Multiple Linear Regression

Multiple linear regression models a continuous outcome as a linear function of two or more predictors, estimating each predictor's association with the outcome while holding the other predictors constant.

다중선형회귀는 연속형 결과변수를 둘 이상의 예측변수의 선형함수로 모형화하여, 다른 예측변수를 고정한 상태에서 각 예측변수와 결과변수의 연관성을 추정합니다.

How do I estimate the effect of several predictors on a continuous outcome at the same time?

여러 예측변수가 연속형 결과변수에 미치는 영향을 동시에 어떻게 추정하나요?

Multiple linear regression estimates how a continuous outcome changes with each predictor while adjusting for the other predictors in the model. It fits when the outcome is continuous, relationships are approximately linear, and residuals are roughly normal with constant variance.

When to use Multiple Linear Regression

• A continuous outcome explained by several numeric or categorical predictors
• Estimating one predictor's association while adjusting for covariates
• Comparing the relative contribution of predictors with standardized coefficients

When to use something else

• Binary outcome: use logistic regression
• Observations nested in clusters or repeated over time: use a multilevel (mixed-effects) model

Assumptions and requirements

• Linear relationship between predictors and outcome
• Independent errors
• Homoscedastic, approximately normal residuals
• No severe multicollinearity among predictors

What the analysis reports

• Unstandardized (B) and standardized (β) coefficients with standard errors
• t tests, p-values, and confidence intervals for coefficients
• R², adjusted R², and overall F test
• Variance inflation factors
• Residual diagnostic plots

How to report it

The model explained a significant proportion of variance in [outcome], R² = [value], F([df1], [df2]) = [value], p = [value], and [predictor] was a significant predictor, β = [value], t([df]) = [value], p = [value].

Related methods

• Simple Linear Regression
• Regularized Regression (Ridge, Lasso, ElasticNet)
• Logistic Regression

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