10.9: Detailed Figure Captions - Chapter 10

Chapter 10: Predictive Analytics and Machine Learning Basics — Figure Specifications

Overview

• Chapter: 10 — Predictive Analytics and Machine Learning Basics

• Total Figures Proposed: 9

• Figure Types Used: Comparison Table, Flowchart, Conceptual Illustration, Data Chart, Architecture Diagram, Infographic

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Figure 10.1.1

Title: Three Types of Analytics: Descriptive, Predictive, and Prescriptive

Detailed Caption: A three-column comparison table presents the analytics spectrum across four labeled row dimensions — Question, Methods, Time, and Example — with alternating white and light-gray row backgrounds to aid horizontal scanning. Each column is headed by a color-coded rounded rectangle: navy "Descriptive" on the left, teal "Predictive" in the center, and warm-gold "Prescriptive" on the right. Reading across the Question row, the cells answer "What happened?", "What will happen?", and "What should we do?" in sequence; the Methods row progresses from "Reporting, dashboards, summaries" through "Regression, ML, forecasting" to "Optimization, simulation, decision models"; the Time row moves from Past through Future to Future + Action; and the Example row grounds each type in a familiar business scenario — last quarter's sales report, customer churn prediction, and optimal pricing recommendation. By placing all three analytics types on a single canvas keyed to the same four dimensions, the table makes the chapter's positioning argument concrete: predictive analytics occupies the middle of a deliberate sequence, building on descriptive foundations while stopping short of the action-recommendation mandate that defines prescriptive work, so students can locate it precisely rather than conflating the three modes.

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Figure 10.2.1

Title: Supervised vs. Unsupervised Learning

Detailed Caption: Two side-by-side panels — navy-bordered on the left for Supervised Learning, teal-bordered on the right for Unsupervised Learning — present each paradigm as a three-stage data-flow diagram with summary metadata below. In the supervised panel, a small dataset box with labeled rows (marked with check and cross symbols indicating known outcomes) feeds via a right-pointing arrow into a navy Model box, which then outputs to a teal Prediction box labeled "Spam / Not"; below the diagram three bold-label lines confirm Input: Labeled Data, Tasks: Classification, Regression, and Example: Email spam detection. In the unsupervised panel, an equivalent dataset box with unlabeled rows feeds into a teal Model box, whose output is a loose cluster of warm-gold and teal circles labeled "Clusters" — the absence of any explicit prediction label visually encoding the paradigm's defining property; the three summary lines below confirm Input: Unlabeled Data, Tasks: Clustering, Dimensionality Reduction, and Example: Customer segmentation. By mirroring the layout of both panels while deliberately swapping labeled tags for unlabeled rows and a clean prediction box for ambiguous cluster blobs, the figure makes the structural difference between the two paradigms legible at a glance: everything about the workflow is identical except the presence or absence of known answers attached to the training data, and that single difference redirects the model's task from predicting a specified outcome to discovering an unspecified structure.

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Figure 10.3.1

Title: Linear Regression — Line of Best Fit

Detailed Caption: A scatter plot with axes labeled "Square Footage" (horizontal) and "House Price ($)" (vertical) displays approximately twenty teal data points arranged in a broadly positive linear trend, with a navy best-fit regression line running from the lower-left to the upper-right of the plot. Three gold dashed vertical segments — short residual markers — connect individual data points to the regression line, with one labeled "residual" to name the concept, illustrating that the line minimizes these vertical gaps rather than passing exactly through any single observation. The regression equation y = b₀ + b₁ · x appears in italic text in the upper-left area of the plot, linking the visual line to its algebraic form. A small legend at the bottom identifies the teal circles as Data points and the navy line as the Regression line. By grounding the abstract formula in a concrete housing-price example and annotating the residuals geometrically, the figure gives students a lasting spatial intuition for what linear regression actually optimizes: it is not about drawing any line through the cloud but about finding the unique line for which the collective squared residual distance is as small as possible.

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Figure 10.3.2

Title: Logistic Regression — Sigmoid Function and Decision Boundary

Detailed Caption: A line plot with horizontal axis labeled "z (linear combination of inputs)" spanning −6 to 6 and vertical axis labeled "P(y=1)" spanning 0 to 1 displays the characteristic S-shaped sigmoid curve in navy, rising from near zero on the left and asymptoting toward one on the right. A horizontal gold dashed line at P = 0.5 is labeled "Threshold = 0.5", and the region above it carries the label "Predict Class 1" in teal while the region below carries "Predict Class 0" in gray, dividing the plot into two clearly demarcated decision zones. Three annotated example points — a navy circle at z = −3 showing P ≈ 0.05, one at z = 0 showing P = 0.5, and one at z = 3 showing P ≈ 0.95 — anchor the abstract curve to concrete probability values, and the equation P(y=1) = 1 / (1 + e⁻ᶻ) appears in italic in the upper-left. By superimposing the threshold line directly on the sigmoid and shading the two classification regions, the figure resolves the core question students encounter when moving from linear to logistic regression: the model does not output a class label directly but rather a continuous probability, and the 0.5 threshold is simply a post-hoc rule applied to that probability — a rule that can be shifted if the costs of the two error types differ.

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Figure 10.3.3

Title: Decision Tree Structure — Classification Example

Detailed Caption: A top-down decision tree diagram shows a four-level hierarchy of navy rounded-rectangle decision nodes and teal rounded-rectangle leaf nodes, connected throughout by warm-gold arrows. The root node at the top asks "Petal Width ≤ 0.8?"; the Yes branch leads immediately to a teal leaf labeled "Setosa (50 samples, Gini=0.0)", while the No branch descends to a second decision node asking "Petal Length ≤ 4.75?"; that node's Yes branch reaches a teal leaf labeled "Versicolor (47 samples, Gini=0.04)" and its No branch continues to a third decision node asking "Petal Width ≤ 1.75?", whose Yes and No branches terminate in leaves labeled "Versicolor (3)" and "Virginica (46)" respectively. A small legend in the lower-left identifies navy boxes as Decision Nodes and teal boxes as Leaf Nodes. By encoding a well-known real dataset — the Iris flower classification problem — the figure lets students trace a concrete prediction path from root to leaf while simultaneously reading off the sample counts and Gini impurity values that quantify how cleanly each split separates the classes, transforming the abstract notion of a "sequence of feature-based questions" into a walkable artifact they can interrogate one branch at a time.

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Figure 10.3.4

Title: Random Forest — Ensemble of Decision Trees

Detailed Caption: An architecture diagram flows from a single navy "Training Data" box at the top through three dashed bootstrap arrows labeled Bootstrap 1, Bootstrap 2, and Bootstrap 3 down to three teal tree boxes — Tree 1, Tree 2, and Tree 3 — arranged horizontally in the middle tier. Below each tree a navy label shows the individual prediction it would make: Class A from Tree 1, Class B from Tree 2, and Class A from Tree 3. Gold arrows from all three predictions converge into a warm-gold "Majority Vote / Averaging" box, which feeds a final navy "Final: Class A" output box at the bottom. A small annotation tile on the left reads "Bagging: different data" to name the bootstrap sampling mechanism. By making the vote count visible — two Class A votes against one Class B — the figure demonstrates why majority voting reduces variance without requiring students to follow any mathematics: the individual trees disagree, yet the ensemble arrives at a stable answer because independent errors tend to cancel out when enough diverse models are aggregated together.

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Figure 10.4.1

Title: K-Fold Cross-Validation Process

Detailed Caption: A five-row grid shows 5-fold cross-validation, with each row labeled Fold 1 through Fold 5 on the left and consisting of five equal rectangular blocks colored either warm-gold (Validation) or teal (Train). Across the five rows the gold Validation block steps through each position in turn — leftmost in Fold 1, second in Fold 2, third in Fold 3, fourth in Fold 4, and rightmost in Fold 5 — so that every block eventually serves once as the held-out validation set while the remaining four serve as training data. A per-row accuracy label appears to the right of each row (0.82, 0.85, 0.81, 0.84, 0.83), and a navy summary box at the bottom reads "Average CV Accuracy = 0.83." By making the rotation of the validation block visible across all five rows simultaneously rather than describing it verbally, the figure resolves the most common student confusion about cross-validation: no single fold is privileged as "the" test set; instead, every data point participates in validation exactly once, so the average accuracy is a genuinely unbiased estimate of how the model generalizes to unseen data.

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Figure 10.4.2

Title: Confusion Matrix for Binary Classification

Detailed Caption: A 2×2 confusion matrix occupies the left portion of the figure, with column headers "Predicted Positive" and "Predicted Negative" across the top and row headers "Actual Positive" and "Actual Negative" down the left side. The top-left cell (True Positive, TP = 5) and bottom-right cell (True Negative, TN = 3) are rendered with teal-tinted backgrounds and teal borders to mark correct predictions, while the top-right cell (False Negative, FN = 1) and bottom-left cell (False Positive, FP = 1) carry salmon-red backgrounds and coral borders to mark errors. To the right, a warm-gold-bordered panel lists the four derived metrics with their computed values: Accuracy = (5+3)/10 = 0.80, Precision = 5/(5+1) = 0.83, Recall = 5/(5+1) = 0.83, and F1 = 2×(0.83×0.83)/(0.83+0.83) = 0.83. By pairing the matrix cells directly with the formulas that reference them, the figure prevents the common failure mode of memorizing metric definitions in isolation: students can trace each formula back to the specific cell or pair of cells it draws on, making the relationship between a model's error pattern and its aggregate evaluation scores structurally transparent rather than merely stated.

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Figure 10.5.1

Title: Bias-Variance Tradeoff

Detailed Caption: A line chart with horizontal axis labeled "Model Complexity →" and vertical axis labeled "Error" shows two smooth curves traced over a shared complexity range. The navy Training Error curve descends monotonically from upper-left toward lower-right, flattening near the bottom as complexity grows, reflecting the fact that a sufficiently expressive model can fit training data nearly perfectly. The teal Test Error curve follows a U-shape: it begins high on the left, descends to a minimum in the center of the chart, then curves back upward toward the right, capturing the degradation caused by overfitting. A vertical gold dashed line at the minimum of the test curve is labeled "Optimal Complexity," and lightly shaded rectangular overlays on each side are labeled "Underfitting" on the left and "Overfitting" on the right, with axis annotations "Simple (High Bias)" and "Complex (High Variance)" anchoring the ends of the complexity axis. By superimposing both error curves on the same axes and marking the optimal point explicitly, the figure converts the bias-variance tradeoff from a qualitative idea into a geometric fact: the ideal model is not the one that fits training data best, nor the simplest model possible, but the one positioned at the bottom of the test-error U — the point where added expressiveness stops reducing generalization error and starts increasing it.