The Regression Line and Making Predictions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Fitting a line, trusting it wisely

Mathematics · Data & Statistics · ages 17-18
Name ______________________   Date ____________

  1. A regression of marks on hours studied has gradient 2. What does it mean?

    • Each extra hour goes with 2 extra marks on average
    • Everyone who studies exactly 1 hour scores 2 marks
    • The top mark in the class must be 2
    • Studying causes exactly 2 marks per hour, no exceptions

  2. A fitted line is y = 5 + 2x, where x is hours studied and y is marks. Predict y for x = 6.

    Answer: ______________

  3. A fitted line is y equals 5 plus 2 x, where x is hours studied and y is marks. Predict y for x equals 6.

    Answer: ______________

  4. Data cover x from 1 to 8. Kim predicts y at x equals 30 and trusts it fully. Kim is right to trust it.

    Circle one:   True   False

  5. A regression of weight on weeks of training has gradient minus 0.4 kg per week. What does it mean?

    • Everyone loses exactly 0.4 kg each week
    • Training always removes 0.4 kg total
    • Each extra week goes with 0.4 kg lost on average

  6. A regression of weight on weeks of training has gradient -0.4 kg per week. What does it mean?

    • Each week goes with 0.4 kg lower weight on average
    • Everyone loses exactly 0.4 kg every week
    • The starting weight must have been 0.4 kg
    • Exercise causes exactly 0.4 kg loss per week, guaranteed

  7. A fitted line is y = 1.5 + 2x. Predict y at x = 4.

    Answer: ______________

  8. A fitted line is y equals 1.5 plus 2 x. Predict y at x equals 4.

    Answer: ______________

  9. Weight falls 0.4 kg per week on average. How many kg are lost over 5 weeks? Give the change with its sign.

    Answer: ______________

  10. The class line covers x from 1 to 8. Which prediction is safe to trust?

    • x equals 7, inside the range
    • x equals 30, far outside
    • Both are equally safe
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Fitting a line, trusting it wisely W1-mt_tsjctRmkyE-s1

  1. Each extra hour goes with 2 extra marks on average · The gradient is an average rate in the units of the situation: marks gained per hour studied.
  2. 17 · Put x = 6 into 5 + 2x: 5 + 12 = 17 marks.
  3. 17 · Swap 6 into the line: 5 plus 12 is 17 marks.
  4. False · 30 sits far outside the data, so the line is guessing and trust is unsafe.
  5. Each extra week goes with 0.4 kg lost on average · The negative gradient is an average weekly fall in the units of the story.
  6. Each week goes with 0.4 kg lower weight on average · A negative gradient means y drifts down as x rises: 0.4 kg per week on average, not a promise for any one person.
  7. 9.5 · Put x = 4 into 1.5 + 2x: 1.5 + 8 = 9.5.
  8. 9.5 · Swap 4 into the line: 1.5 plus 8 is 9.5.
  9. -2 · Five weeks at minus 0.4 each gives minus 2 kg in total.
  10. x equals 7, inside the range · 7 sits among observed neighbours so the line interpolates fairly, while 30 guesses blind.
Worksheet · LightMySky