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Math: Problem-Solving and Data Analysis, 3 original questions

SAT Scatterplots and Data Models Practice: Questions and Answers

Interpret fitted lines, compare linear and exponential patterns and separate association from cause in three original SAT-style questions with explained answers.

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The short answer

A scatterplot shows paired measurements, with each point representing one observation. Identify the variables and units on both axes, then describe the direction, shape and strength of the association. A fitted model can estimate an output for a given input, but it need not pass through every point. Equal differences suggest linear behavior; equal ratios can suggest exponential behavior. Predictions far outside the observed range deserve caution, and an observational association does not by itself demonstrate a causal relationship.

Method at a glance

  1. 1Read the axes and paired units
  2. 2Inspect the pattern
  3. 3Use the model as an estimate
  4. 4Respect the evidence limits

Try the 3 questionsRead the full method

Step-by-step method

Use these steps in order, then apply them to the questions below.

  1. Step 1: Read the axes and paired units

    State what one point represents. Distinguish the explanatory input from the measured output.

  2. Step 2: Inspect the pattern

    Look for increasing or decreasing association, a straight or curved shape, and points far from the main trend.

  3. Step 3: Use the model as an estimate

    Substitute the input into the given fitted rule. Distinguish a predicted value from an exact observed value.

  4. Step 4: Respect the evidence limits

    Check whether the input is within the observed range. Avoid claiming cause and effect from association alone.

Try 3 SAT-style questions

These are original SAT-style questions written by PeakSAT, not official College Board questions. Choose an answer and check it to see why each choice is right or wrong, or open the worked answer.

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Question 1 of 3

A fitted model for plant height is h = 4.5w + 12, where w is weeks after observation begins and h is centimeters. What height does the model predict at w = 4?

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Correct answer

Choice C: 30 centimeters

Explanation

Substitute w = 4: h = 4.5 × 4 + 12 = 18 + 12 = 30 centimeters. This is the model's predicted height; an actual observed plant may differ from the fitted value.

Why each choice is right or wrong

  1. Choice A

    This includes the growth term but omits the starting height 12.

  2. Choice B

    This does not evaluate the given slope term correctly.

  3. Choice C

    Correct answer

    Correct: the model gives 30 centimeters at week 4.

  4. Choice D

    This multiplies the intercept by 4 rather than adding it once.

Question 2 of 3

A paired data table is: x: 0, 1, 2, 3 y: 5, 10, 20, 40 Which model matches every listed pair?

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Correct answer

Choice B: y = 5·2^x

Explanation

Each one-unit increase in x doubles y, and y = 5 when x = 0. The model y = 5·2^x therefore gives 5, 10, 20 and 40 at the four inputs. The output differences are not constant, so one fixed-slope linear model does not fit all four.

Why each choice is right or wrong

  1. Choice A

    It gives 15 at x = 2 instead of 20, so it fails the doubling pattern.

  2. Choice B

    Correct answer

    Correct: the initial value is 5 and the factor per input step is 2.

  3. Choice C

    It gives 0 at x = 0 rather than 5.

  4. Choice D

    It gives 2 at x = 0 rather than 5 and uses the wrong growth factor.

Question 3 of 3

In an observational data set comparing cities, higher average summer temperature is associated with more bottled-water sales. Which statement is supported by that pattern alone?

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Correct answer

Choice D: Temperature and sales have a positive association

Explanation

The stated pattern means that higher temperatures tend to accompany higher sales, a positive association. The observational data alone do not rule out population, tourism or other explanatory factors, and do not prove causation or an identical change in every city.

Why each choice is right or wrong

  1. Choice A

    An observational association alone does not prove that one variable causes the other.

  2. Choice B

    Association does not imply an exact equal sales change in every city.

  3. Choice C

    The prompt explicitly describes a relationship.

  4. Choice D

    Correct answer

    Correct: the observed tendency is a positive association.

Common mistakes

  • Expecting every observed point to lie on a fitted line. A model summarizes a pattern and can have residual errors.

  • Calling repeated doubling linear because values keep increasing. Compare ratios as well as differences.

  • Treating correlation as proof of an intervention's effect. Other variables may explain an observational pattern.

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Common questions

Must a fitted line pass through every point?

No. It summarizes the relationship. An observed value can lie above or below the prediction.

What is extrapolation?

It is prediction outside the observed input range. The original pattern may not continue there, so interpret such a prediction cautiously.

Does a strong correlation prove causation?

No. Strength of association alone does not establish cause and effect; study design and other explanations matter.

Sources

  1. College Board: Math section overviewsatsuite.collegeboard.org
  2. College Board: Student Question Bank Math skillssatsuite.collegeboard.org

Sources are linked for reference; they do not endorse PeakSAT. How we prepare our guides