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United StatesMathsSyllabus dot point

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.

Generated by Claude Opus 4.811 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

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  1. What this skill is asking
  2. Reading a scatterplot
  3. A worked interpretation and prediction
  4. Slope and intercept in context
  5. Choosing a model and predicting safely

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 bb 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 xx, 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 p=1500a+24000p = -1500a + 24000. 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 zero
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The correct answer is (B), the price drops by $1500 per year of age.

In a line of best fit p=ma+bp = ma + b, the slope mm is the rate of change of price with age. Here m=1500m = -1500, so on average the price falls by \1500 for each additional year of age. The intercept \24000 is the modeled price at age 00 (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 relationship
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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.

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