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Modeling and predicting outcomes -- continuous, binary, ordinal, count, or time-to-event -- from one or more predictors.
Related Calculators
Simple Linear RegressionPredicts a continuous outcome from a single continuous predictor.Multiple Linear RegressionPredicts a continuous outcome from two or more predictors simultaneously, adjusting for confounders.Logistic RegressionPredicts the probability of a binary outcome from one or more predictors, expressed as Odds Ratios.Cox Proportional Hazards RegressionMultivariable survival model estimating adjusted hazard ratios for time-to-event outcomes with censoring.Poisson RegressionModels count outcomes (events per unit time/space) via Incidence Rate Ratios.Ordinal Logistic RegressionProportional-odds model for ordered categorical outcomes (severity grade, NYHA class, Likert scale).
Related Articles
Medical Research Examples
Simple Linear Regression: A pulmonologist studies whether FEV1 (% predicted) predicts 6-Minute Walk Distance in 45 COPD patients: 6MWD = 112.4 + 3.8×FEV1%, R²=0.63, p<0.001.
Multiple Linear Regression: A geriatrician models hospital length of stay from Age, BMI, and comorbidity count in 60 elderly patients: F(3,56)=12.4, p<0.001, R²=0.40; Age and comorbidities are independent predictors, BMI is not.
Logistic Regression: A cardiologist predicts in-hospital MACE in 120 ACS patients from Age, BMI, and Smoking: Smoking OR=3.2 (95% CI 1.4-7.1, p=0.005) after adjustment.
Cox Proportional Hazards: 120 post-MI patients followed 3 years: Age HR=1.08 (95% CI 1.03-1.14, p=0.002); concordance c=0.78 (good discrimination).
Poisson Regression: COPD exacerbations per year modeled from FEV1% and inhaled steroid use in 80 patients: ICS IRR=0.61 (95% CI 0.42-0.89, p=0.009), a 39% reduction.
Ordinal Logistic Regression: NYHA functional class (I-IV) modeled from BNP and age in 150 heart-failure patients: BNP (per 100 pg/mL) OR=1.42 (95% CI 1.18-1.71, p<0.001).
Common Mistakes
- Using linear regression on a binary or count outcome instead of logistic or Poisson regression.
- Extrapolating predictions beyond the observed range of the predictor variable.
- Ignoring multicollinearity among predictors (check VIF; values above 10 are problematic).
- Reporting only a p-value without the effect estimate (β, OR, HR, or IRR) and its 95% confidence interval.
- Running logistic regression with too few events per predictor (EPV < 10), producing unstable odds ratios.
- Treating an ordinal outcome as continuous (e.g. averaging Likert scores) instead of using ordinal logistic regression.
Reporting Recommendations
Journals expect more than a p-value. For each test, report the effect estimate and its 95% confidence interval alongside the p-value:
Simple Linear Regressionβ coefficient, 95% CI, R², F statistic, p-value, standard error of estimate
Multiple Linear Regressionβ coefficients, 95% CIs, adjusted R², F statistic, VIF for multicollinearity
Logistic RegressionOR, 95% CI, p-value for each predictor; Nagelkerke R²; Hosmer-Lemeshow test
Cox Proportional Hazards RegressionHR, 95% CI, p-value per covariate; concordance index (c-statistic)
Poisson RegressionIRR, 95% CI, p-value per covariate; likelihood ratio χ² test; deviance/df for overdispersion
Ordinal Logistic RegressionOR, 95% CI, p-value per covariate; proportional-odds assumption checked via Brant’s test
Recommended Learning Order
- Correlation Analysis — understand basic association between two variables first
- Simple Linear Regression — predict a continuous outcome from a single predictor
- Multiple Linear Regression — extend to several predictors and adjust for confounders
- Logistic Regression — move to binary outcomes and odds ratios
- Ordinal Logistic / Poisson Regression — specialized outcome types (ordered categories, counts)
- Cox Proportional Hazards Regression — most advanced: time-to-event outcomes with censoring
Frequently Compared Tests
Simple Linear vs. Multiple Linear vs. Logistic vs. Cox Regression
Choice depends on outcome type (continuous/binary/time-to-event) and predictor count -- see the Regression Wizard.
Frequently Asked Questions
What's the difference between linear and logistic regression?
Linear regression predicts a continuous outcome. Logistic regression predicts the probability of a binary outcome and reports the result as an odds ratio rather than a raw coefficient.
When do I need multiple regression instead of simple linear regression?
When you want to adjust for confounders or include more than one predictor variable at the same time.
How many subjects do I need per predictor?
Rule of thumb: 10-20 subjects per predictor for linear regression; a minimum of 10 events per predictor (EPV = 10) for logistic regression.
What's the difference between logistic regression and Cox regression?
Logistic regression treats the outcome as a fixed yes/no measured at one point in time. Cox regression models the time until the event occurs and correctly handles patients censored (lost to follow-up, or the study ended) before the event happened.
My outcome is a count (e.g. number of hospitalizations) -- which regression?
Use Poisson regression (or Negative Binomial if overdispersed), not linear regression, since counts are non-negative integers and are often right-skewed.
My outcome has ordered categories (mild/moderate/severe) -- can I use linear regression?
No. Use ordinal logistic regression, which respects the ordering of categories without assuming the distance between them is equal.