Cogito
AP Statistics · Chapter 5 · Lesson 2
Residuals and Model Fit
Checking whether a line was the right choice.
12 problems · about 22 minutes · DAT-1.G, DAT-1.H
What this lesson teaches
The student computes residuals, reads residual plots, and interprets r squared.
- A residual is actual minus predicted.
- A patterned residual plot rejects the linear model, however high r is.
- r squared is the proportion of variation in y explained by x.
Warm Up
Straightforward practice. Get the method working first.
5 problemsr = 0.9. What is r squared?
Answer 0.81
Why 0.81.
What should a residual plot look like for a good linear model?
Answer Random scatter with no pattern.
Why Random scatter.
Predicted 20, actual 17. Residual?
Answer -3
Why 17 − 20.
A negative residual means the model did what? 1 overestimated, 2 underestimated.
Answer 1
Why Predicted higher than actual.
r = 0.6. What is r squared?
Answer 0.36
Why 0.6².
Build It Up
The same ideas with more to keep track of.
3 problemsr squared = 0.49. What percentage of variation is explained?
Answer 49
Why As a percentage.
A curved residual plot. Is a line appropriate? 1 yes, 0 no.
Answer 0
Why A pattern means something was missed.
What does least squares minimise? 1 the sum of squared residuals, 2 the largest residual.
Answer 1
Why Its name says so.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsWhich statements about r squared are true?
Answer It is the proportion of variation in y explained by x; It is the square of the correlation
Why Nothing in regression establishes causation.
r = 0.5. What is r squared?
Answer 0.25
Why 0.5².
The Residual: Predicted 9, actual 11. What is the residual?
Answer 2
Why 2.
The Explained Variation: r = 0.8. What is r squared?
Answer 0.64
Why 0.64.