Scatterplots & Line of Fit at the 700-800 Level

At this tier the arithmetic is trivial. What is tested is whether you know exactly what a line of best fit claims — and, more often, what it does not claim.

Six archetypes cover the bank. The residual, with its sign intact: residual $=$ actual $-$ predicted, positive means above the line, and hard items run it backwards as actual $=$ predicted $+$ residual. Slope and intercept as sentences, always phrased as associated with rather than causes. Extrapolation beyond the data — a model built from cars 1 to 8 years old says nothing reliable about a 15-year-old car, and often predicts something impossible as a confirming clue. Two competing models, asking when they are equal, which changes faster, or which starts higher. Which model fits better, decided by residual magnitudes and never by their signed sum. What one new point does: a point at a typical $x$ raises the intercept and barely moves the slope, while a point at an extreme $x$ can swing the slope.

The recurring trap is reporting the input when the output was asked, or the reverse — circle the unit in the final clause before you solve.