SAT — Scatterplots and Lines of Best Fit

Chapter Overview & Weightage

Scatterplots and lines of best fit are part of the Problem-Solving and Data Analysis domain on the SAT — a domain that contributes about 15% of the math section. Within this domain, scatterplot questions are among the most reliable: 2–3 appear per test, and they’re typically in the easy-to-medium range.

SAT Math Domains and Approximate Counts

Domain	% of Math Section	Scatterplot Relevance
Algebra	35%	Some line of best fit overlap
Advanced Math	35%	Quadratic fits
Problem-Solving and Data Analysis	15%	Most scatterplot questions here
Geometry and Trigonometry	15%	Less relevant

Key Concepts You Must Know

Scatterplot: A graph of paired data points $(x, y)$ , used to visualise the relationship between two variables.

Correlation:

Positive: as $x$ increases, $y$ tends to increase
Negative: as $x$ increases, $y$ tends to decrease
No correlation: no clear pattern

Linear vs nonlinear fit: A straight line fits well when the data shows a roughly linear trend; otherwise, a curve (quadratic, exponential) is better.

Line of best fit: The straight line that minimises total vertical distance to data points (least squares). Equation: $y = mx + b$ .

Interpreting slope and intercept in context:

Slope $m$ : change in $y$ per unit change in $x$ (in real units)
Intercept $b$ : predicted $y$ when $x = 0$

Predicting values: Use the line of best fit equation to predict $y$ for any $x$ . Predictions within the data range are reliable; outside is extrapolation (less reliable).

Strategy: The 4-Step Read

1. Read the axes. Note the variables and their units. SAT often gives temperature in °F, time in hours, etc.

2. Identify the line of best fit equation. It might be given directly, or you might need to read the slope (rise/run from two clear points on the line).

3. Apply the equation to the question. Predict, interpret slope, or compare actual data point to predicted value.

4. Verify against the graph. Does your numerical answer make sense visually?

Worked Examples

Example 1 — Slope Interpretation (Easy)

Setup: A scatterplot shows the relationship between hours studied per week ( $x$ ) and SAT math score ( $y$ ). The line of best fit is $y = 15x + 500$ .

Q: What does the slope of 15 represent in context?

Answer: “For every additional hour studied per week, the SAT math score is predicted to increase by 15 points.”

The slope is change in $y$ per unit change in $x$ , expressed in the original units. Don’t say “15 points” alone — connect to “per hour studied”.

Example 2 — Prediction (Medium)

Setup: Same line $y = 15x + 500$ . A student studies 20 hours per week.

Q: What is the predicted SAT math score?

Answer: $y = 15(20) + 500 = 300 + 500 = 800$ .

(Note: SAT math scaled scores cap at 800, so this is at the maximum. The model breaks down at extremes — useful for “limitations of extrapolation” questions.)

Example 3 — Comparing Actual to Predicted (Hard)

Setup: Same line. A student studies 10 hours and scored 700.

Q: How does the student’s actual score compare to the predicted score?

Predicted: $y = 15(10) + 500 = 650$ .

Actual: 700. Difference: $700 - 650 = 50$ points.

Answer: The student scored 50 points higher than predicted by the line of best fit.

This is the residual (vertical distance from data point to line). SAT often phrases as “how many points above/below the line”.

Example 4 — Identifying Strongest Correlation (Easy)

Q: Which scatterplot shows the strongest negative correlation?

Among 4 plots, pick the one where points cluster tightly along a downward-sloping line. Tight clustering = strong correlation; downward = negative.

Difficulty Distribution

Difficulty	%	Question Types
Easy	40%	Reading axes, identifying correlation type
Medium	50%	Slope interpretation in context, simple prediction
Hard	10%	Multi-step prediction, extrapolation limitations

Expert Strategy

Master the slope-in-context phrasing. Always state slope as “for every unit increase in $x$ , $y$ increases/decreases by [slope] [units]”. This phrasing is what SAT scores reward.

Practice extrapolation traps. SAT often provides a line valid for $x$ in a small range, then asks for a prediction outside it. The right answer is usually “the prediction is unreliable because we’re outside the data range”.

Speed tip for the digital SAT: scatterplot questions on the digital test are usually 1–1.5 minutes each. If the answer requires reading slope from the graph, pick two well-separated lattice points on the line and compute rise/run. Don’t squint at decimals.

Common Traps

Trap 1: Confusing slope sign with correlation strength.

A slope of $-2$ doesn’t mean “weak negative”. The sign tells direction; the closeness of points to the line tells strength. Both must be evaluated separately.

Trap 2: Using actual data instead of predicted values.

“What does the line predict for $x = 10$ ?” requires plugging into the equation, NOT reading the actual data point at $x = 10$ . The actual point may be above or below the line.

Trap 3: Forgetting units in slope interpretation.

Slope without units gets partial credit on student-produced response questions. Always say “100 dollars per year” not just “100”.

Trap 4: Misreading the y-intercept.

When $x = 0$ is outside the data range, the y-intercept is a mathematical artefact, not a meaningful prediction. SAT sometimes asks “what does the y-intercept mean?” — the answer might be “it has no real-world meaning here”.

Trap 5: Treating correlation as causation.

A strong correlation between $x$ and $y$ doesn’t mean $x$ causes $y$ . SAT explicitly tests this in some scatterplot prompts. The right answer for “which conclusion is supported?” is usually a correlational, not causal, statement.