Interpreting Regression Coefficients

A regression model's coefficients are only useful if you can interpret them correctly — a skill that separates practitioners who can explain their models from those who cannot.

Raw vs. Standardised Coefficients

Raw coefficients are expressed in the units of the feature. Standardised (beta) coefficients are dimensionless and allow you to compare the relative importance of features on the target.

Standardising for Comparability

<pre><code class="language-python">from sklearn.preprocessing import StandardScaler from sklearn.linear_model import LinearRegression from sklearn.pipeline import make_pipeline from sklearn.datasets import fetch_california_housing from sklearn.model_selection import train_test_split import pandas as pd data = fetch_california_housing() X_train, X_test, y_train, y_test = train_test_split( data.data, data.target, test_size=0.2, random_state=0 ) pipeline = make_pipeline(StandardScaler(), LinearRegression()) pipeline.fit(X_train, y_train) coefs = pd.Series( pipeline.named_steps["linearregression"].coef_, index=data.feature_names ).sort_values(key=abs, ascending=False) print(coefs)</pre>

Caveats in Interpretation

Coefficients describe association, not causation, and their values depend on which other features are in the model.

Correlation is Not Causation

A large positive coefficient for a feature does not mean that feature causes the target to increase. Confounding variables, data collection bias, and model misspecification can all produce misleading coefficients. Always pair statistical interpretation with domain knowledge.

Coefficient Sign Flipping

Adding or removing a correlated feature can flip the sign of a coefficient — a symptom of multicollinearity. If you observe this, check VIF scores and consider regularisation (Ridge or Lasso) before drawing conclusions.