00 // MACHINE LEARNING/MODULE 02 // REGRESSION PLAYGROUND

Regression PlaygroundLEAST SQUARES

Polynomial curve fitting, residual error computation (SS_res), and test-train variance inspection via exact analytical least squares.

03 // Cartesian Regression Stage

CLICK CANVAS TO INJECT SAMPLES

ŷ = 0.829x + 13.890(Degree 1)

Target Domain: [0, 100] × [0, 100]

TRAIN (27)

TEST (8)

FITTED MODEL

RESIDUAL (y − ŷ)

01 // Polynomial Model Spec

Order & Dynamics

POLYNOMIAL DEGREE (d)1 // LINEAR

UNDERLYING SYNTHETIC FUNCTION

GAUSSIAN NOISE (σ)6

SAMPLE DENSITY (N)35

TRAIN / TEST SPLIT (75% / 25%)

02 // Residual Telemetry & Gauges

Analytical Least Squares

TRAIN27 PTS

MSE:41.1055

MAE:5.1951

R²:0.9186

TEST8 PTS

MSE:30.1183

MAE:4.089

R²:0.9534

Strong Generalization: Degree 1 fits the underlying structure well, maintaining consistent test R² (95.3%) close to training R² (91.9%).

04 // Statistical Rigor: Zero-Variance Target Behavior

R² = 1 − (SS_res / SS_tot). If all target values are identical, total variance SS_tot = ∑(y_i − ȳ)² = 0.

In this degenerate edge case, dividing by zero renders R² mathematically undefined. ThinkViz explicitly reports N/A rather than silently outputting misleading finite numbers.