Bivariate data
Two quantities are measured on the same individuals. How do you tell whether they move together, how tightly, and what a fitted line can be trusted to say?
Where you are 9 inside
What this area is about
Bivariate data pairs two numbers, x and y, for each individual. This area turns a scatter plot into a number for strength, a line for prediction, and a check on whether that line was the right model. Each tool here describes association only: none, by itself, shows that x causes y.
How these fit together
Measuring the pattern. Correlation gives one number, r, between -1 and 1, for the direction and strength of a straight-line pattern. Lurking and confounding variables says why a strong r still does not prove cause.
Fitting a line. A line of best fit is a trend line drawn to follow the dots. Least squares regression gives exactly one line by rule, provided the x-values are not all equal.
Judging the line. Residuals, y - \hat{y}, show how far off predictions are and whether a line was the right shape. Outliers and influential points asks whether one point is steering the slope. Reading regression output finds the line and its fit in a software table.
When the plot curves. Transforming to linearity fits exponential models through \log y; log-log transforms fit power models through \log x and \log y.
A path through it
Start with a line of best fit and correlation, in either order. Confounding variables can come any time after correlation. Least squares regression needs both, then outliers and residuals follow it. After residuals come reading output and transforming to linearity, and log-log transforms last.
This area leads to inference for slopes.