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Predict with a regression line and judge reliability

12th grade (Year 13 in England) · 16 questions · Common Core: HSS.ID.B.6.A, HSS.ID.C.7 · England: A-level Statistics

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  1. Question 1

    For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 0.4x. What does −0.4 tell you?

    • A. The correlation coefficient is −0.4
    • B. Screen time causes 0.4 hours less sleep
    • C. Each extra hour of screen time goes with about 0.4 fewer hours of sleep per week, on average
    • D. A teenager with no screen time sleeps 0.4 hours

  2. Question 2

    A regression line was found from data with x between 1 and 14 and strong correlation. How reliable is a prediction for x = 42?

    • A. Reliable: it is interpolation within the data
    • B. Unreliable: it is extrapolation beyond the data

  3. Question 3

    For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 14 + 5x. Predict the score for 8 hours of revision.

    Answer

  4. Question 4

    For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 0.8x. What does −0.8 tell you?

    • A. The correlation coefficient is −0.8
    • B. A teenager with no screen time sleeps 0.8 hours
    • C. Screen time causes 0.8 hours less sleep
    • D. Each extra hour of screen time goes with about 0.8 fewer hours of sleep per week, on average

  5. Question 5

    A regression line was found from data with x between 2 and 15 and strong correlation. How reliable is a prediction for x = 28?

    • A. Reliable: it is interpolation within the data
    • B. Unreliable: it is extrapolation beyond the data

  6. Question 6

    For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 28 + 1.5x. Predict the score for 7 hours of revision.

    Answer

  7. Question 7

    For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 1.6x. What does −1.6 tell you?

    • A. Each extra hour of screen time goes with about 1.6 fewer hours of sleep per week, on average
    • B. The correlation coefficient is −1.6
    • C. A teenager with no screen time sleeps 1.6 hours
    • D. Screen time causes 1.6 hours less sleep

  8. Question 8

    A regression line was found from data with x between 5 and 19 and strong correlation. How reliable is a prediction for x = 41?

    • A. Reliable: it is interpolation within the data
    • B. Unreliable: it is extrapolation beyond the data

  9. Question 9

    For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 25 + 7.5x. Predict the score for 8 hours of revision.

    Answer

  10. Question 10

    For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 1.1x. What does −1.1 tell you?

    • A. The correlation coefficient is −1.1
    • B. Each extra hour of screen time goes with about 1.1 fewer hours of sleep per week, on average
    • C. A teenager with no screen time sleeps 1.1 hours
    • D. Screen time causes 1.1 hours less sleep

  11. Question 11

    A regression line was found from data with x between 1 and 11 and strong correlation. How reliable is a prediction for x = 38?

    • A. Reliable: it is interpolation within the data
    • B. Unreliable: it is extrapolation beyond the data

  12. Question 12

    For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 57 + 5x. Predict the score for 11 hours of revision.

    Answer

  13. Question 13

    For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 1.2x. What does −1.2 tell you?

    • A. Each extra hour of screen time goes with about 1.2 fewer hours of sleep per week, on average
    • B. Screen time causes 1.2 hours less sleep
    • C. The correlation coefficient is −1.2
    • D. A teenager with no screen time sleeps 1.2 hours

  14. Question 14

    A regression line was found from data with x between 1 and 14 and strong correlation. How reliable is a prediction for x = 32?

    • A. Reliable: it is interpolation within the data
    • B. Unreliable: it is extrapolation beyond the data

  15. Question 15

    For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 9 + 3.5x. Predict the score for 3 hours of revision.

    Answer

  16. Question 16

    For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 3x. What does −3 tell you?

    • A. Screen time causes 3 hours less sleep
    • B. Each extra hour of screen time goes with about 3 fewer hours of sleep per week, on average
    • C. A teenager with no screen time sleeps 3 hours
    • D. The correlation coefficient is −3

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Answer key: Predict with a regression line and judge reliability

  1. 1. C. Each extra hour of screen time goes with about 0.4 fewer hours of sleep per week, on average

  2. 2. B. Unreliable: it is extrapolation beyond the data

  3. 3. 54

  4. 4. D. Each extra hour of screen time goes with about 0.8 fewer hours of sleep per week, on average

  5. 5. B. Unreliable: it is extrapolation beyond the data

  6. 6. 38.5

  7. 7. A. Each extra hour of screen time goes with about 1.6 fewer hours of sleep per week, on average

  8. 8. B. Unreliable: it is extrapolation beyond the data

  9. 9. 85

  10. 10. B. Each extra hour of screen time goes with about 1.1 fewer hours of sleep per week, on average

  11. 11. B. Unreliable: it is extrapolation beyond the data

  12. 12. 112

  13. 13. A. Each extra hour of screen time goes with about 1.2 fewer hours of sleep per week, on average

  14. 14. B. Unreliable: it is extrapolation beyond the data

  15. 15. 19.5

  16. 16. B. Each extra hour of screen time goes with about 3 fewer hours of sleep per week, on average