Revision sheet

Two-way tables

• Joint: cell / total. Marginal: margin / total.
• Conditional: cell / its group total.

Watch out: name the group you condition on.

Association

• Compare conditional proportions across groups.
• Different: associated. Equal: not associated.

Watch out: association is not causation; counts are not rates.

Correlation

• $-1 \le r \le 1$; sign = direction, size = linear strength.
• Unitless; symmetric in $x$ and $y$.

Watch out: $r$ only sees straight lines.

Least-squares line

$b = r\,s_y/s_x$, $a = \bar{y} - b\bar{x}$, through $(\bar{x}, \bar{y})$.

Watch out: $s_y$ on top.

Residuals

• $e = y - \hat{y}$; positive is above the line.
• Residual plot: no pattern means a linear model is appropriate.

Watch out: observed minus predicted, in that order.

Interpreting regression

• Slope: predicted change per unit of $x$.
• $r^2$: share of variation explained.
• No extrapolation.

Watch out: $r^2$, not $r$, is the explained fraction.

Unusual points

• Outlier: large residual. Leverage: extreme $x$.
• Influential: removing it changes the line.

Watch out: leverage, not residual size, drives influence.