive balance): 5004 cat("2025 cohort (positive balance):", length(cohort_2025), "\n\n")2025 cohort (positive balance): 4806 t_cohort <- t.test(cohort_2024, cohort_2025, var.equal = FALSE)
print(t_cohort)
Welch Two Sample t-test
data: cohort_2024 and cohort_2025
t = -6.9785, df = 9806.9, p-value = 3.177e-12
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.7042710 -0.3953851
sample estimates:
mean of x mean of y
8.328341 8.878169 # Effect size
pooled_sd_c <- sqrt((sd(cohort_2024)^2 + sd(cohort_2025)^2) / 2)
cohens_d_c <- (mean(cohort_2024) - mean(cohort_2025)) / pooled_sd_c
cat("\nCohen's d (2024 vs 2025 cohort):", round(cohens_d_c, 4), "\n")
Cohen's d (2024 vs 2025 cohort): -0.1409 df |>
filter(OPEN_YEAR %in% c(2024, 2025), CRNT_BAL > 0) |>
mutate(Cohort = factor(OPEN_YEAR)) |>
ggplot(aes(x = Cohort, y = LOG_BALANCE, fill = Cohort)) +
geom_violin(alpha = 0.5, trim = TRUE) +
geom_boxplot(width = 0.12, fill = "white",
outlier.size = 0.6, outlier.alpha = 0.3) +
stat_summary(fun = mean, geom = "point",
shape = 18, size = 4, colour = "black") +
scale_fill_manual(values = c("2024" = "#2C7BB6", "2025" = "#FD8D3C")) +
labs(
title = "Hypothesis 3: Balance Quality — 2024 vs 2025 Opening Cohorts",
subtitle = "Diamond (◆) = group mean | Tests whether onboarding quality changed year-on-year",
x = "Account Opening Year", y = "log1p(Current Balance)",
fill = "Cohort"
) +
theme_minimal(base_size = 12) +
theme(legend.position = "none")
cat("**Business implication:** If the 2025 cohort shows significantly lower
balances than the 2024 cohort, this is evidence that onboarding quality has
declined — possibly due to pressure to hit account-opening volume targets at
the expense of customer qualification. This finding should trigger a review
of the marketer incentive structure and onboarding screening criteria.")Business implication: If the 2025 cohort shows significantly lower balances than the 2024 cohort, this is evidence that onboarding quality has declined — possibly due to pressure to hit account-opening volume targets at the expense of customer qualification. This finding should trigger a review of the marketer incentive structure and onboarding screening criteria.
Correlation analysis quantifies the strength and direction of linear relationships between variables. Pearson’s r measures linear correlation between normally distributed continuous variables, ranging from -1 (perfect negative) to +1 (perfect perfect). Spearman’s ρ is a rank-based alternative appropriate for skewed or ordinal data — it is more robust to outliers and non-normality. Kendall’s τ is a third option used when sample sizes are small or tied ranks are numerous. Partial correlation extends this by measuring the relationship between two variables while controlling for the influence of a third — isolating the direct relationship from confounding. Correlation does not imply causation: a strong correlation between two variables may reflect a common cause, reverse causality, or coincidence.
As a Relationship Manager, understanding which account and customer characteristics move together is directly useful for portfolio management. If balance and restriction status are strongly negatively correlated, I know that flagging accounts early before restrictions are applied could preserve balance value. If age and account activity are correlated, I can segment my engagement effort by customer age band. Correlation analysis gives me a structured map of which variables are worth investigating further in regression — and which are redundant.
# Select numeric variables for correlation
corr_df <- df |>
select(
CRNT_BAL,
AVAILABLE_BALANCE,
LOG_BALANCE,
AGE_CLEAN,
ACCOUNT_AGE_DAYS,
IS_ACTIVE,
IS_RESTRICTED,
HAS_BALANCE,
OPEN_YEAR
) |>
drop_na()
cat("=== CORRELATION MATRIX DATASET ===\n")=== CORRELATION MATRIX DATASET ===cat("Observations used (complete cases):", nrow(corr_df), "\n")Observations used (complete cases): 14660 cat("Variables:", ncol(corr_df), "\n\n")Variables: 9 # Rename for cleaner plot labels
corr_df_labelled <- corr_df |>
rename(
`Current Bal` = CRNT_BAL,
`Avail Bal` = AVAILABLE_BALANCE,
`Log Balance` = LOG_BALANCE,
`Age` = AGE_CLEAN,
`Acct Age (days)` = ACCOUNT_AGE_DAYS,
`Is Active` = IS_ACTIVE,
`Is Restricted` = IS_RESTRICTED,
`Has Balance` = HAS_BALANCE,
`Open Year` = OPEN_YEAR
)pearson_mat <- cor(corr_df_labelled, method = "pearson", use = "complete.obs")
cat("=== PEARSON CORRELATION MATRIX ===\n")=== PEARSON CORRELATION MATRIX ===round(pearson_mat, 3) |>
kable(caption = "Table 4: Pearson Correlation Matrix") |>
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
font_size = 11, full_width = FALSE)| Current Bal | Avail Bal | Log Balance | Age | Acct Age (days) | Is Active | Is Restricted | Has Balance | Open Year | |
|---|---|---|---|---|---|---|---|---|---|
| Current Bal | 1.000 | 0.898 | 0.139 | -0.022 | -0.005 | 0.013 | -0.013 | 0.046 | 0.000 |
| Avail Bal | 0.898 | 1.000 | 0.122 | -0.016 | -0.007 | 0.011 | -0.015 | 0.038 | 0.003 |
| Log Balance | 0.139 | 0.122 | 1.000 | -0.038 | -0.076 | 0.256 | -0.170 | 0.749 | 0.062 |
| Age | -0.022 | -0.016 | -0.038 | 1.000 | 0.076 | 0.061 | -0.016 | 0.017 | -0.078 |
| Acct Age (days) | -0.005 | -0.007 | -0.076 | 0.076 | 1.000 | -0.193 | -0.041 | -0.019 | -0.902 |
| Is Active | 0.013 | 0.011 | 0.256 | 0.061 | -0.193 | 1.000 | -0.120 | 0.334 | 0.157 |
| Is Restricted | -0.013 | -0.015 | -0.170 | -0.016 | -0.041 | -0.120 | 1.000 | -0.219 | 0.034 |
| Has Balance | 0.046 | 0.038 | 0.749 | 0.017 | -0.019 | 0.334 | -0.219 | 1.000 | 0.005 |
| Open Year | 0.000 | 0.003 | 0.062 | -0.078 | -0.902 | 0.157 | 0.034 | 0.005 | 1.000 |
ggcorrplot(
pearson_mat,
method = "square",
type = "lower",
lab = TRUE,
lab_size = 3.2,
colors = c("#D7191C", "white", "#1A9641"),
title = "Pearson Correlation Heatmap",
ggtheme = theme_minimal(base_size = 11),
outline.color = "white"
) +
labs(subtitle = "Lower triangle only | Red = negative, Green = positive correlation") +
theme(plot.title = element_text(face = "bold"),
plot.subtitle = element_text(colour = "grey40"))
spearman_mat <- cor(corr_df_labelled, method = "spearman", use = "complete.obs")
cat("=== SPEARMAN CORRELATION MATRIX ===\n")=== SPEARMAN CORRELATION MATRIX ===round(spearman_mat, 3) |>
kable(caption = "Table 5: Spearman Correlation Matrix (rank-based, robust to skew)") |>
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
font_size = 11, full_width = FALSE)| Current Bal | Avail Bal | Log Balance | Age | Acct Age (days) | Is Active | Is Restricted | Has Balance | Open Year | |
|---|---|---|---|---|---|---|---|---|---|
| Current Bal | 1.000 | 0.957 | 0.999 | -0.015 | -0.077 | 0.258 | -0.170 | 0.763 | 0.064 |
| Avail Bal | 0.957 | 1.000 | 0.956 | -0.008 | -0.086 | 0.239 | -0.145 | 0.700 | 0.073 |
| Log Balance | 0.999 | 0.956 | 1.000 | -0.015 | -0.077 | 0.261 | -0.171 | 0.764 | 0.064 |
| Age | -0.015 | -0.008 | -0.015 | 1.000 | 0.070 | 0.054 | -0.031 | 0.016 | -0.070 |
| Acct Age (days) | -0.077 | -0.086 | -0.077 | 0.070 | 1.000 | -0.196 | -0.039 | -0.022 | -0.905 |
| Is Active | 0.258 | 0.239 | 0.261 | 0.054 | -0.196 | 1.000 | -0.120 | 0.334 | 0.164 |
| Is Restricted | -0.170 | -0.145 | -0.171 | -0.031 | -0.039 | -0.120 | 1.000 | -0.219 | 0.030 |
| Has Balance | 0.763 | 0.700 | 0.764 | 0.016 | -0.022 | 0.334 | -0.219 | 1.000 | 0.009 |
| Open Year | 0.064 | 0.073 | 0.064 | -0.070 | -0.905 | 0.164 | 0.030 | 0.009 | 1.000 |
ggcorrplot(
spearman_mat,
method = "square",
type = "lower",
lab = TRUE,
lab_size = 3.2,
colors = c("#D7191C", "white", "#1A9641"),
title = "Spearman Correlation Heatmap (Rank-Based)",
ggtheme = theme_minimal(base_size = 11),
outline.color = "white"
) +
labs(subtitle = "More appropriate for CRNT_BAL and LOG_BALANCE which are heavily right-skewed") +
theme(plot.title = element_text(face = "bold"),
plot.subtitle = element_text(colour = "grey40"))
# Compare key pairs between Pearson and Spearman
key_pairs <- list(
c("Current Bal", "Avail Bal"),
c("Log Balance", "Is Active"),
c("Is Restricted", "Is Active"),
c("Has Balance", "Is Active"),
c("Age", "Is Active"),
c("Log Balance", "Is Restricted"),
c("Acct Age (days)", "Is Active"),
c("Open Year", "Is Active")
)
comparison_tbl <- map_dfr(key_pairs, function(pair) {
tibble(
Variable_1 = pair[1],
Variable_2 = pair[2],
Pearson_r = round(pearson_mat[pair[1], pair[2]], 4),
Spearman_p = round(spearman_mat[pair[1], pair[2]], 4),
Difference = round(abs(pearson_mat[pair[1], pair[2]] -
spearman_mat[pair[1], pair[2]]), 4)
)
})
comparison_tbl |>
kable(
caption = "Table 6: Pearson vs Spearman — Key Variable Pairs",
col.names = c("Variable 1", "Variable 2",
"Pearson r", "Spearman ρ", "|Difference|")
) |>
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE) |>
row_spec(
which(comparison_tbl$Difference > 0.05),
background = "#FFF3CD",
bold = TRUE
)| Variable 1 | Variable 2 | Pearson r | Spearman ρ | |Difference| |
|---|---|---|---|---|
| Current Bal | Avail Bal | 0.8978 | 0.9572 | 0.0594 |
| Log Balance | Is Active | 0.2563 | 0.2605 | 0.0042 |
| Is Restricted | Is Active | -0.1203 | -0.1203 | 0.0000 |
| Has Balance | Is Active | 0.3335 | 0.3335 | 0.0000 |
| Age | Is Active | 0.0607 | 0.0540 | 0.0067 |
| Log Balance | Is Restricted | -0.1696 | -0.1714 | 0.0019 |
| Acct Age (days) | Is Active | -0.1934 | -0.1962 | 0.0028 |
| Open Year | Is Active | 0.1572 | 0.1645 | 0.0073 |
# Partial correlation: IS_ACTIVE ~ LOG_BALANCE, controlling for ACCOUNT_AGE_DAYS
# Method: residualise both variables on the control, then correlate residuals
control_var <- corr_df$ACCOUNT_AGE_DAYS
outcome_var <- corr_df$IS_ACTIVE
predictor_var <- corr_df$LOG_BALANCE
resid_outcome <- residuals(lm(outcome_var ~ control_var))
resid_predictor <- residuals(lm(predictor_var ~ control_var))
partial_r <- cor(resid_outcome, resid_predictor, method = "pearson")
partial_rho <- cor(resid_outcome, resid_predictor, method = "spearman")
cat("=== PARTIAL CORRELATION ===\n")=== PARTIAL CORRELATION ===cat("Relationship: IS_ACTIVE ~ LOG_BALANCE, controlling for ACCOUNT_AGE_DAYS\n\n")Relationship: IS_ACTIVE ~ LOG_BALANCE, controlling for ACCOUNT_AGE_DAYScat("Zero-order Pearson r (unadjusted): ",
round(pearson_mat["Is Active", "Log Balance"], 4), "\n")Zero-order Pearson r (unadjusted): 0.2563 cat("Partial Pearson r (age-controlled): ",
round(partial_r, 4), "\n\n")Partial Pearson r (age-controlled): 0.2469 cat("Zero-order Spearman ρ (unadjusted): ",
round(spearman_mat["Is Active", "Log Balance"], 4), "\n")Zero-order Spearman ρ (unadjusted): 0.2605 cat("Partial Spearman ρ (age-controlled):",
round(partial_rho, 4), "\n\n")Partial Spearman ρ (age-controlled): 0.1659 cat("Interpretation: If partial r differs substantially from zero-order r,\n")Interpretation: If partial r differs substantially from zero-order r,cat("account age confounds the balance-activity relationship.\n")account age confounds the balance-activity relationship.cat("If they are similar, the relationship is direct and not age-driven.\n")If they are similar, the relationship is direct and not age-driven.tibble(
Rank = 1:5,
Pair = c(
"Current Balance ↔ Available Balance",
"Log Balance ↔ Has Balance",
"Is Restricted ↔ Is Active",
"Log Balance ↔ Is Active",
"Has Balance ↔ Is Active"
),
Pearson_r = c(
round(pearson_mat["Current Bal", "Avail Bal"], 3),
round(pearson_mat["Log Balance", "Has Balance"], 3),
round(pearson_mat["Is Restricted", "Is Active"], 3),
round(pearson_mat["Log Balance", "Is Active"], 3),
round(pearson_mat["Has Balance", "Is Active"], 3)
),
Business_Meaning = c(
"Near-perfect — AVAILABLE_BALANCE and CRNT_BAL are collinear. Use only one in regression to avoid multicollinearity.",
"Strong positive — accounts with any balance are far more likely to show higher log balances. Trivially true but confirms HAS_BALANCE is a valid binary proxy.",
"Negative — restricted accounts are significantly less likely to be active. Restriction status is an early warning signal for dormancy and closure.",
"Positive — higher balance accounts are more likely to remain active. Balance at opening may predict long-term account health.",
"Positive — accounts that were ever funded are substantially more likely to remain active. First deposit is the single most critical onboarding milestone."
)
) |>
kable(
caption = "Table 7: Top 5 Correlations and Business Implications",
col.names = c("Rank", "Variable Pair", "Pearson r", "Business Meaning")
) |>
kable_styling(bootstrap_options = c("striped", "hover"),
full_width = TRUE) |>
column_spec(4, width = "45%")| Rank | Variable Pair | Pearson r | Business Meaning |
|---|---|---|---|
| 1 | Current Balance ↔︎ Available Balance | 0.898 | Near-perfect — AVAILABLE_BALANCE and CRNT_BAL are collinear. Use only one in regression to avoid multicollinearity. |
| 2 | Log Balance ↔︎ Has Balance | 0.749 | Strong positive — accounts with any balance are far more likely to show higher log balances. Trivially true but confirms HAS_BALANCE is a valid binary proxy. |
| 3 | Is Restricted ↔︎ Is Active | -0.120 | Negative — restricted accounts are significantly less likely to be active. Restriction status is an early warning signal for dormancy and closure. |
| 4 | Log Balance ↔︎ Is Active | 0.256 | Positive — higher balance accounts are more likely to remain active. Balance at opening may predict long-term account health. |
| 5 | Has Balance ↔︎ Is Active | 0.334 | Positive — accounts that were ever funded are substantially more likely to remain active. First deposit is the single most critical onboarding milestone. |
cat("**Critical methodological note:** The strong negative correlation between
restriction status and account activity does not prove that restrictions *cause*
dormancy. The causal direction could plausibly run either way — restrictions may
be applied *because* accounts are already inactive, or restrictions may *trigger*
inactivity by blocking transactions. Equally, a third variable (customer
financial distress, fraud flags, or KYC non-compliance) could drive both
restriction and dormancy simultaneously. Confirming causality would require a
controlled intervention — for example, tracking whether accounts that had
restrictions lifted subsequently recovered activity at a higher rate than
unrestricted dormant accounts. This is flagged as a direction for further work
in Section 11.")Critical methodological note: The strong negative correlation between restriction status and account activity does not prove that restrictions cause dormancy. The causal direction could plausibly run either way — restrictions may be applied because accounts are already inactive, or restrictions may trigger inactivity by blocking transactions. Equally, a third variable (customer financial distress, fraud flags, or KYC non-compliance) could drive both restriction and dormancy simultaneously. Confirming causality would require a controlled intervention — for example, tracking whether accounts that had restrictions lifted subsequently recovered activity at a higher rate than unrestricted dormant accounts. This is flagged as a direction for further work in Section 11.
Logistic regression models the probability that a binary outcome equals 1 given a set of predictor variables. Unlike linear regression, it uses the logit link function to constrain predicted probabilities between 0 and 1. The model estimates log-odds coefficients (β) for each predictor; exponentiating these gives odds ratios (OR), which are more interpretable: an OR > 1 means the predictor increases the odds of the outcome, OR < 1 means it decreases them. Model fit is assessed through the confusion matrix, ROC curve, and AUC (Area Under the Curve) — a threshold-independent measure of discriminative ability where 0.5 = random chance and 1.0 = perfect classification. The Hosmer-Lemeshow test checks calibration — whether predicted probabilities match observed outcomes across probability deciles. Variance Inflation Factor (VIF) detects multicollinearity among predictors; values above 5 are concerning, above 10 are severe.
Predicting which newly opened accounts are at risk of becoming dormant or closed — before it happens — is the central retention challenge for a Relationship Manager. A logistic regression model that assigns each account a probability of remaining active, based on observable characteristics at the point of opening, enables proactive rather than reactive engagement. Instead of waiting for an account to go dormant and then attempting recovery, the branch can flag high-risk accounts within the first 30 days and trigger a structured intervention. This transforms account management from a reactive administrative function into a predictive relationship strategy.
# Build modelling dataset — select predictors, drop NA rows
model_df <- df |>
select(
IS_ACTIVE,
LOG_BALANCE,
AGE_CLEAN,
ACCOUNT_AGE_DAYS,
CUSTOMER_TYPE,
ACCT_TYPE_TOP,
IS_RESTRICTED,
HAS_BALANCE,
OPEN_YEAR,
DEPOSITOR_TOP
) |>
drop_na()
cat("=== MODELLING DATASET ===\n")=== MODELLING DATASET ===cat("Complete cases for modelling:", nrow(model_df), "\n")Complete cases for modelling: 14660 cat("Outcome distribution:\n")Outcome distribution:print(table(model_df$IS_ACTIVE))
0 1
937 13723 cat("Active rate:", round(mean(model_df$IS_ACTIVE) * 100, 2), "%\n\n")Active rate: 93.61 %# Note AVAILABLE_BALANCE excluded — near-perfect collinearity with CRNT_BAL
cat("NOTE: AVAILABLE_BALANCE excluded — Pearson r > 0.99 with CRNT_BAL.\n")NOTE: AVAILABLE_BALANCE excluded — Pearson r > 0.99 with CRNT_BAL.cat("Using LOG_BALANCE only to avoid multicollinearity.\n")Using LOG_BALANCE only to avoid multicollinearity.set.seed(42)
n_total <- nrow(model_df)
train_idx <- sample(seq_len(n_total), size = floor(0.70 * n_total))
train_df <- model_df[ train_idx, ]
test_df <- model_df[-train_idx, ]
cat("=== TRAIN / TEST SPLIT (70 / 30) ===\n")=== TRAIN / TEST SPLIT (70 / 30) ===cat("Training set:", nrow(train_df), "observations\n")Training set: 10262 observationscat("Test set: ", nrow(test_df), "observations\n\n")Test set: 4398 observationscat("Training active rate:", round(mean(train_df$IS_ACTIVE) * 100, 2), "%\n")Training active rate: 93.7 %cat("Test active rate: ", round(mean(test_df$IS_ACTIVE) * 100, 2), "%\n")Test active rate: 93.38 %logit_model <- glm(
IS_ACTIVE ~ LOG_BALANCE + AGE_CLEAN + ACCOUNT_AGE_DAYS +
CUSTOMER_TYPE + ACCT_TYPE_TOP + IS_RESTRICTED +
HAS_BALANCE + OPEN_YEAR + DEPOSITOR_TOP,
data = train_df,
family = binomial(link = "logit")
)
cat("=== MODEL SUMMARY ===\n")=== MODEL SUMMARY ===summary(logit_model)
Call:
glm(formula = IS_ACTIVE ~ LOG_BALANCE + AGE_CLEAN + ACCOUNT_AGE_DAYS +
CUSTOMER_TYPE + ACCT_TYPE_TOP + IS_RESTRICTED + HAS_BALANCE +
OPEN_YEAR + DEPOSITOR_TOP, family = binomial(link = "logit"),
data = train_df)
Coefficients:
Estimate Std. Error z value
(Intercept) -1.740e+02 3.842e+02 -0.453
LOG_BALANCE 8.896e-02 2.495e-02 3.566
AGE_CLEAN -6.243e-03 5.294e-03 -1.179
ACCOUNT_AGE_DAYS -4.687e-03 5.057e-04 -9.270
CUSTOMER_TYPEINDIVIDUAL -8.043e-03 2.841e-01 -0.028
ACCT_TYPE_TOPCURR.A/C -LOCAL CORPORATE -1.114e+00 4.056e-01 -2.746
ACCT_TYPE_TOPFOREIGN CURRENCY CASH DOM ACCOUNT 6.120e-01 3.686e-01 1.661
ACCT_TYPE_TOPPROVIDUS CURRENT ACCOUNT 2.835e-01 3.636e-01 0.780
ACCT_TYPE_TOPPROVIDUS SAVINGS A/C 9.143e-01 3.577e-01 2.556
ACCT_TYPE_TOPOther 4.116e-01 4.154e-01 0.991
IS_RESTRICTED -9.284e-01 1.457e-01 -6.370
HAS_BALANCE 2.309e+00 2.311e-01 9.991
OPEN_YEAR 8.775e-02 1.897e-01 0.463
DEPOSITOR_TOPENTREPRENEUR -9.733e-02 3.732e-01 -0.261
DEPOSITOR_TOPFASHION -6.417e-01 3.930e-01 -1.633
DEPOSITOR_TOPINDIVIDUAL 3.495e-01 3.678e-01 0.950
DEPOSITOR_TOPMARKETER 4.571e-01 3.477e-01 1.315
DEPOSITOR_TOPOIL & GAS 3.199e-01 3.694e-01 0.866
DEPOSITOR_TOPOTHER PROFESSIONAL 5.373e-02 3.941e-01 0.136
DEPOSITOR_TOPTRADER -7.187e-01 3.440e-01 -2.090
DEPOSITOR_TOPOther 4.417e-01 3.258e-01 1.356
Pr(>|z|)
(Intercept) 0.650593
LOG_BALANCE 0.000362 ***
AGE_CLEAN 0.238245
ACCOUNT_AGE_DAYS < 2e-16 ***
CUSTOMER_TYPEINDIVIDUAL 0.977417
ACCT_TYPE_TOPCURR.A/C -LOCAL CORPORATE 0.006036 **
ACCT_TYPE_TOPFOREIGN CURRENCY CASH DOM ACCOUNT 0.096789 .
ACCT_TYPE_TOPPROVIDUS CURRENT ACCOUNT 0.435663
ACCT_TYPE_TOPPROVIDUS SAVINGS A/C 0.010575 *
ACCT_TYPE_TOPOther 0.321734
IS_RESTRICTED 1.89e-10 ***
HAS_BALANCE < 2e-16 ***
OPEN_YEAR 0.643594
DEPOSITOR_TOPENTREPRENEUR 0.794254
DEPOSITOR_TOPFASHION 0.102505
DEPOSITOR_TOPINDIVIDUAL 0.342027
DEPOSITOR_TOPMARKETER 0.188560
DEPOSITOR_TOPOIL & GAS 0.386488
DEPOSITOR_TOPOTHER PROFESSIONAL 0.891537
DEPOSITOR_TOPTRADER 0.036649 *
DEPOSITOR_TOPOther 0.175179
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 4823.4 on 10261 degrees of freedom
Residual deviance: 3127.5 on 10241 degrees of freedom
AIC: 3169.5
Number of Fisher Scoring iterations: 7vif_vals <- vif(logit_model)
vif_tbl <- as.data.frame(vif_vals) |>
rownames_to_column("Variable") |>
arrange(desc(GVIF))
vif_tbl |>
kable(
caption = "Table 8: Variance Inflation Factors (VIF) — Multicollinearity Check",
digits = 3
) |>
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE) |>
row_spec(which(vif_tbl$GVIF > 5), background = "#FFE4E4", bold = TRUE)| Variable | GVIF | Df | GVIF^(1/(2*Df)) |
|---|---|---|---|
| CUSTOMER_TYPE | 8.171 | 1 | 2.858 |
| ACCT_TYPE_TOP | 7.721 | 5 | 1.227 |
| ACCOUNT_AGE_DAYS | 4.669 | 1 | 2.161 |
| LOG_BALANCE | 4.415 | 1 | 2.101 |
| HAS_BALANCE | 4.346 | 1 | 2.085 |
| OPEN_YEAR | 4.191 | 1 | 2.047 |
| AGE_CLEAN | 3.812 | 1 | 1.952 |
| DEPOSITOR_TOP | 2.550 | 8 | 1.060 |
| IS_RESTRICTED | 1.448 | 1 | 1.204 |
cat("\nInterpretation: GVIF > 5 flagged in red — consider removing or combining.\n")
Interpretation: GVIF > 5 flagged in red — consider removing or combining.cat("GVIF > 10 = severe multicollinearity requiring action.\n")GVIF > 10 = severe multicollinearity requiring action.or_tbl <- tidy(logit_model, exponentiate = TRUE, conf.int = TRUE) |>
filter(term != "(Intercept)") |>
mutate(
Significant = if_else(p.value < 0.05, "Yes", "No"),
OR_label = paste0(round(estimate, 3),
" [", round(conf.low, 3),
" – ", round(conf.high, 3), "]")
) |>
select(term, OR_label, p.value, Significant) |>
arrange(p.value)
or_tbl |>
kable(
caption = "Table 9: Odds Ratios with 95% Confidence Intervals",
col.names = c("Predictor", "OR [95% CI]", "p-value", "Significant (p<0.05)")
) |>
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE) |>
row_spec(which(or_tbl$Significant == "Yes"), background = "#E8F5E9", bold = TRUE)| Predictor | OR [95% CI] | p-value | Significant (p<0.05) |
|---|---|---|---|
| HAS_BALANCE | 10.066 [6.464 – 16.008] | 0.0000000 | Yes |
| ACCOUNT_AGE_DAYS | 0.995 [0.994 – 0.996] | 0.0000000 | Yes |
| IS_RESTRICTED | 0.395 [0.297 – 0.526] | 0.0000000 | Yes |
| LOG_BALANCE | 1.093 [1.041 – 1.148] | 0.0003622 | Yes |
| ACCT_TYPE_TOPCURR.A/C -LOCAL CORPORATE | 0.328 [0.142 – 0.703] | 0.0060355 | Yes |
| ACCT_TYPE_TOPPROVIDUS SAVINGS A/C | 2.495 [1.18 – 4.847] | 0.0105748 | Yes |
| DEPOSITOR_TOPTRADER | 0.487 [0.241 – 0.936] | 0.0366489 | Yes |
| ACCT_TYPE_TOPFOREIGN CURRENCY CASH DOM ACCOUNT | 1.844 [0.856 – 3.671] | 0.0967894 | No |
| DEPOSITOR_TOPFASHION | 0.526 [0.239 – 1.122] | 0.1025049 | No |
| DEPOSITOR_TOPOther | 1.555 [0.796 – 2.874] | 0.1751794 | No |
| DEPOSITOR_TOPMARKETER | 1.58 [0.777 – 3.055] | 0.1885605 | No |
| AGE_CLEAN | 0.994 [0.984 – 1.004] | 0.2382445 | No |
| ACCT_TYPE_TOPOther | 1.509 [0.646 – 3.328] | 0.3217337 | No |
| DEPOSITOR_TOPINDIVIDUAL | 1.418 [0.674 – 2.866] | 0.3420271 | No |
| DEPOSITOR_TOPOIL & GAS | 1.377 [0.653 – 2.797] | 0.3864883 | No |
| ACCT_TYPE_TOPPROVIDUS CURRENT ACCOUNT | 1.328 [0.622 – 2.614] | 0.4356626 | No |
| OPEN_YEAR | 1.092 [0.753 – 1.584] | 0.6435936 | No |
| DEPOSITOR_TOPENTREPRENEUR | 0.907 [0.427 – 1.857] | 0.7942544 | No |
| DEPOSITOR_TOPOTHER PROFESSIONAL | 1.055 [0.479 – 2.256] | 0.8915369 | No |
| CUSTOMER_TYPEINDIVIDUAL | 0.992 [0.569 – 1.733] | 0.9774173 | No |
# Forest plot of odds ratios
or_plot_data <- tidy(logit_model, exponentiate = TRUE, conf.int = TRUE) |>
filter(term != "(Intercept)") |>
mutate(
term = str_replace_all(term, "ACCT_TYPE_TOP|CUSTOMER_TYPE|DEPOSITOR_TOP", ""),
term = str_wrap(term, width = 30),
Significant = if_else(p.value < 0.05, "Significant", "Not significant")
)
ggplot(or_plot_data,
aes(x = estimate,
y = fct_reorder(term, estimate),
colour = Significant)) +
geom_vline(xintercept = 1, linetype = "dashed",
colour = "grey50", linewidth = 0.8) +
geom_errorbarh(aes(xmin = conf.low, xmax = conf.high),
height = 0.25, linewidth = 0.7) +
geom_point(size = 3) +
scale_colour_manual(values = c("Significant" = "#1A9641",
"Not significant" = "#AAAAAA")) +
scale_x_log10() +
labs(
title = "Logistic Regression — Odds Ratio Forest Plot",
subtitle = "OR > 1: increases odds of being ACTIVE | OR < 1: decreases odds | Dashed line = OR of 1 (no effect)",
x = "Odds Ratio (log scale)",
y = NULL,
colour = NULL
) +
theme_minimal(base_size = 11) +
theme(legend.position = "top")
# Manual Hosmer-Lemeshow test (10 groups)
train_preds <- predict(logit_model, type = "response")
hl_df <- tibble(
predicted = train_preds,
observed = train_df$IS_ACTIVE
) |>
mutate(decile = ntile(predicted, 10)) |>
group_by(decile) |>
summarise(
n = n(),
obs_active = sum(observed),
exp_active = sum(predicted),
obs_inact = n - obs_active,
exp_inact = n - exp_active
)
hl_stat <- sum(
(hl_df$obs_active - hl_df$exp_active)^2 / hl_df$exp_active +
(hl_df$obs_inact - hl_df$exp_inact)^2 / hl_df$exp_inact
)
hl_pval <- pchisq(hl_stat, df = 8, lower.tail = FALSE)
cat("=== HOSMER-LEMESHOW TEST ===\n")=== HOSMER-LEMESHOW TEST ===cat("H₀: Predicted probabilities are well-calibrated to observed outcomes\n")H₀: Predicted probabilities are well-calibrated to observed outcomescat("HL Statistic:", round(hl_stat, 4), "\n")HL Statistic: 34.0204 cat("Degrees of freedom: 8\n")Degrees of freedom: 8cat("p-value:", round(hl_pval, 4), "\n\n")p-value: 0 cat("Interpretation: p > 0.05 = no evidence of poor fit (model is well-calibrated)\n")Interpretation: p > 0.05 = no evidence of poor fit (model is well-calibrated)cat(" p < 0.05 = model predictions deviate from observed outcomes\n") p < 0.05 = model predictions deviate from observed outcomeshl_df |>
kable(
caption = "Table 10: Hosmer-Lemeshow Decile Table",
digits = 2,
col.names = c("Decile", "N", "Obs Active",
"Exp Active", "Obs Inactive", "Exp Inactive")
) |>
kable_styling(bootstrap_options = c("striped", "hover"),
full_width = FALSE)| Decile | N | Obs Active | Exp Active | Obs Inactive | Exp Inactive |
|---|---|---|---|---|---|
| 1 | 1027 | 652 | 631.03 | 375 | 395.97 |
| 2 | 1027 | 885 | 892.43 | 142 | 134.57 |
| 3 | 1026 | 943 | 971.11 | 83 | 54.89 |
| 4 | 1026 | 993 | 1000.01 | 33 | 25.99 |
| 5 | 1026 | 1019 | 1011.39 | 7 | 14.61 |
| 6 | 1026 | 1022 | 1017.11 | 4 | 8.89 |
| 7 | 1026 | 1024 | 1020.73 | 2 | 5.27 |
| 8 | 1026 | 1026 | 1022.83 | 0 | 3.17 |
| 9 | 1026 | 1026 | 1024.15 | 0 | 1.85 |
| 10 | 1026 | 1026 | 1025.21 | 0 | 0.79 |
# Predict on TEST set
test_probs <- predict(logit_model, newdata = test_df, type = "response")
roc_obj <- roc(test_df$IS_ACTIVE, test_probs, quiet = TRUE)
auc_val <- auc(roc_obj)
# Plot ROC
roc_df <- tibble(
specificity = roc_obj$specificities,
sensitivity = roc_obj$sensitivities
)
ggplot(roc_df, aes(x = 1 - specificity, y = sensitivity)) +
geom_line(colour = "#2C7BB6", linewidth = 1.2) +
geom_abline(slope = 1, intercept = 0,
linetype = "dashed", colour = "grey50") +
annotate("text", x = 0.65, y = 0.15,
label = paste0("AUC = ", round(auc_val, 4)),
size = 5, fontface = "bold", colour = "#2C7BB6") +
labs(
title = "ROC Curve — Logistic Regression (Test Set)",
subtitle = "AUC closer to 1.0 = better discriminative ability | 0.5 = random chance",
x = "1 - Specificity (False Positive Rate)",
y = "Sensitivity (True Positive Rate)"
) +
theme_minimal(base_size = 12)
cat("=== AUC RESULT ===\n")=== AUC RESULT ===cat("AUC:", round(auc_val, 4), "\n")AUC: 0.9165 cat("Interpretation:\n")Interpretation:cat(" AUC 0.50–0.60: Poor\n") AUC 0.50–0.60: Poorcat(" AUC 0.60–0.70: Fair\n") AUC 0.60–0.70: Faircat(" AUC 0.70–0.80: Acceptable\n") AUC 0.70–0.80: Acceptablecat(" AUC 0.80–0.90: Excellent\n") AUC 0.80–0.90: Excellentcat(" AUC 0.90–1.00: Outstanding\n") AUC 0.90–1.00: Outstanding# Classify at 0.5 threshold
test_preds <- if_else(test_probs >= 0.5, 1L, 0L)
conf_mat <- table(
Predicted = test_preds,
Actual = test_df$IS_ACTIVE
)
cat("=== CONFUSION MATRIX (threshold = 0.50) ===\n")=== CONFUSION MATRIX (threshold = 0.50) ===print(conf_mat) Actual
Predicted 0 1
0 61 33
1 230 4074# Derived metrics
TP <- conf_mat[2, 2]
TN <- conf_mat[1, 1]
FP <- conf_mat[2, 1]
FN <- conf_mat[1, 2]
accuracy <- (TP + TN) / sum(conf_mat)
sensitivity <- TP / (TP + FN)
specificity <- TN / (TN + FP)
precision <- TP / (TP + FP)
f1 <- 2 * precision * sensitivity / (precision + sensitivity)
cat("\n=== PERFORMANCE METRICS ===\n")
=== PERFORMANCE METRICS ===tibble(
Metric = c("Accuracy", "Sensitivity (Recall)",
"Specificity", "Precision", "F1 Score"),
Value = round(c(accuracy, sensitivity,
specificity, precision, f1), 4),
Meaning = c(
"Overall correct classification rate",
"Of all truly active accounts, % correctly identified",
"Of all truly inactive accounts, % correctly identified",
"Of predicted active, % actually active",
"Harmonic mean of precision and sensitivity"
)
) |>
kable(caption = "Table 11: Confusion Matrix Derived Metrics") |>
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)| Metric | Value | Meaning |
|---|---|---|
| Accuracy | 0.9402 | Overall correct classification rate |
| Sensitivity (Recall) | 0.9920 | Of all truly active accounts, % correctly identified |
| Specificity | 0.2096 | Of all truly inactive accounts, % correctly identified |
| Precision | 0.9466 | Of predicted active, % actually active |
| F1 Score | 0.9687 | Harmonic mean of precision and sensitivity |
cat("### Reading the Model Output\n\n")cat("The logistic regression model produces odds ratios for each predictor.
Below are the five most actionable findings for branch management:\n\n")The logistic regression model produces odds ratios for each predictor. Below are the five most actionable findings for branch management:
cat("**1. IS_RESTRICTED (PND Status):** Accounts with any payment restriction
(debit restriction or total block) have substantially lower odds of remaining
active. This is the strongest behavioural predictor in the model. Operationally,
a restriction flag should trigger an immediate Relationship Manager call — not
a letter, not a system notification. The window between restriction and full
dormancy is narrow.\n\n")1. IS_RESTRICTED (PND Status): Accounts with any payment restriction (debit restriction or total block) have substantially lower odds of remaining active. This is the strongest behavioural predictor in the model. Operationally, a restriction flag should trigger an immediate Relationship Manager call — not a letter, not a system notification. The window between restriction and full dormancy is narrow.
cat("**2. LOG_BALANCE:** Higher balance at the time of the extract is positively
associated with active status. This confirms what practitioners know intuitively
but the model now quantifies: accounts that were funded — even partially — are
dramatically more likely to remain active. The single most important onboarding
milestone is the first deposit. The branch should track 'time to first deposit'
as a KPI for every new account, targeting completion within 7 days of opening.\n\n")2. LOG_BALANCE: Higher balance at the time of the extract is positively associated with active status. This confirms what practitioners know intuitively but the model now quantifies: accounts that were funded — even partially — are dramatically more likely to remain active. The single most important onboarding milestone is the first deposit. The branch should track ‘time to first deposit’ as a KPI for every new account, targeting completion within 7 days of opening.
cat("**3. HAS_BALANCE:** Accounts with any balance at all (binary flag) show
higher odds of being active even after controlling for the log-transformed
balance amount. This means it is not just the size of the balance that matters
— the mere fact of having been funded at all is independently predictive.
Zero-balance accounts at 30 days should be treated as dormancy-in-progress.\n\n")3. HAS_BALANCE: Accounts with any balance at all (binary flag) show higher odds of being active even after controlling for the log-transformed balance amount. This means it is not just the size of the balance that matters — the mere fact of having been funded at all is independently predictive. Zero-balance accounts at 30 days should be treated as dormancy-in-progress.
cat("**4. CUSTOMER_TYPE (INDIVIDUAL vs CORPORATE):** After controlling for
balance and restriction status, customer type remains a significant predictor.
Corporate accounts exhibit different activity patterns than individual accounts.
This justifies maintaining separate onboarding and engagement protocols for
the two segments rather than a one-size-fits-all approach.\n\n")4. CUSTOMER_TYPE (INDIVIDUAL vs CORPORATE): After controlling for balance and restriction status, customer type remains a significant predictor. Corporate accounts exhibit different activity patterns than individual accounts. This justifies maintaining separate onboarding and engagement protocols for the two segments rather than a one-size-fits-all approach.
cat("**5. ACCOUNT_AGE_DAYS:** Older accounts (those opened earlier in the
observation window) are more likely to be active, which partly reflects
survivorship — accounts that opened in 2024 and are still active in April 2026
have proven their persistence. However, this also suggests that newer accounts
(opened late 2025 or 2026) are at higher risk of early exit and deserve
proportionally more intensive early-stage engagement.")5. ACCOUNT_AGE_DAYS: Older accounts (those opened earlier in the observation window) are more likely to be active, which partly reflects survivorship — accounts that opened in 2024 and are still active in April 2026 have proven their persistence. However, this also suggests that newer accounts (opened late 2025 or 2026) are at higher risk of early exit and deserve proportionally more intensive early-stage engagement.
cat("### Which Model and Why?\n\n")cat("This single logistic regression model is recommended for immediate
operational deployment over more complex alternatives (random forest, XGBoost)
for three reasons specific to this banking context:\n\n")This single logistic regression model is recommended for immediate operational deployment over more complex alternatives (random forest, XGBoost) for three reasons specific to this banking context:
cat("**Interpretability:** Branch management and compliance teams require
explainable predictions. A Relationship Manager cannot act on a black-box
score — they need to know *why* an account is flagged as high-risk. Logistic
regression provides exact odds ratios for every predictor, making every
prediction auditable.\n\n")Interpretability: Branch management and compliance teams require explainable predictions. A Relationship Manager cannot act on a black-box score — they need to know why an account is flagged as high-risk. Logistic regression provides exact odds ratios for every predictor, making every prediction auditable.
cat("**Regulatory compatibility:** Nigerian banking regulation (CBN guidelines)
requires that credit and risk decisions be explainable to customers and
auditors. A logistic regression satisfies this requirement; ensemble models
typically do not without additional explainability tooling.\n\n")Regulatory compatibility: Nigerian banking regulation (CBN guidelines) requires that credit and risk decisions be explainable to customers and auditors. A logistic regression satisfies this requirement; ensemble models typically do not without additional explainability tooling.
cat("**Practical deployment:** The model requires only variables available at
account opening — customer type, account type, depositor type, and opening
year — plus early indicators available within 30 days (balance funded, restriction
status). It can be operationalised as a simple scoring spreadsheet or embedded
in the core banking MIS without specialist infrastructure.\n\n")Practical deployment: The model requires only variables available at account opening — customer type, account type, depositor type, and opening year — plus early indicators available within 30 days (balance funded, restriction status). It can be operationalised as a simple scoring spreadsheet or embedded in the core banking MIS without specialist infrastructure.
cat("**Recommended operating threshold:** 0.50 (default). Given the 93.6%
active rate in this dataset, the model is conservative by design — it will
flag fewer false positives, protecting relationship quality. If the branch
wants to cast a wider net and catch more at-risk accounts at the cost of
more false positives, lower the threshold to 0.35–0.40.")Recommended operating threshold: 0.50 (default). Given the 93.6% active rate in this dataset, the model is conservative by design — it will flag fewer false positives, protecting relationship quality. If the branch wants to cast a wider net and catch more at-risk accounts at the cost of more false positives, lower the threshold to 0.35–0.40.
The five analytical techniques applied in this study were not conducted in isolation — each builds on the previous and collectively answers a single overarching business question: what determines whether a newly opened account at the Providus Bank Port Harcourt Branch remains active, and what should the branch do about it?
Exploratory Data Analysis established the foundation. The branch opened 14,714 accounts between January 2024 and April 2026, dominated by individual savings accounts (57.9%) and marketer-driven acquisition (40.6% of depositor types). The balance distribution is severely right-skewed — the median balance is approximately ₦826, while the mean is over ₦1 million — confirming that a small number of high-value accounts mask a large volume of unfunded or near-zero accounts. Two data quality issues were identified and resolved: age outliers (impossible values below 0 and above 100) and systematic high missingness in five columns. The Anscombe demonstration confirmed that summary statistics alone would have given branch management a dangerously misleading picture of portfolio health.
Data Visualisation translated these patterns into a coherent narrative across five plots. Monthly openings peaked in January 2025 and declined through 2025, suggesting acquisition momentum has slowed. Corporate accounts show disproportionately higher dormancy relative to their volume. Savings accounts cluster overwhelmingly at zero balance. Closed and dormant accounts skew towards customers under 30. And the marketer channel dominates acquisition so completely that portfolio quality is structurally dependent on marketer incentive design.
Hypothesis Testing validated three critical assumptions with statistical rigour. Corporate accounts hold significantly higher balances than individual accounts (Welch’s t-test, p < 0.05; Cohen’s d indicating a meaningful effect size) — confirming that corporate onboarding quality deserves disproportionate management attention. Account status is significantly associated with account type (chi-squared, p < 0.05; Cramér’s V quantifying the strength) — meaning product-specific onboarding protocols are justified, not optional. The 2024 vs 2025 cohort comparison tested whether onboarding quality has drifted over time — a finding with direct implications for the marketer incentive structure.
Correlation Analysis mapped the relationship landscape. The strongest actionable finding was the negative correlation between restriction status and account activity — restricted accounts are significantly less likely to remain active, and this relationship persists after controlling for account age via partial correlation. The near-perfect collinearity between CRNT_BAL and AVAILABLE_BALANCE was identified and handled correctly by excluding the latter from regression. The comparison between Pearson and Spearman correlations confirmed that skew in the balance variable materially affects correlation estimates, validating the decision to use log-transformation throughout.
Logistic Regression synthesised all prior findings into a predictive model. Tested on a held-out 30% sample, the model achieves meaningful discriminative ability (AUC reported in Section 9.8). The five most actionable predictors — restriction status, log balance, having any balance at all, customer type, and account age — provide a clear operational playbook. The model is interpretable, auditable, and deployable within existing branch infrastructure without specialist tooling.
cat("The five analyses collectively support one central recommendation:\n\n")The five analyses collectively support one central recommendation:
cat("**Implement a structured 30-60-90 day post-onboarding engagement
protocol, differentiated by account type and customer segment.**\n\n")Implement a structured 30-60-90 day post-onboarding engagement protocol, differentiated by account type and customer segment.
cat("Specifically:\n\n")Specifically:
cat("- **Day 7:** Automated check — has the account received its first deposit?
Zero-balance accounts at Day 7 should trigger a Relationship Manager call,
not a system-generated SMS. The model confirms that the mere fact of being
funded — regardless of amount — is the single strongest early predictor of
long-term account activity.\n\n")cat("- **Day 30:** Restriction status review. Any account with a PND flag at
Day 30 should be escalated immediately. The correlation and regression analyses
both confirm that restriction status is the most powerful predictor of
dormancy — and the window for intervention is narrow.\n\n")cat("- **Day 60:** Segment-specific engagement. Corporate accounts showing
low balance at Day 60 should receive a dedicated Relationship Manager review
given their disproportionate balance contribution. Individual savings accounts
at zero balance at Day 60 should be flagged for a lighter-touch digital
re-engagement campaign.\n\n")cat("- **Day 90:** Dormancy risk scoring. Apply the logistic regression model
to score all accounts opened in the preceding quarter. Accounts with predicted
active probability below 0.50 should be prioritised for the next relationship
management cycle.\n\n")cat("This protocol addresses the root cause identified across all five analyses:
the branch currently treats all newly opened accounts identically after opening,
regardless of funding status, restriction flags, customer type, or product type.
The data shows clearly that these variables have materially different implications
for account survival — and the branch's engagement model should reflect that.")This protocol addresses the root cause identified across all five analyses: the branch currently treats all newly opened accounts identically after opening, regardless of funding status, restriction flags, customer type, or product type. The data shows clearly that these variables have materially different implications for account survival — and the branch’s engagement model should reflect that.
cat("## 11.1 Data Limitations\n\n")cat("**Single branch:** All 14,714 accounts are from the Port Harcourt Branch
only. Findings may not generalise to other Providus Bank branches operating
in different economic environments, customer demographics, or SBU structures.
A multi-branch dataset would allow branch-level fixed effects and substantially
stronger generalisability.\n\n")Single branch: All 14,714 accounts are from the Port Harcourt Branch only. Findings may not generalise to other Providus Bank branches operating in different economic environments, customer demographics, or SBU structures. A multi-branch dataset would allow branch-level fixed effects and substantially stronger generalisability.
cat("**Cross-sectional snapshot:** The dataset captures account status and
balance at a single point in time (April 2026). It does not contain transaction
history, balance trajectories over time, or the sequence of events leading to
dormancy or closure. A longitudinal extract — monthly balance snapshots over
the 28-month window — would enable survival analysis and time-to-dormancy
modelling, which would be far more powerful than the static logistic regression
applied here.\n\n")Cross-sectional snapshot: The dataset captures account status and balance at a single point in time (April 2026). It does not contain transaction history, balance trajectories over time, or the sequence of events leading to dormancy or closure. A longitudinal extract — monthly balance snapshots over the 28-month window — would enable survival analysis and time-to-dormancy modelling, which would be far more powerful than the static logistic regression applied here.
cat("**High missingness in key variables:** RELIGION (62.7% missing), TELL_NAME
(45.5%), and TELEPHONE1 (37.8%) could not be meaningfully used in analysis.
The causes of missingness are unknown — it may be systematic (certain account
types not requiring these fields) rather than random, which could bias
conclusions drawn from the complete-case analysis.\n\n")High missingness in key variables: RELIGION (62.7% missing), TELL_NAME (45.5%), and TELEPHONE1 (37.8%) could not be meaningfully used in analysis. The causes of missingness are unknown — it may be systematic (certain account types not requiring these fields) rather than random, which could bias conclusions drawn from the complete-case analysis.
cat("**Class imbalance:** The outcome variable IS_ACTIVE is 93.6% positive.
While logistic regression handles this, the model's ability to correctly
identify the minority class (inactive accounts) is constrained. With more
data, techniques such as SMOTE oversampling or cost-sensitive learning could
improve minority-class prediction — which is precisely the class the branch
most needs to identify correctly.\n\n")Class imbalance: The outcome variable IS_ACTIVE is 93.6% positive. While logistic regression handles this, the model’s ability to correctly identify the minority class (inactive accounts) is constrained. With more data, techniques such as SMOTE oversampling or cost-sensitive learning could improve minority-class prediction — which is precisely the class the branch most needs to identify correctly.
cat("## 11.2 Methodological Limitations\n\n")cat("**Correlation is not causation:** The correlation and regression findings
establish association, not causality. The relationship between restriction
status and dormancy, for example, could reflect reverse causality — restrictions
may be applied to already-inactive accounts rather than causing inactivity.
A randomised or quasi-experimental design (e.g., difference-in-differences
comparing accounts before and after a policy change) would be required to
establish causality.\n\n")Correlation is not causation: The correlation and regression findings establish association, not causality. The relationship between restriction status and dormancy, for example, could reflect reverse causality — restrictions may be applied to already-inactive accounts rather than causing inactivity. A randomised or quasi-experimental design (e.g., difference-in-differences comparing accounts before and after a policy change) would be required to establish causality.
cat("**Logistic regression assumptions:** The model assumes a linear
relationship between continuous predictors and the log-odds of the outcome.
This assumption was not formally tested for all predictors. Non-linear
extensions (polynomial terms, spline regression) may improve fit, particularly
for AGE_CLEAN and ACCOUNT_AGE_DAYS where non-linear effects are plausible.\n\n")Logistic regression assumptions: The model assumes a linear relationship between continuous predictors and the log-odds of the outcome. This assumption was not formally tested for all predictors. Non-linear extensions (polynomial terms, spline regression) may improve fit, particularly for AGE_CLEAN and ACCOUNT_AGE_DAYS where non-linear effects are plausible.
cat("## 11.3 What Would Be Done Differently With More Resources\n\n")cat("With access to full transaction history, a **survival analysis
(Cox proportional-hazards model)** would replace logistic regression as
the primary technique — modelling time-to-dormancy rather than static
active status, and accounting for censoring (accounts still active at the
observation cutoff). With a multi-branch dataset, **multilevel modelling**
would separate within-branch effects from between-branch variation. With
more computing power and a labelled historical dataset of intervention
outcomes, a **reinforcement learning** approach could optimise the engagement
protocol in real time based on observed customer responses.")With access to full transaction history, a survival analysis (Cox proportional-hazards model) would replace logistic regression as the primary technique — modelling time-to-dormancy rather than static active status, and accounting for censoring (accounts still active at the observation cutoff). With a multi-branch dataset, multilevel modelling would separate within-branch effects from between-branch variation. With more computing power and a labelled historical dataset of intervention outcomes, a reinforcement learning approach could optimise the engagement protocol in real time based on observed customer responses.
cat("Adi, B. (2026). *AI-powered business analytics: A practical textbook for
data-driven decision making — from data fundamentals to machine learning in
Python and R.* Lagos Business School / markanalytics.online.
https://markanalytics.online\n\n")Adi, B. (2026). AI-powered business analytics: A practical textbook for data-driven decision making — from data fundamentals to machine learning in Python and R. Lagos Business School / markanalytics.online. https://markanalytics.online
cat("Anscombe, F. J. (1973). Graphs in statistical analysis. *The American
Statistician, 27*(1), 17–21. https://doi.org/10.1080/00031305.1973.10478966\n\n")Anscombe, F. J. (1973). Graphs in statistical analysis. The American Statistician, 27(1), 17–21. https://doi.org/10.1080/00031305.1973.10478966
cat("R Core Team. (2026). *R: A language and environment for statistical
computing* (Version 4.6.0). R Foundation for Statistical Computing.
https://www.R-project.org/\n\n")R Core Team. (2026). R: A language and environment for statistical computing (Version 4.6.0). R Foundation for Statistical Computing. https://www.R-project.org/
cat("Wickham, H., Averick, M., Bryan, J., Chang, W., McGowan, L., François, R.,
Grolemund, G., Hayes, A., Henry, L., Hester, J., Kuhn, M., Pedersen, T. L.,
Miller, E., Bache, S. M., Müller, K., Ooms, J., Robinson, D., Seidel, D. P.,
Spinu, V., … Yutani, H. (2019). Welcome to the tidyverse. *Journal of Open
Source Software, 4*(43), 1686. https://doi.org/10.21105/joss.01686\n\n")Wickham, H., Averick, M., Bryan, J., Chang, W., McGowan, L., François, R., Grolemund, G., Hayes, A., Henry, L., Hester, J., Kuhn, M., Pedersen, T. L., Miller, E., Bache, S. M., Müller, K., Ooms, J., Robinson, D., Seidel, D. P., Spinu, V., … Yutani, H. (2019). Welcome to the tidyverse. Journal of Open Source Software, 4(43), 1686. https://doi.org/10.21105/joss.01686
cat("Wickham, H. (2016). *ggplot2: Elegant graphics for data analysis.*
Springer. https://doi.org/10.1007/978-3-319-24277-4\n\n")Wickham, H. (2016). ggplot2: Elegant graphics for data analysis. Springer. https://doi.org/10.1007/978-3-319-24277-4
cat("Robin, X., Turck, N., Hainard, A., Tiberti, N., Lisacek, F., Sanchez,
J.-C., & Müller, M. (2011). pROC: An open-source package for R and S+ to
analyze and compare ROC curves. *BMC Bioinformatics, 12*, 77.
https://doi.org/10.1186/1471-2105-12-77\n\n")Robin, X., Turck, N., Hainard, A., Tiberti, N., Lisacek, F., Sanchez, J.-C., & Müller, M. (2011). pROC: An open-source package for R and S+ to analyze and compare ROC curves. BMC Bioinformatics, 12, 77. https://doi.org/10.1186/1471-2105-12-77
cat("Fox, J., & Weisberg, S. (2019). *An R companion to applied regression*
(3rd ed.). Sage. [car package]\n\n")Fox, J., & Weisberg, S. (2019). An R companion to applied regression (3rd ed.). Sage. [car package]
cat("Grolemund, G., & Wickham, H. (2011). Dates and times made easy with
lubridate. *Journal of Statistical Software, 40*(3), 1–25.
https://doi.org/10.18637/jss.v040.i03\n\n")Grolemund, G., & Wickham, H. (2011). Dates and times made easy with lubridate. Journal of Statistical Software, 40(3), 1–25. https://doi.org/10.18637/jss.v040.i03
cat("Tierney, N., & Cook, D. (2023). Expanding tidy data principles to
facilitate missing data exploration, visualization and assessment of
imputations. *Journal of Statistical Software, 105*(7), 1–31.
https://doi.org/10.18637/jss.v105.i07 [naniar package]\n\n")Tierney, N., & Cook, D. (2023). Expanding tidy data principles to facilitate missing data exploration, visualization and assessment of imputations. Journal of Statistical Software, 105(7), 1–31. https://doi.org/10.18637/jss.v105.i07 [naniar package]
cat("Zhu, H. (2024). *kableExtra: Construct complex table with 'kable' and
pipe syntax.* https://CRAN.R-project.org/package=kableExtra\n\n")Zhu, H. (2024). kableExtra: Construct complex table with ‘kable’ and pipe syntax. https://CRAN.R-project.org/package=kableExtra
# Programmatically retrieve package citations for accuracy
pkgs <- c("tidyverse", "lubridate", "janitor", "skimr",
"corrplot", "ggcorrplot", "naniar", "car",
"lmtest", "broom", "pROC", "knitr",
"kableExtra", "scales", "reticulate")
cat("=== PACKAGE VERSIONS USED ===\n")=== PACKAGE VERSIONS USED ===for (pkg in pkgs) {
ver <- tryCatch(
as.character(packageVersion(pkg)),
error = function(e) "not installed"
)
cat(sprintf("%-15s v%s\n", pkg, ver))
}tidyverse v2.0.0
lubridate v1.9.5
janitor v2.2.1
skimr v2.2.2
corrplot v0.95
ggcorrplot v0.1.4.1
naniar v1.1.0
car v3.1.5
lmtest v0.9.40
broom v1.0.12
pROC v1.19.0.1
knitr v1.51
kableExtra v1.4.0
scales v1.4.0
reticulate v1.46.0cat("Claude (Anthropic, claude.ai) was used as a coding assistant throughout
this project. Specifically, AI assistance was used to: (1) generate initial
R code scaffolding for ggplot2 visualisations and logistic regression
diagnostics; (2) debug rendering errors in the Quarto document; and (3)
suggest appropriate chunk options and table formatting syntax.\n\n")Claude (Anthropic, claude.ai) was used as a coding assistant throughout this project. Specifically, AI assistance was used to: (1) generate initial R code scaffolding for ggplot2 visualisations and logistic regression diagnostics; (2) debug rendering errors in the Quarto document; and (3) suggest appropriate chunk options and table formatting syntax.
cat("All analytical decisions were made independently by the author. These
include: the choice of Case Study 1 and the five techniques applied; the
framing of the three research hypotheses and their business interpretation;
the decision to use Welch's t-test over Student's t-test following the
Levene test result; the selection of predictor variables for the logistic
regression model and the exclusion of AVAILABLE_BALANCE due to collinearity;
the interpretation of all model outputs; and the integrated recommendation
in Section 10. The author can explain and defend every analytical choice,
every line of code, and every conclusion drawn in this document.\n\n")All analytical decisions were made independently by the author. These include: the choice of Case Study 1 and the five techniques applied; the framing of the three research hypotheses and their business interpretation; the decision to use Welch’s t-test over Student’s t-test following the Levene test result; the selection of predictor variables for the logistic regression model and the exclusion of AVAILABLE_BALANCE due to collinearity; the interpretation of all model outputs; and the integrated recommendation in Section 10. The author can explain and defend every analytical choice, every line of code, and every conclusion drawn in this document.
cat("Data collection, anonymisation, and the professional disclosure were
authored entirely without AI assistance.")Data collection, anonymisation, and the professional disclosure were authored entirely without AI assistance.