Learning Module

Regression Analysis

Learn regression analysis in biostatistics with dental data. Predict outcomes, interpret relationships, and explore each concept interactively.

Linear Logistic Multiple Assumptions
📈

Predict outcomes
Estimate pocket depth from age, smoking status, and plaque levels.

🦷

Dental research
Identify which risk factors truly influence implant failure or caries.

📋

Report results
Present coefficients, odds ratios, and confidence intervals in papers.

Choose the Right Regression Model
Linear regression

Use when the outcome is continuous, like attachment loss, plaque score, or healing time, and you want to estimate how much it changes with a predictor.

Multiple regression

Use when several predictors may influence the same continuous outcome and you want to adjust for confounding variables at the same time.

Logistic regression

Choose this when the outcome is binary, such as implant failure yes/no or peri-implantitis present/absent.

Model fit matters too

A model is not judged only by p-values. You also need to know how well it explains variation and whether the assumptions are believable.

Before You Trust the Model
Check whether the outcome type really matches the model you chose.
Decide how each predictor is coded so the coefficient has a clear clinical meaning.
Think about confounding before fitting the model, not after reading the result.
Review assumptions and sample size because unstable models can produce very confident-looking but misleading estimates.
Core Regression Concepts

Click a card to learn and try it.

📉
Linear Regression
Continuous outcomes
Tap to try →
🔀
Multiple Regression
Many predictors
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🎲
Logistic Regression
Binary outcomes
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⚖️
Odds Ratio
Effect size for logistic
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Assumptions
Validity checks
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🎯
Model Fit (R²)
How good is the model?
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Interactive Regression Playground

Click the chart to add data points, then fit a regression line. Try preset dental datasets.

Logistic Regression Live Demo

Adjust the slider to see how smoking affects implant failure probability.

Scenario: Predicting Implant Failure from Cigarettes/Day
0 40
10 cigarettes/day
24%
S-Curve (Sigmoid Function)
Dental Research Simulation

Watch a regression study unfold step-by-step: recruit patients, collect data, fit the model, interpret results.

How to Report in a Paper
📐

Linear Regression
Report: B (95% CI), p-value
e.g. B=0.04 (0.02-0.06), p=0.001

🎲

Logistic Regression
Report: OR (95% CI), p-value
e.g. OR=2.5 (1.3-4.8), p=0.006

📋

Model Summary
Report: R², Adjusted R², F-stat
e.g. R²=0.42, F(3,96)=23.1, p<0.001

Model TypeCoefficient95% CIp-valueInterpretation
Linear
Age → CAL
B = 0.040.02 – 0.060.001Each year of age increases CAL by 0.04 mm
Multiple
Age + Smoking → PD
Bage=0.03
Bsmoke=1.2
0.01–0.05
0.6–1.8
0.004
<0.001
Adjusted for confounders
Logistic
Smoking → Implant Failure
OR = 2.51.3 – 4.80.006Smokers have 2.5x odds of implant failure
Example Reporting Text

"Multiple linear regression was performed to examine the effect of age, smoking status, and plaque index on clinical attachment loss. The model was statistically significant, F(3, 96) = 23.1, p < 0.001, R² = 0.42. Age (B = 0.04, 95% CI: 0.02–0.06, p = 0.001) and smoking (B = 1.2, 95% CI: 0.6–1.8, p < 0.001) were significant predictors, while plaque index was not (B = 0.15, 95% CI: -0.1–0.4, p = 0.22)."

Quick Reference Summary

📉 Linear Regression

Continuous outcome. Y = B0 + B1*X. Report B with 95% CI and p-value. Check linearity, normality of residuals.

🔀 Multiple Regression

Multiple predictors. Adjusts for confounders. Check multicollinearity (VIF < 10). Report adjusted R².

🎲 Logistic Regression

Binary outcome (yes/no). Reports odds ratios. Use when predicting implant failure, disease presence.

⚖️ Odds Ratio

OR = 1 (no effect), OR > 1 (increased risk), OR < 1 (protective). Always report with 95% CI.

✅ Key Assumptions

Independence, linearity, no multicollinearity, adequate sample size. EPV >= 10 for logistic regression.

🎯 Model Fit

R² = proportion of variance explained. Higher is better. Adjusted R² penalizes adding useless predictors.

How to Read Regression Output
Coefficient

The sign shows direction and the size shows expected change in the outcome for a one-unit increase in the predictor, holding other variables constant.

Odds ratio

In logistic models, OR greater than 1 means higher odds, OR less than 1 means lower odds. It describes multiplicative change, not direct probability change.

Confidence interval

The interval shows precision. Wide intervals suggest more uncertainty, even if the p-value looks interesting.

R2 and adjusted R2

These tell you how much outcome variability is explained by the model, but a high value alone does not prove causation or good clinical usefulness.

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