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Section 8.11 Key Takeaways
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Linear regression helps us predict one variable (Y) from another (X) using a line of best fit.
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The equation of the line is y = mx + b, where:
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The slope tells us both the direction and strength of the relationship.
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Residuals = actual - predicted values; smaller residuals = better model fit.
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A good model has random, evenly scattered residuals (homoscedasticity).
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R² tells us how much variance in Y is explained by X.
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Adjusted R² penalizes unnecessary predictors in multiple regression models.
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AIC helps compare models: lower AIC = better balance between fit and simplicity.
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Parsimonious models (simpler ones that still explain the data well) are preferred.
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Stepwise regression automatically selects the most parsimonious model using AIC.
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Correlation shows association; regression goes further by predicting and quantifying impact.
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Always visualize both your model fit and your residuals before interpreting results!
