Predictive Analytics and Machine Learning

Introduction and Context

Predictive analytics uses historical and current data to estimate future outcomes, classify cases, identify groups, or detect unusual observations. It is a central capability of modern data analytics because organizations increasingly need to move from describing what happened to anticipating what is likely to happen and deciding what action is justified.

Machine learning (ML) provides a family of computational methods for learning patterns from data. In supervised learning, the target outcome is known for historical observations; in unsupervised learning, the target is not supplied and the objective is to discover structure. Predictive modelling is not synonymous with machine learning: statistical regression models, expert systems, and time-series methods may all be predictive, while some machine-learning applications are descriptive rather than predictive.

A sound predictive-analytics project combines problem formulation, data engineering, statistical reasoning, algorithm selection, validation, deployment, monitoring, and governance. A highly accurate model can still fail commercially if it predicts the wrong outcome, uses unavailable information, creates unacceptable bias, or cannot support an operational decision.

Learning Objectives

By the end of this chapter, a student should be able to:

1. Distinguish regression, classification, clustering, and anomaly detection.

2. Formulate an analytics problem with an appropriate target, observation unit, and prediction horizon.

3. Explain major predictive models and their assumptions.

4. Apply regularization, cross-validation, hyperparameter tuning, and model-selection principles.

5. Evaluate models using technically appropriate and business-relevant metrics.

6. Diagnose overfitting, leakage, imbalance, bias, and deployment risks.

7. Design a defensible predictive-analytics workflow for an organizational case.

1. From Business Question to Learning Problem

A modelling project begins with a decision rather than an algorithm. Important specification questions include:

• What decision will the prediction support?
• What is the unit of analysis: customer, transaction, machine, claim, or time period?
• What exactly is the target variable?
• When must the prediction be available?
• Which information would genuinely be available at that time?
• What are the costs of false positives, false negatives, delays, and interventions?

A target must be defined operationally. “Customer churn” might mean cancellation within 30 days, no transaction for 90 days, or failure to renew a contract. These definitions produce different labels and potentially different models.

The prediction horizon is equally important. A model predicting equipment failure in the next 24 hours cannot use a sensor reading collected after the prediction timestamp. This principle leads to temporal data splitting and is a major defence against data leakage.

A typical dataset contains predictors (features) X and an outcome y. In supervised learning, a model estimates a function f such that y is predicted from X. The model is trained on historical data and evaluated on observations not used to fit its parameters. The objective is generalization: good performance on relevant future or unseen cases, not merely memorization of the training sample.

2. Main Problem Classes

2.1 Regression

Regression predicts a numerical quantity, such as revenue, delivery time, energy demand, or claim cost. The target may be continuous, positive, bounded, or count-valued. Ordinary least squares is suitable only when its assumptions and loss function are reasonable; generalized linear models, tree ensembles, and other methods may be preferable for non-normal or nonlinear outcomes.

2.2 Classification

Classification predicts a category. Binary classification has two classes, such as fraud/not fraud. Multiclass classification has more than two mutually exclusive classes, such as product categories. Multilabel classification allows several labels simultaneously. A classifier often produces probabilities, which must be converted into decisions using a threshold that reflects business costs.

2.3 Clustering

Clustering groups observations without a supplied target. It can support market segmentation, document organization, or exploratory analysis. A cluster is not automatically a naturally existing category. Results depend on features, scaling, distance measure, algorithm, and the chosen number of clusters. Clustering should therefore be interpreted substantively and validated for stability and usefulness.

2.4 Anomaly Detection

Anomaly detection identifies observations that are unusual relative to a reference population. Anomalies may indicate fraud, cyber intrusion, sensor failure, or a legitimate but rare event. The distinction between novelty detection and outlier detection matters: novelty detection learns normality from mostly clean reference data, whereas outlier detection assumes that unusual points may already be present in the training sample.

3. Data Preparation and Representation

Data preparation is part of modelling, not a clerical prelude. Typical activities include correcting data types, resolving duplicate records, handling missingness, encoding categorical variables, scaling numerical features where required, and constructing domain-informed features.

Missing values may arise from random failure, process design, or the value itself. For example, an absent laboratory test may indicate that a clinician did not consider it necessary. Imputation should be performed within each training fold, not on the entire dataset before cross-validation, because global imputation can transmit information from validation observations into training data.

Categorical predictors can be represented using one-hot encoding, ordinal encoding where order is meaningful, or target encoding with strict fold-wise safeguards. Numerical scaling is essential for distance-based methods, principal-component analysis, and regularized linear models when predictors are measured on different scales. It is generally less important for decision trees, although consistent preprocessing remains good practice.

Feature engineering should respect causal and temporal availability. Aggregating a customer’s purchases up to the prediction date may be legitimate; aggregating purchases during the following month is leakage. A reproducible preprocessing pipeline should apply exactly the same transformations during training, validation, and production scoring.

4. Regression Models

4.1 Multiple Linear Regression

The multiple linear regression model is

ŷ = β₀ + β₁x₁ + β₂x₂ + … + β_px_p.

Here, ŷ is the predicted response, x_j is predictor j, β₀ is the intercept, and β_j is the expected change in the response associated with a one-unit increase in x_j when the other included predictors are held constant. The model is linear in its parameters; predictors may be transformed or interaction terms may be added.

Ordinary least squares estimates coefficients by minimizing the residual sum of squares:

RSS = Σᵢ(yᵢ − ŷᵢ)².

For unbiased coefficient interpretation in the classical linear model, important assumptions include linearity in parameters, appropriate treatment of observations, no perfect multicollinearity, and a zero conditional mean error. Homoscedasticity and normally distributed errors are especially relevant to conventional standard errors and small-sample inference, although prediction can remain useful when these assumptions are imperfect. Serial dependence requires time-aware methods or corrected inference.

The coefficient of determination is

R² = 1 − RSS/TSS,

where TSS = Σᵢ(yᵢ − ȳ)² is total variation around the sample mean. R² is the proportion of in-sample variation explained relative to a mean-only model. It can increase when irrelevant predictors are added and should not be treated as a universal measure of predictive quality.

For a test set, common metrics are:

• Mean absolute error (MAE) = (1/n)Σ|yᵢ − ŷᵢ|.
• Mean squared error (MSE) = (1/n)Σ(yᵢ − ŷᵢ)².
• Root mean squared error (RMSE) = √MSE.

MAE has the same units as the target and gives linear penalty to errors. RMSE also has target units but penalizes large errors more strongly. MAPE, defined as the mean of |(yᵢ−ŷᵢ)/yᵢ| multiplied by 100, is unsuitable when actual values are zero or near zero and can behave asymmetrically.

4.2 Polynomial Terms, Interactions, and Generalized Linear Models

Nonlinear relationships may be represented by transformations such as log(x), splines, or polynomial terms. An interaction term x₁x₂ means that the association of one predictor depends on the level of another. These expansions must be validated because flexibility can increase variance.

Generalized linear models connect a transformed expected response to a linear predictor. Logistic regression, for example, models the log-odds of a binary outcome:

log[p/(1−p)] = β₀ + β₁x₁ + … + β_px_p.

Here p is the probability of the positive class. Exponentiating β_j gives an odds ratio for a one-unit increase in x_j, holding other variables constant. Logistic regression is valuable when calibrated probabilities, interpretability, and a transparent relationship are important. It assumes a linear relationship between predictors and log-odds unless transformed terms are included.

4.3 Tree-Based Regression

A decision tree recursively partitions the feature space into regions and predicts a constant, often the mean target, within each terminal region. Trees capture nonlinearities and interactions with limited feature transformation. However, deep trees can fit noise. Limiting depth, requiring a minimum number of observations per leaf, pruning, or using ensembles can improve generalization.

Random forests average many trees trained with sampling and random feature selection. Gradient boosting builds trees sequentially, each focusing on residual patterns left by earlier trees. Boosting often achieves excellent tabular-data accuracy but requires tuning and careful monitoring. Feature importance measures should not automatically be interpreted as causal effects; permutation importance and partial-dependence or conditional-expectation tools can help, but correlated predictors complicate interpretation.

5. Classification Models and Evaluation

Classification models include logistic regression, naive Bayes, k-nearest neighbours, support vector machines, decision trees, random forests, and boosting methods. Selection should consider data size, dimensionality, nonlinear structure, probability calibration, latency, interpretability, and governance requirements.

A confusion matrix for binary classification contains true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN). From it:

• Accuracy = (TP + TN)/(TP + TN + FP + FN).
• Precision = TP/(TP + FP), when the denominator is nonzero.
• Recall or sensitivity = TP/(TP + FN), when the denominator is nonzero.
• Specificity = TN/(TN + FP), when the denominator is nonzero.
• F1 = 2(precision × recall)/(precision + recall), when precision plus recall is nonzero.

Accuracy can be misleading under class imbalance. In a fraud population where only 1% of transactions are fraudulent, predicting every transaction as legitimate yields 99% accuracy but zero recall for fraud. Precision is important when investigations are expensive; recall is important when missing a positive case is dangerous. The desired balance depends on the decision context.

The receiver operating characteristic (ROC) curve plots recall against false-positive rate across thresholds. Its area under the curve summarizes ranking ability across thresholds, but can appear optimistic in highly imbalanced settings. The precision-recall curve is often more informative when the positive class is rare. A model should also be assessed for probability calibration: among cases assigned probability approximately 0.7, about 70% should be positive over a suitable population if the probabilities are well calibrated.

Threshold selection should incorporate costs. If a false negative costs C_FN and a false positive costs C_FP, and predicted probabilities are calibrated, a simplified expected-cost rule predicts positive when the expected cost of acting is lower than the expected cost of not acting. In practice, intervention capacity, benefit of true positives, operational constraints, and fairness requirements must also be included.

6. Unsupervised Learning

6.1 k-Means Clustering

Given k clusters and Euclidean distance, k-means seeks centroids μ₁,…,μ_k that minimize

Σᵢ ||xᵢ − μ_{c(i)}||²,

where c(i) assigns observation i to a cluster. The standard algorithm alternates between assigning each point to its nearest centroid and recomputing each centroid as the mean of its assigned points. It converges to a local optimum, not necessarily the global optimum; multiple initializations are therefore advisable.

The method is sensitive to feature scaling, outliers, the chosen k, and the assumption that compact, approximately spherical groups are meaningful under the selected distance. The elbow plot, silhouette coefficient, stability under resampling, and domain usefulness can inform k, but no single statistic proves that a “true” number of clusters exists.

Hierarchical clustering creates a nested tree of groupings and can be visualized with a dendrogram. Density-based methods such as DBSCAN can identify irregularly shaped groups and noise, but depend on distance parameters and may struggle when cluster densities differ.

6.2 Dimensionality Reduction

Principal component analysis (PCA) transforms centered variables into orthogonal directions of decreasing variance. It can reduce dimensionality, assist visualization, and mitigate collinearity. High variance is not necessarily high predictive relevance, and principal components may be difficult to interpret. PCA must be fitted only on training data when used in a predictive pipeline.

7. Anomaly Detection

Simple methods include robust z-scores, interquartile-range rules, isolation forests, one-class support vector machines, and autoencoders. An isolation forest identifies observations that are isolated by random partitioning; anomalies tend to require fewer partitions. Autoencoders learn to reconstruct normal examples and flag high reconstruction error, but they require careful architecture, regularization, and contamination assumptions.

Evaluation is difficult because labels are scarce, delayed, or biased toward previously detected cases. Analysts should combine known incidents, expert review, simulated perturbations, time-based back-testing, alert volume, investigation yield, and operational cost. An anomaly score is not automatically a probability of fraud or failure.

8. Overfitting, Regularization, and Generalization

Overfitting occurs when a model captures idiosyncratic noise in training data and performs poorly on new data. Underfitting occurs when the model is too inflexible to represent relevant structure. The bias–variance perspective describes a trade-off: increasing flexibility may reduce systematic error but increase sensitivity to sample variation.

For linear regression, ridge regularization minimizes

RSS + λΣⱼβⱼ²,

and lasso minimizes

RSS + λΣⱼ|βⱼ|.

The intercept is normally excluded from the penalty. λ ≥ 0 controls shrinkage and must be selected using validation. Ridge generally shrinks correlated coefficients together and does not usually set them exactly to zero. Lasso can produce sparse coefficients, although selection can be unstable when predictors are highly correlated. Elastic net combines L1 and L2 penalties and can be useful in such settings.

Regularization does not replace sound feature design or leakage prevention. Standardization is commonly required before penalizing coefficients so that the penalty is not determined merely by measurement units.

9. Validation, Model Selection, and Hyperparameter Tuning

A robust workflow separates three activities:

1. Training estimates model parameters.

2. Validation selects algorithms, features, and hyperparameters.

3. Testing provides a final, relatively unbiased estimate after choices are complete.

A single random split can produce unstable results, particularly with small data. k-fold cross-validation divides training data into k folds, fits on k−1 folds, and evaluates on the remaining fold, repeating until each fold has served as validation. The mean estimates expected validation performance; its variation should also be reported. Stratified folds preserve class proportions for classification. Grouped folds prevent records from the same patient, household, or machine appearing in both training and validation. Time-series validation must preserve temporal order.

Nested cross-validation is useful when an unbiased estimate is required while hyperparameters are tuned. The inner loop selects the model; the outer loop estimates performance. For a final deployment model, after evaluation, preprocessing and model parameters may be refitted on all permitted development data, but the untouched test result must not be repeatedly used to guide choices.

Grid search evaluates a specified set of hyperparameter combinations. Random search can be more efficient when only a few hyperparameters strongly affect performance. Bayesian optimization uses prior evaluations to propose promising configurations. All search procedures must be constrained by computational budget, reproducibility, and the risk of optimizing a metric that does not represent business value.

10. Model Interpretation and Explainability

Interpretability has several meanings. A linear model may be intrinsically interpretable, while a complex model may require post hoc explanations. Local explanations describe one prediction; global explanations summarize overall model behaviour. SHAP-style additive attributions, permutation importance, partial-dependence plots, and counterfactual explanations can be useful, but each has assumptions and limitations.

An explanation is not proof of causation. A feature may be predictive because it is a proxy for another variable, because of selection effects, or because it records a downstream consequence. Causal decisions require a causal design, suitable identification assumptions, and often experimental or quasi-experimental evidence.

11. An Illustrative Case: Predicting Subscription Churn

Background

A fictional streaming-service company has 1.2 million subscribers and wants to reduce cancellations. The retention team can contact at most 30,000 customers per month. A campaign costs €2 per contact and is expected to produce value only when an intervention is directed at a customer who would otherwise cancel.

Problem Definition

The analytics team defines churn as cancellation within the next 30 days, measured at a monthly prediction date. Features include recent viewing days, failed payments, service complaints, tenure, plan type, and prior contact history. Only information available at the prediction date is permitted.

Analysis and Approach

The team creates a time-based development set using earlier months and reserves the most recent month as a final test period. A random split is rejected because customer behaviour and pricing policies change over time. Missing values are imputed within each training fold, categorical features are encoded in a pipeline, and customer records are grouped so that duplicate account events do not cross folds.

Three models are compared: regularized logistic regression, random forest, and gradient boosting. The baseline is the current rule-based campaign. Because campaign capacity is limited, the primary operational measure is precision among the top 30,000 ranked customers, together with recall, calibration, and estimated net benefit. ROC-AUC is reported as a secondary ranking metric, not as the sole decision criterion.

Suppose the final test set contains 100,000 customers, of whom 8,000 churn. At the chosen threshold, the model contacts 30,000 customers and identifies 4,800 of the churners. It therefore has recall 4,800/8,000 = 0.60. If 7,200 of the contacted customers are true churners, precision is 7,200/30,000 = 0.24. These figures are illustrative and would need comparison with the baseline and confidence intervals or repeated time periods.

The apparent inconsistency between the two illustrative counts—4,800 identified churners and 7,200 true churners—demonstrates why a confusion matrix must be internally checked before reporting results. A valid report cannot contain both values for TP. The team corrects the data pipeline and confirms that TP is 4,800; precision is therefore 4,800/30,000 = 0.16, while recall remains 0.60. This quality-control step is itself an important analytics practice.

The model is calibrated and the threshold is selected after estimating contact capacity and intervention economics. A fairness audit compares recall and precision across relevant customer groups, while avoiding use of protected attributes for inappropriate targeting. The model card records training dates, feature definitions, limitations, validation design, and monitoring responsibilities.

Outcome and Learning Points

After deployment, performance is monitored monthly for drift in feature distributions, calibration, subgroup outcomes, contact volume, and incremental retention. Because contacting a customer may itself affect churn, the company conducts a controlled experiment among eligible high-risk customers to estimate incremental treatment effect. A high churn probability alone does not prove that a customer is persuadable; uplift modelling may eventually improve targeting.

The case shows that model selection must reflect capacity and economics, that temporal leakage can invalidate results, and that validation is not complete until data consistency and operational impact have been checked.

12. Deployment, Monitoring, and Governance

A model is a component of a socio-technical system. Deployment requires versioned code, reproducible data transformations, access control, logging, rollback procedures, and clearly assigned ownership. Batch and real-time systems impose different latency and reliability requirements.

Monitoring should cover:

• Data drift: changes in predictor distributions.
• Concept drift: changes in the relationship between predictors and outcome.
• Performance drift: deterioration in relevant metrics.
• Calibration drift: mismatch between predicted probabilities and observed frequencies.
• Fairness indicators: differences in error rates or access across groups.
• Operational drift: changing intervention capacity, costs, or user behaviour.

Privacy principles include purpose limitation, data minimization, retention control, secure processing, and transparent communication where required by law. In regulated settings, decisions may require explanation, human review, documentation, and appeal mechanisms. Sensitive attributes should not be used casually, but excluding them does not remove bias because proxy variables may remain. Fairness criteria can conflict; for example, equalized error rates and equal calibration may not simultaneously be achievable when base rates differ. Governance therefore requires an explicit choice of harms, legal duties, and organizational values.

13. Challenges and Best Practices

Common failure modes include target leakage, random splitting of temporal data, tuning on the test set, optimizing accuracy for imbalanced classes, treating correlation as causation, ignoring intervention effects, and deploying without monitoring. Small data, label noise, sample-selection bias, and changing policies can limit generalization even when algorithms are technically correct.

Best practice is to establish a simple baseline, define the decision and metric before tuning, use leakage-safe pipelines, preserve an untouched test period, report uncertainty and subgroup performance, compare against operational rules, and document assumptions. Reproducible experiments should record data versions, code versions, random seeds where relevant, hyperparameters, and evaluation protocols. Human expertise remains essential for label definition, error analysis, exception handling, and responsible use.

Contemporary Developments

Modern tabular modelling increasingly combines gradient boosting with automated but constrained feature processing. Representation learning and deep neural networks are especially influential for images, speech, text, and high-dimensional sequences. Foundation models can provide useful embeddings and generative capabilities, but they introduce risks of hallucination, hidden training data, privacy leakage, and difficult validation. AutoML can accelerate model comparison, yet it does not automate problem definition, causal reasoning, governance, or business interpretation.

Research and practice are also moving toward uncertainty quantification, conformal prediction, causal and uplift modelling, federated learning, privacy-preserving computation, and energy-aware model development. These methods should be selected because they address a real decision need, not merely because they are novel.

Chapter Summary

Predictive analytics transforms data into estimates that support decisions, but successful modelling requires more than choosing an algorithm. Regression predicts numerical outcomes; classification predicts categories and often requires threshold and calibration decisions; clustering discovers possible structure without labels; and anomaly detection identifies unusual observations under an explicitly defined reference population. Linear and generalized linear models provide interpretable baselines, while tree ensembles capture nonlinearities and interactions. Regularization controls complexity, and cross-validation, temporal splitting, grouped sampling, and nested evaluation help estimate generalization honestly. Metrics must reflect the outcome, class distribution, operational capacity, and cost of errors. Deployment adds responsibilities for monitoring drift, calibration, fairness, privacy, security, and documentation. The central professional principle is to align data, model, metric, decision, and governance throughout the complete lifecycle.

Key Terms

Predictive analytics: Analysis that estimates future or unknown outcomes to support decisions.

Feature: An input variable used by a model.

Target: The outcome a supervised model is trained to predict.

Regression: Prediction of a numerical outcome.

Classification: Prediction of a categorical outcome.

Clustering: Unsupervised grouping of observations according to selected similarities.

Anomaly detection: Identification of observations that differ substantially from a reference pattern.

Overfitting: Learning noise or sample-specific patterns that do not generalize.

Regularization: Penalization or constraint used to control model complexity.

Cross-validation: Repeated partitioning of data for model training and validation.

Data leakage: Use of information unavailable at prediction time or improperly shared across evaluation partitions.

Calibration: Agreement between predicted probabilities and observed frequencies.

Precision: Proportion of predicted positives that are actually positive.

Recall: Proportion of actual positives that are detected.

ROC-AUC: Area under the receiver operating characteristic curve.

Hyperparameter: A modelling choice set outside the fitted parameters, such as tree depth or penalty strength.

Concept drift: Change over time in the relationship between predictors and the outcome.

Feature importance: A measure of a feature’s contribution to model predictions, subject to method-specific limitations.

Uplift modelling: Estimation of how an intervention changes an individual’s outcome.

Model governance: Processes for accountability, documentation, monitoring, and responsible model use.

Review Questions

Short Answer Questions

1. Distinguish supervised learning from unsupervised learning.

2. Why can accuracy be misleading for an imbalanced classification problem?

3. State one important difference between ridge and lasso regularization.

4. Why should preprocessing be fitted within cross-validation folds?

5. What is the difference between data drift and concept drift?

Long Answer Questions

1. Explain the complete workflow for developing and deploying a predictive model, from business formulation to monitoring.

2. Compare linear regression, logistic regression, decision trees, random forests, and gradient boosting in terms of assumptions, flexibility, interpretability, and risks.

3. Explain how MAE, RMSE, precision, recall, F1, ROC-AUC, and calibration support different evaluation decisions.

4. Discuss how temporal splitting, grouped splitting, stratification, and nested cross-validation address different validation problems.

5. Examine the ethical, legal, and governance issues involved in using machine learning for customer or citizen decisions.

Analytical / Application Questions

1. A fraud model detects 900 fraudulent transactions out of 1,000 frauds and flags 3,000 transactions, of which 900 are fraudulent. Calculate recall and precision, and explain which operational constraint each metric may represent.

2. Design a leakage-safe validation strategy for predicting machine failure using sensor data collected continuously from many machines. Justify your treatment of time and machine identity.

3. A company can contact only 10% of customers and wants to maximize retained revenue rather than classification accuracy. Propose a model-selection and thresholding framework, including experiments needed to determine whether predictions identify persuadable customers.

Multiple Choice Questions with Answers

Question 1

Which metric is generally most appropriate when the positive class is rare and the cost of investigating false positives is high?

A. Recall only

B. Precision

C. Accuracy only

D. R-squared

Correct Answer: B. Precision

Question 2

What is the primary purpose of regularization?

A. To guarantee causal interpretation

B. To increase training-set complexity without limit

C. To control model complexity and reduce overfitting

D. To remove the need for validation

Correct Answer: C. To control model complexity and reduce overfitting

Question 3

Which validation approach is most appropriate when predicting future outcomes from time-ordered data?

A. Randomly mixing all observations before splitting

B. Time-respecting train-validation splits

C. Using only the training error

D. Duplicating recent observations in every fold

Correct Answer: B. Time-respecting train-validation splits

Question 4

In logistic regression, the coefficient exponentiated, exp(βj), represents the multiplicative change in which quantity for a one-unit increase in xj, holding other variables constant?

A. Odds

B. Residual variance

C. Mean squared error

D. Euclidean distance

Correct Answer: A. Odds

Question 5

Which statement about k-means clustering is correct?

A. It requires a labelled target variable

B. It is unaffected by feature scaling

C. It minimizes within-cluster squared Euclidean distances for a specified k

D. It always finds the unique global optimum

Correct Answer: C. It minimizes within-cluster squared Euclidean distances for a specified k

Question 6

A model has TP = 80 and FN = 20. What is its recall?

A. 20%

B. 50%

C. 80%

D. 100%

Correct Answer: C. 80%

Question 7

Why is fitting an imputer on the full dataset before cross-validation problematic?

A. It always reduces the number of features to zero

B. It can allow validation-set information to influence training transformations

C. It prevents models from handling numerical variables

D. It guarantees underfitting

Correct Answer: B. It can allow validation-set information to influence training transformations

Question 8

Which measure is especially useful for evaluating the ranking quality of a rare positive class when precision matters?

A. Precision-recall curve

B. Training accuracy alone

C. R-squared

D. Mean absolute error

Correct Answer: A. Precision-recall curve

Question 9

What does calibration mean for a probabilistic classifier?

A. Every prediction has the same probability

B. Predicted probabilities correspond reasonably to observed frequencies

C. The model has no false positives

D. The model uses only standardized features

Correct Answer: B. Predicted probabilities correspond reasonably to observed frequencies

Question 10

Which statement best distinguishes prediction from causal inference?

A. Prediction always requires a randomized experiment

B. A predictive feature is automatically a cause of the outcome

C. Predictive association alone does not establish that changing a feature will change the outcome

D. Causal inference never uses observational data

Correct Answer: C. Predictive association alone does not establish that changing a feature will change the outcome