Two-variable data: Models and scatterplots

Every scatterplot question on the SAT boils down to three skills: reading the pattern, choosing a model that fits, and interpreting what the model's pieces (slope, intercept, curvature) actually mean in context.

When you look at a scatterplot, start with the big picture. Are the points going up or down? Are they tight around a line or loosely scattered? Is the shape straight, curved, or something else? Any point way off by itself?

Once you've described the pattern, the next step is modeling. The SAT will ask you to pick or use a line of best fit, a quadratic, or an exponential curve. The key is matching the shape of the data to the shape of the equation.

Finally, interpretation. Slope tells you the rate of change — how much 𝑦 changes per unit of 𝑥. The intercept tells you the starting value when 𝑥 =0, but only if 𝑥 =0 makes sense in the problem. And if they give you the equation, you can plug in values to predict or estimate.

The pattern in the data determines the model. The model determines the predictions.