SAT Math: Interpret residuals (difference between actual and predicted values)
12+ practice questions in Praczo
The concept, explained
- 1
A residual is the difference between the actual y-value and the predicted y-value: residual = actual − predicted.
- 2
A positive residual means the actual value is above the model's prediction; a negative residual means below.
- 3
Small residuals (scattered randomly around zero) suggest a good fit. A clear pattern in residuals means the model is not capturing the data well.
- 4
The sum of residuals for a least-squares line of best fit is approximately zero.
- ✗ Computing predicted − actual instead of actual − predicted. The SAT uses actual minus predicted.
- ✗ Confusing a large positive residual with a good fit — residuals near zero indicate good fit, not large ones.
SAT-style practice
The line of best fit predicts y = 3x + 2. A data point has actual values x = 4 and y = 17. What is the residual at this point?
Ready to master this concept?
Praczo tracks your mastery on all 183 SAT concepts — not just broad topics. One sample question is a start; drilling to mastery is how scores move.
3-day free trial — no credit card required