SAT Math · Problem-Solving and Data Analysis · Skill 4 of 7

Two-variable data

Read scatterplots, fit a line of best fit, explain what its slope and intercept mean, and decide when a prediction can be trusted. Then spot when the data wants a curve instead of a line.

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Hi, I’m Io. A scatterplot is a cloud of points. The line of best fit tells its story.
Tap Io

Fit the line yourself

Explore · 5 min

Each point shows one student: hours studied and test score. Drag the two lens points to place a line of best fit through the middle of the cloud. The fit score compares your line with the best possible straight line.

Reading an association

Game · 4 min

An association describes how two variables move together.

  • Positive: as x increases, y tends to increase
  • Negative: as x increases, y tends to decrease
  • No association: no clear pattern
  • Strong means the points lie close to a line or curve. Weak means they are widely scattered
Sort each pair of variables

What the numbers mean

Learn · 4 min

SAT questions often give a line of best fit and ask what a number in it means. Use the units in the story.

  • The slope is the predicted change in y for each increase of 1 in x
  • The y-intercept is the predicted value of y when x = 0
  • Both are predictions from the model, so SAT answers say “predicted” or “estimated”
The price of a used car, y thousand dollars, is modelled by y = −1.8x + 24, where x is the car’s age in years.

Predictions and residuals

Practise · 5 min

To predict, substitute x into the model. The residual measures how far the actual point is from that prediction.

residual = actual − predicted

A positive residual means the point sits above the line. A negative residual means it sits below.

When to trust a prediction

Learn · 3 min

A model is built from data in a certain range. Predicting inside that range is called interpolation and is usually reliable. Predicting far outside it is extrapolation: the pattern may change, so treat those predictions with care.

Linear or exponential?

Explore · 4 min

Some data curves. A bacteria count that grows by the same percent each hour bends upward, so a straight line misses the pattern. Compare both models on the same points.

Real-life models

Scenarios · 6 min

Each scenario gives a line of best fit. Pick one and answer the questions.

Regression in Desmos

Tools · 3 min

If a question gives a table of data, Desmos can find the line or curve of best fit for you. Add a table, enter the x1 and y1 columns, then type a model with a ~ instead of an equals sign.

Spot the trap

Detective · 3 min

Each solution has one faulty step. These are the three most common slips with scatterplot models.

Final challenge

8 questions · 10 min

Key ideas to carry in
AssociationPositive, negative or none. Strong or weak.
SlopePredicted change in y for each 1 unit of x.
InterceptPredicted y when x = 0.
ResidualActual − predicted. Positive: above the line.
TrustInside the data range, yes. Far outside, take care.
CurvesSame percent change each step: exponential.
Challenge