Residual — Grade 8 Math, what it means and where it is taught
The gap between an actual value and the line's prediction.
Taught in Grade 8 Math.
Where it is taught
What uses it later
This idea is needed for:
- Residual plot — A plot of residuals against x, used to judge whether a line was the right model.
Practise this idea
10 questions in the course bank use Residual, in Lines of Best Fit, Bivariate Data & Correlation. The first 8 are below; the rest are in those units.
Problem 1
A line predicts y = 34 but the actual value was 40. Find the residual.
Worked answer
6
40 - 34 = 6
Positive, so the point sits above the line
Problem 2
A line predicts y = 88 but the actual value was 81. Find the residual.
Worked answer
-7
81 - 88 = -7
Negative, so the point sits below the line
Problem 3
Line A has residuals 1, -2, 2, -1. Line B has residuals 6, -5, 4, -5. Which fits better?
- A
- B
- Equally well
- Cannot be determined
Worked answer
A
A misses by at most 2
B misses by up to 6
So A fits better
Problem 4
A line is y = 3x + 4. A data point is (5, 22). Find the residual.
Worked answer
3
Predicted: 3(5) + 4 = 19
Residual: 22 - 19 = 3
Problem 5
A line predicts 50 and the actual value is 56. Find the residual.
Worked answer
6
56 - 50 = 6
Problem 6
A line predicts 120 and the actual value is 113. Find the residual.
Worked answer
-7
113 - 120 = -7
Problem 7
A regression line is y = 4x + 6. For x = 7 the actual value was 30. Find the residual.
Worked answer
-4
Predicted: 4(7) + 6 = 34
30 - 34 = -4
Problem 8
A residual plot shows a clear curved arch. This means
- a line is the wrong model
- the line fits perfectly
- r must be zero
- the data has no outliers
Worked answer
a line is the wrong model
Structure in the residuals means the model missed something
A curve needs a curved model