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Cogito

AP Statistics · Chapter 5 · Lesson 1

Practice Worksheet

Least-Squares Regression

The line, the slope, and what r² means.

11 problems · about 25 minutes · AP Statistics 2.5, 2.7, 2.8

NameDate

Figure — use these to answer the problems

Fit the line to the cloud and read its slope.
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y = x + 1
Slope1
Intercept1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. r = 0.9. What is r²?

    Answer

  2. r = 0.5. What is r²?

    Answer

  3. ŷ = 3x + 4. What is y predicted at x = 2?

    Answer

  4. r² = 0.9. Percent of variation explained?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. A residual is actual minus predicted. Actual 12, predicted 10. Residual?

    Answer

  2. Does a strong r² prove causation? 1 for yes, 0 for no.

    Answer

  3. r = −0.8. Is the slope negative? 1 for yes, 0 for no.

    Answer

Stretch Yourself

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

4 problems

  1. Data covers x from 1 to 10. Is predicting at x = 50 sound? 1 for yes, 0 for no.

    Answer

  2. Match each quantity to what it tells you.

    Draw a line from each item on the left to its match on the right.

    • Slope
    • r²
    • Residual
    • Predicted change in y per unit of x
    • Proportion of variation explained
    • How far one point sits from the line

  3. From r to r²

    r = 0.6. What is r²?

    Answer

  4. Unexplained

    r² = 0.75. What proportion of the variation is not explained?

    Answer