SAT Two-variable data: models & scatterplots
Read lines of best fit and pick the right model.
How to score it
- Read predictions off the line of best fit, not the scattered dots.
- Residual = actual − predicted; positive means the point sits above the line.
- Curving-then-leveling data is exponential; constant curvature is quadratic.
Common traps
- Reads a data point instead of the fit line.
- Picks linear for data that clearly curves.
- Confuses residual sign (above vs. below the line).
The 4 question types, with real examples
Line-of-best-fit prediction
“At x = [k], which value is closest to the y predicted by the line of best fit?”
The scatterplot shows the relationship between x, the number of practice tests taken, and y, the final test score out of 100. The scatterplot has 12 data points roughly along the line , with x ranging from 4 to 16. A line of best fit passes through approximately (4, 75) and (16, 105).
According to the line of best fit, what is the predicted final test score for a student who took 11 practice tests?
- A
- B
- C✓
- D
The line of best fit has a slope of (105 - 75) / (16 - 4) = 30 / 12 = 2.5. Using the equation , when , (11) + 65 = 92.5.
Choose the best model type
“Which model best fits the data shown?”
The table shows several values of x and their corresponding values of y. x | y 1 | 3 2 | 6 3 | 12 4 | 24 5 | 48 Which of the following equations best models the relationship between x and y?
- A
- B✓
- C
- D
The y-values double each time x increases by 1, indicating exponential growth with base 2. Testing the equation : when , ; when , ; when , . This pattern continues and matches all data points.
Identify the line-of-best-fit equation
“The line of best fit passes through approximately [(a,b), (c,d)]. Which equation best represents the line of best fit shown?”
A scatterplot shows 11 data points representing the relationship between years of experience, x, and annual salary in thousands of dollars, y. The points follow a linear pattern trending upward from left to right, with approximate coordinates (1, 42), (2, 48), (3, 54), (4, 60), (5, 66), (6, 72), (7, 78), (8, 84), (9, 90), (10, 96), and (11, 102). A line of best fit passes through approximately (1, 42) and (11, 102).
The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown. Which of the following equations best represents the line of best fit for the data?
- A
- B✓
- C
- D
The line of best fit has slope (102 - 42)/(11 - 1) = 60/10 = 6. Using point (1, 42): 42 = , so . The equation is .
Model fit interpretation
“[FIGURE: scatterplot titled context]. [real-world question about the modeled relationship]”
The scatterplot shows the relationship between study hours per week, x, and test scores, y, for 16 students. The data points range from (5, 62) to (20, 94). A line of best fit passes through approximately (8, 70) and (17, 88).
According to the line of best fit, what is the meaning of the slope in this context?
- AThe predicted test score for a student who studies 0 hours per week
- BThe predicted increase in test score for each additional hour studied per week✓
- CThe predicted decrease in test score for each additional hour studied per week
- DThe maximum possible test score for students in the data set
The slope of the line of best fit is (88-70)/(17-8) = 18/9 = 2. Since x represents study hours and y represents test scores, the slope indicates that for each additional hour studied per week, the test score is predicted to increase by 2 points.
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