How do you read scatterplots, fit a line or curve of best fit, and use a model to predict?
Two-variable data: read scatterplots, choose a linear, quadratic or exponential model of best fit, interpret slope and intercept of a line of best fit, and use the model to predict and interpolate.
A focused answer to the Digital SAT Problem-Solving and Data Analysis skill of two-variable data: reading scatterplots, choosing a line or curve of best fit, interpreting its slope and intercept, and using the model to predict.
Reviewed by: AI editorial process; not yet individually human-reviewed
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What this skill is asking
Two-variable data is displayed as a scatterplot, and the SAT asks you to describe the relationship, fit a model (line or curve of best fit), interpret the model's slope and intercept in context, and use it to predict. The Digital SAT (Problem-Solving and Data Analysis domain) keeps the statistics light: you read and interpret models rather than derive them, and you choose between linear, quadratic, and exponential shapes.
Reading a scatterplot
Describe the pattern, then fit the matching model.
A worked interpretation and prediction
Models are read in the units of the problem.
Slope and intercept in context
The whole point of fitting a model is interpretation. The slope of a line of best fit is an average rate of change, carrying units (dollars per year, cm per week) and a direction (a negative slope means the quantity decreases as the input increases). The intercept is the model's prediction when the input is zero, which may be a meaningful starting value or, sometimes, an extrapolation with no real-world meaning. SAT questions reliably ask "what does the slope represent" or "what does the value mean", and the expected answer names the rate or starting value with its units and direction, exactly as for any linear function.
Choosing a model and predicting safely
Match the shape to the model: a straight trend is linear, a single hump or valley is quadratic, and a curve that grows slowly then steeply (or decays toward a floor) is exponential. Once a model is chosen, you predict by substituting, but with a caution: predictions are most trustworthy inside the range of the data (interpolation) and become unreliable outside it (extrapolation), because the pattern may not continue. A question may ask you to estimate a value from the line of best fit at a given , or to judge how good a prediction is; reading the fit at a point inside the cloud of data is sound, while a far-future extrapolation should be treated with suspicion.
Exam-style practice questions
Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Digital SAT Math (style)1 marksA line of best fit for a scatterplot of price (dollars) versus age (years) is . What does the slope represent? (A) The starting price (B) The price drops by \1500 per year of age (C) The car is worth \24000 when new (D) The age when the price is zeroShow worked answer →
The correct answer is (B), the price drops by $1500 per year of age.
In a line of best fit , the slope is the rate of change of price with age. Here , so on average the price falls by \1500 for each additional year of age. The intercept \24000 is the modeled price at age (choice C describes the intercept, not the slope).
Digital SAT Math (style)1 marksA scatterplot of data shows points that rise, level off, and then rise steeply again, curving upward. Which model best fits this pattern? (A) Linear (B) Exponential (C) A horizontal line (D) No relationshipShow worked answer →
The correct answer is (B), exponential.
A pattern that grows slowly at first and then increasingly steeply, curving upward, is characteristic of exponential growth. A linear model would rise at a constant rate (a straight line), and a horizontal line would show no change, so the curving, accelerating shape points to an exponential model.
Related dot points
- Ratios, rates, proportional relationships, and units: solve proportions, work with unit rates and constant of proportionality, and convert between units including compound units.
A focused answer to the Digital SAT Problem-Solving and Data Analysis skill of ratios, rates and proportional relationships: setting up proportions, finding unit rates and the constant of proportionality, and converting units including speeds and densities.
- Percentages: compute a percent of a number, percent increase and decrease, percent change, successive percent changes, and find an original amount from a percentage (reverse percent).
A focused answer to the Digital SAT Problem-Solving and Data Analysis skill of percentages: percent of a number, percent increase and decrease, percent change, successive percentages, and finding an original amount from a known percentage.
- One-variable data: mean, median, mode and range, standard deviation as spread, the effect of outliers, and inference from sample statistics including margin of error and evaluating statistical claims.
A focused answer to the Digital SAT Problem-Solving and Data Analysis skill of one-variable data: mean, median, mode and range, standard deviation as spread, outlier effects, and reasoning about sampling, margin of error, and statistical claims.
- Probability and conditional probability: compute simple probability as favorable over total, read probabilities from two-way frequency tables, and compute conditional probability given a restricted group.
A focused answer to the Digital SAT Problem-Solving and Data Analysis skill of probability and conditional probability: simple probability, reading two-way frequency tables, and computing conditional probability within a restricted row or column.
Sources & how we know this
- Math Specifications — College Board (2024)
- What Are Content Domains? — College Board (2024)