Revise — Business Analytics | Business Analytics Atlas

DR. PHIL'S QUANT LAB

Business Analytics Atlas

An independent study reference written by Dr Phuc V. Nguyen. It is not official subject material — for assessment requirements always follow your subject outline and vUWS.

Revision Cards

72 concepts

What Business Analytics Is

What business analytics is

V = N \times \Delta q \times S

Analytics needs three things: a decision, data, and a method joining them

What Business Analytics Is

Business intelligence, analytics and data science

BI monitors agreed metrics from governed data on a fixed cadence

What Business Analytics Is

Descriptive, predictive and prescriptive analytics

a^{\star} = \arg\max_{a \in A} \sum_{s} P(s \mid x)\, u(a, s)

Descriptive = what happened, diagnosis included

What Business Analytics Is

The analytics workflow

Frame, acquire, prepare, analyse, interpret, communicate, act, monitor

What Business Analytics Is

Where analytics is applied

R_{12} = (1 - c)^{12}

The same moves recur: segment, forecast, score, rank, route, attribute

What Business Analytics Is

Why analytics work stalls

Most failed analytics is unused rather than incorrect

What Business Analytics Is

Correlation and causation

r_{XY} = \frac{\operatorname{cov}(X, Y)}{s_X \, s_Y}

Sources of correlation: cause, reverse cause, confounding, selection, chance

Data Foundations

What big data means

N = s \times t \times 365

Volume, velocity and variety were the original three properties (Laney, 2001)

Data Foundations

Structured and unstructured data

Structured: schema declared before the data arrives, fixed columns and types

Data Foundations

The data warehouse

Inmon: subject-oriented, integrated, time-variant, non-volatile

Data Foundations

ETL and ELT

r = \dfrac{N}{w}

Extract, transform, load; ELT swaps the last two and transforms in the warehouse

Data Foundations

Metadata

Descriptive: names, definitions, the business meaning of a measure

Data Foundations

The star schema

N_{\text{distinct}} \;\le\; \prod_{i=1}^{k} |D_i|

Fact table in the centre: measures plus one foreign key per dimension

Data Foundations

Measures and dimensions

R_{\text{total}} = \dfrac{\sum_{g} n_g}{\sum_{g} d_g} \quad \ne \quad \frac{1}{G}\sum_{g} \frac{n_g}{d_g}

Measure: a number you aggregate. Dimension: an attribute you slice by

Data Foundations

Cloud for analytics

C = q \times v \times p

Five essential characteristics include on-demand self-service, rapid elasticity and measured service

Data Foundations

Data quality as fitness for use

Quality is fitness for use, judged against a stated purpose

Data Foundations

Data quality dimensions

C = \dfrac{n_{\text{populated}}}{n_{\text{required}}} \times 100\%

Completeness, accuracy, consistency, timeliness, uniqueness, validity

Data Foundations

Why data goes bad

A_t = A_0 \, (1 - d)^{\,t}

Three entry points: capture, integration, decay

Data Foundations

Data cleansing

P = \dfrac{n(n-1)}{2}

Profile first: counts, distinct values, ranges, patterns, null rates

Data Foundations

Sampling bias

SE(\hat{p}) = \sqrt{\dfrac{p(1-p)}{n}}

Random error shrinks with the square root of sample size; bias does not shrink at all

Decisions and Models

What a decision actually is

EV(a) = \sum_{i=1}^{n} p_i \, v_i(a)

A decision commits resources to one option when others were open

Decisions and Models

The decision process

\text{choose the first } a \text{ such that } u(a) \ge \bar{u}

Simon: intelligence, design, choice; later work adds implementation and review

Decisions and Models

Models as deliberate abstraction

y = f(x_1, x_2, \dots, x_k) + \varepsilon

A model is a purposeful simplification, not a miniature of reality

Decisions and Models

Decision support systems

Support rather than replace: judgement and accountability stay with the person

Decisions and Models

Supervised and unsupervised learning

\hat{f} = \arg\min_{f} \; \frac{1}{n} \sum_{i=1}^{n} L\big(y_i,\, f(x_i)\big)

Supervised needs labelled outcomes, unsupervised has none

Decisions and Models

Experiments and A/B testing

\Delta = p_T - p_C, \qquad \text{lift} = \frac{p_T - p_C}{p_C}

Random assignment balances groups in expectation, which licenses the causal reading

Decisions and Models

Designing a KPI that works

R = V \times c \times \bar{A}

A KPI carries consequences, which is why it changes behaviour

Visual Communication

The purpose of visualisation

r = \dfrac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2}\,\sqrt{\sum_{i=1}^{n}(y_i - \bar{y})^2}}

Three jobs: exploration, confirmation, explanation

Visual Communication

Visual variables

\psi = k \, \phi^{\beta}

Bertin visual variables: position, size, shape, value, hue, orientation, texture

Visual Communication

Choosing a chart

\sum_{i=1}^{k} x_i = T, \qquad x_i \ge 0

Question family first, variable type second, chart form last

Visual Communication

Dashboards

v_{\text{rel}} = \dfrac{A - T}{T}, \qquad v_{\text{abs}} = A - T

A dashboard is a standing monitoring instrument, not a report

Visual Communication

Data storytelling

Lead with the finding, not with the method

Visual Communication

Common visualisation mistakes

\text{data-ink ratio} = \dfrac{\text{ink used to display data}}{\text{total ink in the graphic}}

Most bad charts come from unchanged software defaults

Visual Communication

Truncated axes

\text{lie factor} = \dfrac{\text{size of effect shown in the graphic}}{\text{size of effect in the data}}

Bars encode by length from the baseline, so bars need a zero baseline

Visual Communication

The ethics of charts

\text{rate}_{i} = \dfrac{c_{i}}{n_{i}}

The test is the impression a reasonable reader takes, not component-level accuracy

What social network analysis is

\binom{n}{2} = \frac{n(n-1)}{2}

Unit of analysis is the tie, not the individual actor

Actors and ties

a_{ij} = \begin{cases} 1 & \text{if a tie runs from } i \text{ to } j \\ 0 & \text{otherwise} \end{cases}

Actors are nodes, ties are edges, and both are defined by the research question

Weighted ties and tie strength

s_i = \sum_{j} w_{ij}, \qquad s_i^{\text{in}} = \sum_{j} w_{ji}

Strength is the sum of the weights on every tie touching an actor

Degree centrality

C_D(i) = k_i = \sum_{j \ne i} a_{ij}

Degree is the count of ties; normalised degree divides by n-1

Closeness centrality

C_C(i) = \frac{n-1}{\sum_{j \ne i} d(i,j)}

Closeness inverts the summed shortest-path distance to all other actors

Betweenness centrality

C_B(i) = \sum_{s < t,\; s,t \ne i} \frac{g_{st}(i)}{g_{st}}

Counts the share of shortest paths between other pairs that run through the actor

Network density

\Delta = \frac{L}{n(n-1)/2} = \frac{2L}{n(n-1)}

Density is observed ties divided by possible ties, bounded between 0 and 1

Bridges, cliques and components

C_i = \frac{2 e_i}{k_i (k_i - 1)}

A component is a set of mutually reachable actors; an isolate is a component of one

Running a network study

P(\text{both ends respond}) \approx r^{2}

Design order: question, then boundary, then relation, then collection method

Text and Social Data

Social media analytics

\text{ER} = \frac{\text{reactions} + \text{comments} + \text{shares}}{\text{reach}}

Three jobs: listening (what is said), measuring (how far it travels), acting (what changes)

Text and Social Data

Where social data comes from

\mathrm{SE}(\hat{p}) = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}

Routes: platform interfaces, licensed providers, direct web collection, first-party channels, panels

Text and Social Data

Natural language processing

P(w_{n} \mid w_{n-1}) = \frac{C(w_{n-1}, w_{n})}{C(w_{n-1})}

Layers: tokenise, normalise, tag, recognise entities, represent as numbers

Text and Social Data

Sentiment analysis

\text{NSS} = \frac{n_{+} - n_{-}}{n_{+} + n_{-} + n_{0}}

Three approaches: lexicon rules, classical supervised classifiers, fine-tuned pretrained models (supervised too)

Text and Social Data

The text mining pipeline

\mathrm{tf}_{t,d} = \text{count of term } t \text{ in document } d, \qquad \mathrm{df}_{t} = \text{number of documents containing } t

Stages: collect, clean, tokenise and normalise, build the matrix, weight, analyse, act

Text and Social Data

Web mining

PR(p) = \frac{1 - d}{N} + d \sum_{q \to p} \frac{PR(q)}{L(q)}

Three branches: content (what pages say), structure (who links to whom), usage (what visitors did)

How Analytics Gets Built

Why analytics needs a methodology

Methodology = agreed steps, each with a named output

How Analytics Gets Built

CRISP-DM, the standard analytics cycle

Six phases: business understanding, data understanding, preparation, modelling, evaluation, deployment

How Analytics Gets Built

Analytics capability

C = \min\left(d_{\text{data}},\, d_{\text{people}},\, d_{\text{process}},\, d_{\text{tech}},\, d_{\text{govern}},\, d_{\text{act}}\right)

Capability = repeatable ability to turn data into decisions, not one good project

How Analytics Gets Built

Structuring a messy problem

Situations arrive as problem situations, not problems

How Analytics Gets Built

Mapping the business model

\text{LTV} = m \times \frac{s}{1 + d - s}, \qquad \text{ratio} = \frac{\text{LTV}}{\text{CAC}}

Canvas: nine blocks covering customers, value, channels, revenue, resources, activities, partners, costs

How Analytics Gets Built

Where analytics has leverage

V = N \times \Delta

Annual value equals frequency times stake times recoverable share

How Analytics Gets Built

Getting analytics into production

P(X, Y) = P(Y \mid X)\, P(X)

Production means input contract, loud failure, named owner, monitoring, retirement plan

How Analytics Gets Built

Design thinking

Five modes: empathise, define, ideate, prototype, test

How Analytics Gets Built

Agile ways of working in analytics

Four manifesto preferences, with the right-hand items still valued; "working software" reads as usable analytical output here

Ethics and Governance

Why ethics belongs in analytics

Legality is a floor; ethics asks whether a lawful use is defensible

Ethics and Governance

PAPA: privacy, accuracy, property, accessibility

Mason (1986): privacy, accuracy, property, accessibility

Ethics and Governance

GDPR and what it requires

\text{Cap} = \max\bigl(\text{EUR } 20{,}000{,}000,\; 0.04 \times \text{worldwide annual turnover}\bigr)

Regulation (EU) 2016/679, applying since May 2018

Ethics and Governance

Personalisation and the privacy trade-off

The paradox: stated privacy preference is high, revealed trade-off is cheap

Ethics and Governance

Filter bubbles and echo chambers

r = \dfrac{\text{items from the opposing side at that stage}}{\text{total items at that stage}}

Pariser (2011): ranking content for one person narrows what that person sees

Ethics and Governance

Algorithmic bias

P(\hat{Y}=1 \mid A=a) \;=\; P(\hat{Y}=1 \mid A=b)

Bias enters via the label, the sample and historical outcomes, not a protected column

Ethics and Governance

Data governance

\forall r \in T:\quad \bigl|\{\, s \in T \;:\; s[Q] = r[Q] \,\}\bigr| \;\ge\; k

Khatri and Brown: principles, quality, metadata, access, lifecycle

Ethics and Governance

Ethics by design

Build the safeguard in; do not review it at the end

The Analyst and What Comes Next

Analytics as a service

C_{\text{rent}} = h \times r, \qquad C_{\text{own}} = \frac{K}{m} + f

Renting the analytics stack instead of owning it, billed by use

The Analyst and What Comes Next

Agentic AI

P(\text{all } n \text{ steps succeed}) = \prod_{i=1}^{n} p_i = p^{\,n}

Agent = a goal plus a loop of observe, decide, act, observe

The Analyst and What Comes Next

Human and machine agency

a_{\text{system}} = (1 - r)\,a_{\text{model}} + r\,a_{\text{human}}

Agency = the capacity to choose plus answerability for the choice

The Analyst and What Comes Next

Roles in an analytics team

Distinct jobs: data engineer, analyst, data scientist, ML engineer, steward

The Analyst and What Comes Next

How the analyst role is changing

Automation removes tasks, not whole jobs