What you'll learn
Describing relationships between two variables (~5–7%).
Scatterplots
Describe direction (positive/negative), form (linear/curved), strength, and outliers.
Correlation (r)
Measures strength and direction of a linear relationship; −1 ≤ r ≤ 1. r is unitless and not affected by changing units. Correlation ≠ causation.
Least-squares regression line
ŷ = a + bx minimizes squared residuals.
- Slope b: predicted change in y per 1-unit increase in x (interpret in context).
- Intercept a: predicted y when x = 0.
Residuals & fit
- Residual = observed − predicted. A residual plot with no pattern supports a linear model; a curve/pattern means linear is a poor fit.
- r² (coefficient of determination): proportion of variation in y explained by the model.
Cautions
Extrapolation (predicting outside the data range) and influential/outlier points can mislead.
Exam tips
- Interpret slope and r² in context with units.
- Use the residual plot to judge model appropriateness.
Common mistakes
- Saying correlation proves causation.
- Confusing r and r²; misinterpreting the intercept.