Scatterplot questions are some of the most visual on the SAT. You'll look at a graph, identify trends, and use a line of best fit to make predictions.
What Is a Scatterplot?
A scatterplot displays data points for two variables. Each dot represents one observation.
For example, a scatterplot might show study hours (x-axis) vs. test score (y-axis) for 20 students.
Identifying Correlations
| Pattern | Correlation | Description |
|---|---|---|
| Dots trend upward | Positive | As increases, increases |
| Dots trend downward | Negative | As increases, decreases |
| No clear pattern | None | No relationship |
Strength: If dots are clustered tightly around a line, the correlation is strong. If they're scattered loosely, it's weak.
The Line of Best Fit
The line of best fit (regression line) is the straight line that best represents the overall trend. It minimizes the total distance between the line and all data points.
On the SAT, you won't need to calculate this line — it will be given to you, either drawn on the graph or as an equation.
Example 1: A line of best fit is , where = hours studied and = test score.
- Slope interpretation: for each additional hour studied, the predicted score increases by 2.5 points
- y-intercept interpretation: a student who studies 0 hours is predicted to score 30 points
Making Predictions
Example 2: Using , predict the score for a student who studies 8 hours.
Predicted score: 50 points.
Important: Predictions within the data range (interpolation) are more reliable than predictions outside it (extrapolation).
Residuals
A residual is the difference between the actual value and the predicted value.
- Positive residual: actual is above the line
- Negative residual: actual is below the line
Example 3: If a student studied 8 hours and scored 55, but the predicted score was 50:
The student scored 5 points higher than predicted.
Outliers
An outlier is a data point far from the overall trend. On the SAT, you might be asked to identify which point is the outlier or how removing it would affect the line of best fit.
Removing an outlier typically makes the correlation stronger.
SAT Question Types
- "Which scatterplot shows a strong negative correlation?" — Look for dots trending downward in a tight pattern
- "What does the slope represent?" — The rate of change of per unit of
- "Which point is an outlier?" — The dot farthest from the line of best fit
- "Predict the value of when " — Plug into the equation
Practice Problems
Problem 1: A line of best fit is . What does the slope tell you?
Solution
For each 1-unit increase in , decreases by 1.5 units. This is a negative correlation.
Problem 2: Using , find the residual if and the actual is 35.
Solution
Predicted: . Residual = .
Problem 3: A scatterplot shows a roughly linear trend with one point far above all others. If that point is removed, how would the correlation coefficient most likely change?
Solution
would increase (correlation becomes stronger) since removing the outlier makes the data fit the line better.
Key Takeaways
- Scatterplots show relationships between two variables
- Slope of the best-fit line = rate of change in context
- Residual = actual minus predicted
- Don't extrapolate too far beyond the data
- Removing outliers strengthens the correlation
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