PSAT Data — scatterplots, lines of fit, and linear versus exponential growth

Two-variable data is one of the skills College Board lists under Problem-Solving and Data Analysis for the PSAT/NMSQT, and its description asks for two things: fitting models to data, and comparing linear and exponential growth. This material trains both, with the data printed in every question so nothing depends on a picture you cannot see.

The quiz has twelve questions, each on a different move. Two come with a drawn scatterplot as well as the list of points: one asks you to describe the association (direction, and whether it is close to a straight line), the other asks you to pick the best of four lines of fit, where one tempting line matches the first two points exactly and then drifts badly away. Then come a prediction from a line of fit where an observed value sits next to it as a trap, a residual whose sign you must turn into "above" or "below the line", and a slope read with its units, in thousands of dollars.

The second half is about growth. Two tables look alike until you subtract and divide: one rises by the same amount each year, the other by the same factor. A question asks which everyday situation is exponential, one asks what 18,000 and 0.85 mean in a depreciation model, one compares a fixed yearly addition with a percentage growth at two different dates, and one computes a decay three steps ahead, where subtracting a fixed amount is the error on offer. The last question shows a line of fit used far outside its data and asks what went wrong.

The flashcards hold the vocabulary and rules: residual, line of fit, positive and negative association, constant differences against constant ratios, growth and decay factors, extrapolation, and how to read a slope.

The printable written work has eight open problems in the style of the test's own answer-entry questions, with no options to lean on: computing residuals and placing points, classifying tables, judging whether an intercept means anything, compound against simple growth, finding the year one plan overtakes another, a leak that removes a fraction of what remains, an impossible prediction, and two subscriber forecasts.

The oral exam asks one question at a time about the same ideas and wants the reasoning said out loud: why a pattern is linear, what a residual's sign means, what a factor in a formula tells you.

Every situation and data set here is invented for practice, and no question is taken from any published test. A calculator is welcome, as it is on the real test.

• Describe the direction and form of an association from a list of points or a scatterplot
• Choose the best line of fit by checking it against the data at both ends
• Distinguish a model's prediction from an observed value
• Compute a residual as actual minus predicted and interpret its sign
• Interpret the slope of a line of fit with the units of both variables
• Classify a table as linear (constant differences) or exponential (constant ratios)
• Interpret a and b in y = a(b)^x as a starting value and a growth or decay factor
• Compare linear and exponential growth at different times
• Explain why predictions far outside the data range are unreliable

Practice material written by Zestly, based on the PSAT/NMSQT Math skill "Two-variable data: models and scatterplots" as described in College Board's Fall 2026 PSAT/NMSQT Student Guide and the Assessment Framework for the Digital SAT Suite (version 3.01, August 2024). All data sets are invented. Zestly is not affiliated with College Board.