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Cogito

AP Statistics · Chapter 5 · Lesson 2

Practice Worksheet

Residuals and Model Fit

Checking whether a line was the right choice.

12 problems · about 22 minutes · DAT-1.G, DAT-1.H

NameDate

Figure — use these to answer the problems

Adjust the line until roughly as many points sit above as below. That is what least squares finds exactly.
-10-10-5-5551010
y = x + 1
Slope1
y-intercept1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. r = 0.9. What is r squared?

    Answer

  2. What should a residual plot look like for a good linear model?

    • Random scatter with no pattern.
    • A clear straight line.

  3. Predicted 20, actual 17. Residual?

    Answer

  4. A negative residual means the model did what? 1 overestimated, 2 underestimated.

    Answer

  5. r = 0.6. What is r squared?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. r squared = 0.49. What percentage of variation is explained?

    Answer

  2. A curved residual plot. Is a line appropriate? 1 yes, 0 no.

    Answer

  3. What does least squares minimise? 1 the sum of squared residuals, 2 the largest residual.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Which statements about r squared are true?

    • It is the proportion of variation in y explained by x
    • It is the square of the correlation
    • It gives the percentage of points on the line
    • It proves the relationship is causal
    • Tick every box that applies.

  2. r = 0.5. What is r squared?

    Answer

  3. The Residual

    Predicted 9, actual 11. What is the residual?

    Answer

  4. The Explained Variation

    r = 0.8. What is r squared?

    Answer