Multiple Linear Regression

Multiple Linear Regression predicts a continuous outcome from several predictors simultaneously, isolating each predictor's effect while holding others constant.

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Step 1 — Provide your data

• One dependent variable (continuous)
• Two or more predictor variables (numeric)

Supports Excel Import, Sample Data Generator, and Manual Entry.

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Step 2 — Results

Coefficients table:

• B (unstandardised), Std. Error, Beta (standardised), t-value, p-value, 95% CI

Model fit:

• R-squared, Adjusted R-squared
• Standard error of estimate
• F-statistic with df and p-value

Diagnostics:

• VIF per predictor (multicollinearity)
• Durbin-Watson (autocorrelation)

A UniversalChatBot is available for discussion.

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Statistical methods used

Model: Y = beta0 + beta1*X1 + ... + betap*Xp + epsilon

Estimation: OLS via beta = (X'X)^-1 X'y

F-test: F = MS_regression / MS_residual with df = (p, n-p-1).

H0: all betas = 0. H1: at least one != 0. alpha = 0.05.

Per-coefficient: t = B/SE, two-tailed p from t-distribution.

Standardised Beta: beta_std = B * SD(predictor) / SD(outcome)

VIF: 1 / (1 - R2_j) where R2_j = R-squared of predictor j on others.

VIF	Interpretation
1-5	Acceptable
5-10	High multicollinearity
> 10	Serious multicollinearity

Durbin-Watson: ~2 = no autocorrelation, <1.5 = positive, >2.5 = negative.