Regression Summary

Statistics · Axiom Academy

Key concepts, formulas, and methods for understanding relationships between variables. Definition: Measures the strength and direction of the linear relationship between two quantitative variables Range: Correlation coefficient r ranges from -1 to +1 Properties: No units, symmetric (r xy = r yx ), sensitive to outliers Interpretation: |r| near 1 indicates strong linear relationship; near 0 indicates weak linear relationship Important Note: Correlation does not imply causation Purpose: Model the relationship between a response variable (y) and an explanatory variable (x) Components: β₀ is the y-intercept, β₁ is the slope Goal: Find the line that best fits the data by minimizing prediction errors Application: Predict values of y for given values of x Slope (β₁): The predicted change in y for a one-unit increase in x Intercept (β₀): The predicted value of y when x = 0 (may not be meaningful) Sign: Positive slope indicates positive relationship; negative slope indicates negative relationship Magnitude: Larger |β₁| indicates stronger effect of x on y Units: Slope has units of (y units)/(x units) Definition: The proportion of variation in y explained by the regression model Range: 0 ≤ R² ≤ 1 (often expressed as percentage) Interpretation: R² = 0.75 means 75% of variability in y is explained by x Relationship: In simple linear regression, R² = r² Example Recap: Fitting a Regression Model

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