Two-variable data questions put a scatterplot in front of you and ask what it means. Almost all of them come down to three things: the direction of the association, what the line of best fit’s slope represents, and using that line to predict.
Key takeaways
- Association: points trending up = positive; down = negative; no pattern = none.
- The line of best fit is the straight line that best models the cloud of points.
- Its slope is the predicted change in y per 1-unit increase in x (a rate).
- Predict by plugging an x into the line’s equation. Read the model, not individual dots.
See the trend
Here’s a scatterplot with a positive association and its line of best fit. The dots scatter, but the line captures the overall trend, and the line is what predictions come from. Strength is a separate call from direction: the tighter the dots hug the line, the stronger the association; a loose cloud around the same line is a weak one.
Try one
A line of best fit for a data set is y = 1.2x + 3. Based on this model, what is the predicted value of y when x = 10?
What the slope and intercept mean
- Slope = predicted change in y for each +1 in x: in context, the rate (e.g. dollars per year), the same slope you know from linear functions.
- Y-intercept = the model’s predicted y when x = 0, the starting value.
- Predicting within the data is reliable; far outside it (extrapolation) is shakier. The SAT sometimes tests that caution.
The dot or the line?
The most-missed scatterplot question isn’t about reading the graph; it’s about which thing to read. "Predicted" means the line. "Actual" or "measured" means the dot. The SAT’s favorite version asks for the gap between them: how far a real data point sits above or below the model. Compute both values, then subtract.
If the question says predicted by the line of best fit, ignore the dots entirely, even the one sitting right at that x-value. If it says actual, read the dot. Mixing the two is the built-in wrong answer on nearly every one of these.
A line of best fit for a data set is y = 1.2x + 3, and one data point in the set is (5, 12). The actual y-value at x = 5 exceeds the y-value predicted by the line by how much?
Read scatterplots and lines of best fit with a tutor that ties slope to meaning.
Practice two-variable data →Frequently asked questions
- What is a line of best fit on the SAT?
- It’s the straight line that best models the overall trend in a scatterplot. You use its equation to describe the association and to predict y-values for given x-values.
- What does the slope of a line of best fit mean?
- It’s the predicted change in the y-variable for each one-unit increase in the x-variable, a rate in the context of the problem.
- How do I predict a value from a scatterplot?
- Use the line of best fit’s equation, not individual points: plug the given x into the equation to get the predicted y. Individual dots are actual measurements, not the model’s prediction.
- What does it mean when a point is above the line of best fit?
- The actual measured y-value is higher than what the model predicts for that x. The vertical gap between the point and the line is the size of that difference, and the SAT often asks you to compute it.