Scatterplots, models and inference on the SAT
A line of best fit gives predictions: its slope is the predicted change in y per unit of x, and a residual is actual minus predicted. For conclusions from data, remember two rules: a random sample supports conclusions only about the population it came from, and only a randomized experiment supports a claim about cause.
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| Study design | Can conclude |
|---|---|
| Random sample of one school | About that school only |
| Randomized experiment | Cause and effect for similar people |
| Observational data | Association only, not cause |
Residuals
Actual 64 → residual 64 − 66 = −2 (below the line)
Common mistakes
Sample questions with answers
1. y = 10x + 30 models ice creams sold (y) by temperature (x). What does 10 mean?
- Sales at 0°C
- Predicted increase per extra degree (correct)
- Exact increase for every day
- Sales after 1 degree
The slope is the predicted change per unit of x.
2. Model y = 12x + 30; data point (3, 64). Residual?
- 2
- −2 (correct)
- 64
- 66
Predicted 66; 64 − 66 = −2.
3. Random sample of 200 students from one Lahore school: 64% use a study app. Best conclusion?
- 64% of all Pakistani students do
- About 64% of that school’s students do (correct)
- Apps improve grades
- Exactly 128 do
Results apply to the population sampled: that school.
Frequently asked questions
What is a line of best fit?
A line that models the trend in a scatterplot. It gives predictions, not exact values. Problem-Solving and Data Analysis makes up about 15% of SAT Math, roughly 5 to 7 questions.
What is a residual?
Actual value minus predicted value. Points above the line have positive residuals.
When can a study show cause and effect?
Only when subjects are randomly assigned to treatments in an experiment.