What this SAT skill is testing
Two-variable data questions ask you to interpret scatterplots, lines of best fit, residuals, and real-world meaning. The SAT cares less about drawing a perfect line than about understanding what a model says—and what it does not say.
Describing a scatterplot
- Direction: positive, negative, or no clear association.
- Form: linear or nonlinear.
- Strength: how closely the points follow the overall pattern.
- Unusual features: clusters, gaps, and outliers.
Association does not prove causation. A scatterplot can show that variables move together without showing that one causes the other.
Interpreting a line of best fit
For a model (y=mx+b), the slope (m) is the predicted change in (y) for a 1-unit increase in (x). The intercept (b) is the predicted value of (y) when (x=0), but it is meaningful only when (x=0) makes sense in context.
Example. A model (y=2.8x+14) predicts plant height (y), in centimeters, after (x) weeks. The slope means the model predicts an increase of 2.8 centimeters per week. The intercept predicts 14 centimeters at week 0.
Predictions and residuals
Substitute an (x)-value into the model to obtain a predicted (y)-value. A residual is
(\text{residual}=\text{observed value}-\text{predicted value}).
A positive residual means the observed point lies above the model; a negative residual means it lies below. A line of best fit balances the data overall, so it is not expected to pass through every point.
Interpolation and extrapolation
- Interpolation predicts within the observed range and is usually more reliable.
- Extrapolation predicts beyond the observed range and may be unreliable if the pattern changes.
Step-by-step method
- Read both axes, units, and scale.
- Describe the overall direction and form.
- Translate slope or intercept using the variables and units.
- Use the model only for the prediction requested.
- Check whether the prediction is interpolation or extrapolation.
Common traps
- Describing a positive association as a positive slope without reading which variable is on each axis.
- Claiming the model causes the observed relationship.
- Interpreting the intercept when (x=0) is outside the meaningful context.
- Computing residual as predicted minus observed.
- Assuming an outlier must be removed rather than evaluating its effect.
Practice strategy
Always state slope in a full sentence with units: “For each additional ___, the model predicts ___ more/less ___.” If that sentence sounds wrong, revisit the axes before calculating.
