Data Scientist in Toronto 🇨🇦🍁. Learning in public. Python, data viz, ML/AI, causal inference. Ravenclaw 🦅. 🏳️🌈 www.franciscoyira.com
![A data science flashcard titled "BREUSCH-PAGAN TEST" on a dark blue background. The card explains that this is a statistical test that checks whether the variance of the residuals in a regression model is constant (i.e., tests for heteroskedasticity).
The flashcard is divided into sections explaining how the test works:
1. First, we fit our regression model and compute the residuals, shown with mathematical equations.
2. Then an auxiliary regression is run using the squared residuals as response variable, while keeping the original predictors.
3. The Breusch-Pagan statistic is just the F-statistic of this auxiliary regression, testing whether any predictors have explanatory power over the squared residuals. The F-statistic formula is provided.
4. This F-statistic is compared against a table to return a p-value. A value less than 0.05 usually results in rejecting the null hypothesis that the residuals have constant variance.
The card includes Python code showing how to implement the test:
```python
import statsmodels.api as sm
from statsmodels.stats.diagnostic import het_breuschpagan
model = sm.OLS(y, sm.add_constant(X)).fit()
bp_test = het_breuschpagan(model.resid, model.model.exog)
stat, pval = bp_test[0], bp_test[1]
print(f"BP stat: {stat:.2f}, p-value: {pval:.4f}")
```
A section titled "WHY IT MATTERS" explains that if residuals don't have constant variance, confidence intervals and p-values from standard OLS regression can't be trusted. The Breusch-Pagan test helps catch heteroskedasticity early and apply corrective measures like weighted least squares or robust standard errors.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:ub5ufkyiedg3bxsix6nkp3gj/bafkreifiyc4w6aej6ozxg663g5vdixpcm2hzm7x2elojq65vujl3j6bgzi)
Data Scientist in Toronto 🇨🇦🍁. Learning in public. Python, data viz, ML/AI, causal inference. Ravenclaw 🦅. 🏳️🌈 www.franciscoyira.com