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Statistics — Data Analysis

Chapter 2 · Bivariate Data

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Correlation coefficient
−1≤r≤1-1 \le r \le 1
Sign = direction; ∣r∣|r| = strength. Near ±1 strong, near 0 weak.
Correlation ≠ causation
A relationship in data doesn't prove one variable causes the other (watch for confounders).
Regression line
y=a+bxy = a + bx
Least-squares: minimises Σ(residuals)².
Passes through
(xˉ,yˉ)(\bar{x}, \bar{y})
The mean point always lies on the regression line.
Prediction caution
Interpolation (within data) is reliable; extrapolation far beyond it is risky.
Correlation r
−1 ≤ r ≤ 1; near ±1 strong linear; r ≈ 0 no LINEAR link (may still be related).
Regression line
y−yˉ=b(x−xˉ)y - \bar y = b(x - \bar x)
Passes through (x̄, ȳ); use to predict y from x only.
Common trap
Correlation ≠ causation; do not extrapolate far outside the data range.