What is multiple linear regression and when should I use it?

Multiple linear regression models the linear relationship between one continuous outcome (Y) and two or more predictors (X1, X2, ...). Use it when you want to estimate how each predictor influences the outcome while statistically controlling for the others.

What is the difference between simple and multiple linear regression?

Simple linear regression uses one predictor; multiple linear regression uses two or more. Multiple regression returns partial regression coefficients that represent each predictor's unique effect after holding the other predictors constant.

How do I interpret R squared in multiple regression?

R² is the proportion of variance in the outcome explained by all predictors combined. R² = 0.65 means 65% of the variation in Y is explained by your model. Adjusted R² is preferred when comparing models with different numbers of predictors because it penalises adding non-informative variables.

What is VIF and when is multicollinearity a problem?

VIF (Variance Inflation Factor) measures how much a predictor's variance is inflated by correlations with other predictors. VIF > 5 is concerning and VIF > 10 indicates serious multicollinearity. Drop one of the correlated predictors, combine them, or use ridge regression.

What assumptions does multiple linear regression require?

Linearity, independence of residuals, homoscedasticity (constant residual variance), normality of residuals, and no severe multicollinearity. The tool reports VIF, residual plots and a Q-Q-style residual histogram so you can check each one visually.

How large a sample do I need for multiple linear regression?

A common rule of thumb is at least 10–20 observations per predictor. For 3 predictors that is 30–60 cases minimum. Power analysis gives the exact n; very small samples (n < 5×predictors) produce unstable coefficients and unreliable p-values.

How do I report multiple regression results in APA 7 format?

Report the full model F-statistic with degrees of freedom, p-value, R² and adjusted R², followed by each predictor's unstandardised coefficient (B), standard error, standardised coefficient (β), t-statistic, p-value and 95% confidence interval. The tool generates this paragraph automatically.

What is the difference between B and beta coefficients?

B (unstandardised) is in the original units — for every one-unit increase in X, Y changes by B units. Beta (standardised) is unit-free and lets you compare predictors directly: a beta of 0.45 means a one standard-deviation increase in X moves Y by 0.45 standard deviations.

Can multiple regression prove causation?

No. Multiple regression quantifies association while controlling for measured confounders. Causal claims require an experimental design (random assignment), instrumental variables, or strong theoretical and contextual support.

What should I do if my residuals are not normal?

With large samples (n > 100) the central limit theorem makes the test relatively robust. Otherwise, transform Y (log, square root), use robust standard errors, or switch to a generalised linear model (GLM) appropriate for the outcome distribution.

Multiple Linear Regression Calculator – Free Online OLS Tool with Coefficients, R² & VIF | StatsUnlock

📊 Linear Models · OLS · Free Online Tool

Multiple Linear Regression Calculator

Run multiple linear regression online with multiple predictors — get OLS coefficients, standard errors, t-statistics, p-values, R², adjusted R², F-statistic, VIF (multicollinearity check), confidence intervals, colorful residual diagnostics, and APA-format results in one click.

Multiple Regression OLS Estimation R² & Adjusted R² F-Statistic & p-value VIF Multicollinearity APA 7 Reporting

1 Enter Your Data

📂 Sample Datasets (5 built-in)

Dataset 1 is loaded by default.

🎯 Significance Level (α)

95% CI is the default for most research.

📌 Enter values as comma-separated numbers (e.g., 52, 48, 55, 61, 47). Each predictor must have the same number of values as the outcome (Y). You can rename each predictor (group name) below.

🎯 Outcome Variable (Y) — name is editable Y

Upload a .csv, .txt, .xlsx or .xls file. After upload, mark each column as Predictor (X), Outcome (Y), or Ignore. You must select exactly one Y and at least one X.

Enter each value separately, one per row, then add more rows. Manual entry uses the same predictor blocks above — switch back to Type Data to add or remove rows by editing the comma-separated list.