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Also known as: Beta Coefficient, Weight
A parameter in a regression model that quantifies the change in the outcome associated with a unit change in a predictor.
DESCRIPTION
Regression coefficients parameterize the relationship between predictors and an outcome in regression models. In linear regression, each coefficient represents the expected change in the dependent variable per unit change in a predictor, holding others constant. Their uncertainty is assessed via standard errors and confidence intervals. Statistical significance tests and regularization affect estimates and interpretation. Standardization facilitates comparing effect sizes across variables. Coefficients may be biased by collinearity or omitted variables, requiring diagnostics and domain knowledge. Proper interpretation depends on model form, link function, and feature preprocessing.
ALTERNATIVE DEFINITIONS
Encyclopaedia Britannica
Regression coefficients are estimates of the parameters that describe the relation between a dependent variable and one or more independent variables.
Situates coefficients within the broader framework of regression analysis.
Penn State STAT 462
The regression coefficient for a predictor is the expected change in the mean response for a one-unit increase in the predictor, holding all other predictors constant.
Gives a clear conditional interpretation for multiple regression.
UCLA Statistical Consulting
Regression coefficients represent the relationship between a predictor variable and the response variable in a regression model.
Plain-language characterization for practitioners across software packages.
RELATED TERMS
Linear Model Logistic Regression R-squared Standard Error p-value Confidence Interval Regularization Feature Scaling Multicollinearity
COMPETING TERMS
Pearson Correlation Coefficient
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist Data Analyst Information Analyst
EXTERNAL SOURCES
- Wikipedia - Regression analysis
- Penn State - Course notes on regression analysis
- An Introduction to Statistical Learning - ISL book resources on regression
- scikit-learn - Linear models and coefficient estimation
TOP QUESTIONS
What is a Regression Coefficient?
It quantifies how the expected outcome changes with a one-unit change in a predictor, controlling for other variables in the model.
Category: Definition
How do I interpret standardized Regression Coefficients?
Standardized coefficients (betas) express effects in standard deviation units, enabling comparison of relative importance across predictors.
Category: Example
What are common pitfalls in interpreting Regression Coefficients?
Confusing correlation with causation, ignoring confounders, and overlooking multicollinearity can mislead interpretations.
Category: Mistakes
How does Regularization affect Regression Coefficients?
Lasso can shrink some coefficients to zero for feature selection; Ridge shrinks coefficients toward zero, reducing variance.
Category: Topic
What does a p-value for a coefficient indicate?
It tests the null that the true coefficient is zero. Low p-values suggest the predictor contributes beyond noise under assumptions.
Category: Testing
How do interactions affect coefficients?
Interaction terms change the interpretation: main effects are conditional on interacting variables, requiring careful plotting and explanation.
Category: Requirements
How does feature scaling change coefficients?
Scaling changes coefficient magnitude but not predictions for linear models; interpretation shifts to scaled units.
Category: Misunderstanding
What is multicollinearity’s impact on coefficients?
It inflates variance, making coefficients unstable and less interpretable. Remedies include regularization or variable selection.
Category: Risks
Can coefficients be interpreted causally?
Only under strong assumptions or with causal designs. Otherwise, they are associational.
Category: Opinion