SAT Math — scatterplots, lines of best fit and choosing a model

Two-variable data is one of the skills College Board lists for the Problem-Solving and Data Analysis domain of SAT Math. Its description asks students to analyze and interpret scatterplots, to make predictions from them, to fit linear, quadratic and exponential models, and to compare linear and exponential growth. On the test these questions usually come with a drawn scatterplot, so this material puts real drawings in front of you: five of the twelve questions show a plotted data set, and every value you need is also given in words for anyone reading without the picture.

The quiz starts with the line of best fit. You predict the number of visitors at a pool from the line drawn through ten summer days, with the observed value of a neighboring day offered as a trap. You turn a difference in package weight into a difference in shipping cost, which is the slope times the difference, since the intercept cancels. You decide what a y-intercept means when x = 0 lies far outside the data, and you meet residuals twice: once by counting how many points of a plotted data set sit above the line, and once by computing actual minus predicted and reading its sign.

The middle of the set is about choosing a model. You pick the equation that best fits a plotted cloud of used-car prices, recognize data that rise to a peak and fall again as a downward-opening parabola, interpret the base of an exponential decay model as a percent change of the current value, and decide from a table of counts that constant ratios mean exponential growth.

The last questions are about what a scatterplot can and cannot tell you. A child-growth line used at age 40 shows why extrapolation fails; a survey of commute times and sleep shows a strong association that still does not prove cause; and a data set with one point far from the others in x shows how a single point can control the slope of the line.

Every explanation names the slip behind each wrong answer, so a miss tells you what to fix. The flashcards collect the vocabulary and rules worth knowing by heart: slope and intercept in context, residuals and their signs, extrapolation, constant differences against constant ratios, growth and decay factors, and influential points.

A calculator is welcome, as it is throughout the digital SAT Math section. The material offers a quiz and flashcards. It is independent practice, with invented data sets, and no question is taken from any published test.

• Predict a value from a line of best fit and tell it apart from an observed data point
• Interpret the slope and y-intercept of a line of best fit in context, including when the intercept has no meaning
• Compute a residual as actual minus predicted and read its sign as above or below the line
• Choose the equation that best fits a plotted data set
• Recognize when a linear, quadratic or exponential model is appropriate
• Interpret the base of an exponential model as a percent change
• Explain why extrapolation and causal claims from observational data are unreliable
• Identify the point that most influences the slope of a line of best fit

Practice material written by Zestly, based on the SAT Math skill "Two-variable data: models and scatterplots" in the Problem-Solving and Data Analysis domain, as described in College Board's Assessment Framework for the Digital SAT Suite (version 3.01, August 2024, Appendix B). All data sets and situations are invented. Zestly is not affiliated with College Board.