Regression
A statistical method used to model the relationship between a dependent variable and one or more independent variables.
What is Regression?
Regression analysis estimates the conditional expectation of a dependent variable given the independent variables. Unlike correlation, which is symmetric, regression involves proposing a directional model where predictors (X) explain the outcome (Y).
Why Regression Matters
It goes beyond simple association to allow for prediction, forecasting, and inferring causal relationships (when properly designed). Multiple regression can isolate the effect of one variable while controlling for confounders.
How to Interpret
The regression coefficients (betas) indicate the average change in the dependent variable for a one-unit increase in the independent variable, holding all other variables constant.
Example
A real estate model uses regression to predict a house's price (dependent variable) based on its square footage, number of bedrooms, and distance to the city center (independent variables).
Common Mistakes
- Extrapolating predictions far outside the range of the observed data.
- Ignoring regression assumptions like linearity, independence of errors, and homoscedasticity.