A coefficient is a numerical parameter estimate that quantifies a modeled term’s contribution or association. In regression, each coefficient is multiplied by its corresponding predictor value and combined with the intercept to estimate an outcome. section 9.1.2
Coefficients help analysts interpret individual predictors, while evaluation metrics and residuals describe overall performance and prediction discrepancies. Their meaning depends on the chosen model and the data relationships it approximates. section 9.1.2 section 9.1
Use coefficients to:
- Estimate an outcome from new predictor values using the fitted model equation. section 9.1.2
- Compare the modeled contribution or association of individual predictors, while recognizing that coefficient interpretation is model-dependent. section 9.1.2 section 9.1
- Assess results alongside evaluation metrics and residuals rather than treating coefficients as a complete measure of model quality. section 9.1.2
Housing-price regression
A linear model can estimate house prices from square footage and number of bedrooms. Each predictor receives a coefficient; multiplying those values by new inputs and adding the intercept produces an estimated price. section 9.1.2
import statsmodels.api as sm
import pandas as pd
housing_prices = pd.read_csv("housing_prices.csv") #1
X = housing_prices[["sq_footage", "n_bedrooms"]]
y = housing_prices["price"] #2
X = sm.add_constant(X) #3
model = sm.OLS(y, X).fit() #4
print(model.summary())
Fit an ordinary least squares model with square footage and bedrooms, add an intercept, and inspect the coefficient output with statsmodels. section 9.1.2
