Logistic Regression Lab

Logistic Regression Metabolic Lab

We predict the probability of developing Type 2 Diabetes based on Fasting Glucose and BMI.

Enter patient values → adjust model → watch the risk probability update on the sigmoid curve.

How Are β Coefficients Calculated?

In a real clinical model, β values are never manually chosen. They are learned from patient training data using Maximum Likelihood Estimation (MLE):

Training data → MLE → optimal β₀, β₁, β₂ MLE finds β values that make the observed outcomes (diabetic / not) most probable. Solved iteratively via gradient descent. The sliders let you explore — click "Auto-Fit" to learn betas from data.

Sensitivity & Specificity

When the model classifies each patient using the threshold, four groups emerge:

Sensitivity =TP/(TP+FN)
Of all diabetics, what % did we catch?
Specificity =TN/(TN+FP)
Of all healthy, what % were cleared?

Drag the yellow line — watch both metrics trade off live.

⚖️ Ethical Reality

A threshold of 0.5 is mathematically symmetric but clinically arbitrary. Missing one diabetic delays life-saving insulin. Thresholds must reflect clinical consequence — not mathematical convenience.

① Patient Input

Fasting Glucose

mg / dL

Patient BMI

kg / m²

Decision Threshold 0.50

or drag yellow line on chart

② Model Coefficients

β₀ · Risk Baseline -8.0

log-odds at zero glucose & BMI

β₁ · Glucose Sensitivity 0.040

risk increase per mg/dL

β₂ · BMI Sensitivity 0.100

risk increase per kg/m²

③ Prediction Output

Diabetes Risk Probability

—

LOW RISK

P = 1 / (1 + e^−z)
z = -8.0 + 0.040·G
+ 0.100·BMI

—

Sensitivity

—

Specificity

④ Sigmoid Curve — Glucose vs Risk Probability (at subject's BMI · drag yellow line to adjust threshold)