Correlation and Simple Linear Regression
Correlation measures the direction and strength of a linear association between two quantitative variables.
Summary
Correlation measures the direction and strength of a linear association between two quantitative variables. Simple linear regression predicts a response from one predictor within the observed setting.
| Method | Main purpose | Key interpretation |
|---|---|---|
| Pearson correlation | Summarize linear association | The sign of gives direction; $ |
| Simple linear regression | Estimate a prediction line | The slope gives predicted response change per unit increase in the predictor. |
Pearson correlation satisfies . The fitted regression line is , with and .
🧠 Key Concepts
- Pearson Correlation
- Regression Slope
- Regression Intercept
- Ordinary Least Squares
- Residuals
- Coefficient of Determination
- Regression Assumptions
- Extrapolation
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Correlation and Simple Linear Regression
📘 Overview Correlation measures the direction and strength of a linear association between two quantitative variables. Simple linear regression models a response using one predictor and supports prediction within the observed setting. Neither method alone establishes causation.
🧠 Key Idea Correlation summarizes how closely paired observations follow a straight-line pattern; regression estimates the line that predicts a response from a predictor. A strong association does not eliminate confounding or guarantee accurate predictions.
⚔️ Core Details: - Pearson correlation is
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