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Math lesson plan · 12th grade (Year 13 in England) · 30 minutes

Predict with a regression line and judge reliability

Statistics and probability

CCSS HSS.ID.B.6.ACCSS HSS.ID.C.7England: A-level Statistics

Objective and success criteria

Students will: Predict with a regression line and judge reliability.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Linear regression and correlation coefficient

Leads to: the next skill in this area.

Materials: Squared paper for charts, Class survey data, Sticky notes for a live chart, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 4 min

  • Quick retrieval from earlier learning (Linear regression and correlation coefficient). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A correlation coefficient is r = 0.95. How would you describe the correlation? (strong positive / strong negative / weak positive / weak negative / no linear correlation) → strong positivePrompt: The sign gives the direction.
  2. The regression line is ŷ = x + 18. A data point is (15, 36). What is its residual (actual − predicted)? → 3Prompt: Find the predicted value ŷ at this x.
  3. The regression line is ŷ = 4x + 18. A data point is (16, 86). What is its residual (actual − predicted)? → 4Prompt: Find the predicted value ŷ at this x.

Hook · 3 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Predict with a regression line and judge reliability. Read the success criteria together.

I do: model it · 7 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 22 + 7x. Predict the score for 10 hours of revision.
  • Step 1: 22 + 7 × 10 = 92
  • Answer: 92
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 6 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 33 + 5x. Predict the score for 10 hours of revision. → 83Prompt: Substitute the x-value into the equation.
  2. A regression line was found from data with x between 1 and 15 and strong correlation. How reliable is a prediction for x = 8? (Reliable: it is interpolation within the data / Unreliable: it is extrapolation beyond the data) → Reliable: it is interpolation within the dataPrompt: Is the x-value inside the range of the data?

You do: independent practice · 7 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 6 questions are on the student sheet below, with answers in the key.

Exit ticket · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 36 + 4x. Predict the score for 9 hours of revision. → 72Prompt: Substitute the x-value into the equation.
  2. For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 1.9x. What does −1.9 tell you? (A teenager with no screen time sleeps 1.9 hours / Each extra hour of screen time goes with about 1.9 fewer hours of sleep per week, on average / The correlation coefficient is −1.9 / Screen time causes 1.9 hours less sleep) → Each extra hour of screen time goes with about 1.9 fewer hours of sleep per week, on averagePrompt: The gradient is the change in s for each extra 1 unit of x.

Watch out for

  • Forgetting to put data in order before finding the median.
  • Reading a bar's height wrongly when the scale goes up in 2s or 5s.

Support and stretch

Support

  • Review first: Linear regression and correlation coefficient.
  • Use concrete materials: squared paper for charts.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-12.

Free lesson plan from eurekami.com/lesson-plan-builder

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Predict with a regression line and judge reliability

Name

Date

Score/ 6

  1. Question 1

    A regression line was found from data with x between 4 and 12 and strong correlation. How reliable is a prediction for x = 26?

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

  2. Question 2

    For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 2x. What does −2 tell you?

    • A. Each extra hour of screen time goes with about 2 fewer hours of sleep per week, on average
    • B. The correlation coefficient is −2
    • C. A teenager with no screen time sleeps 2 hours
    • D. Screen time causes 2 hours less sleep

  3. Question 3

    For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 38 + 1x. Predict the score for 4 hours of revision.

    Answer

  4. Question 4

    A regression line was found from data with x between 2 and 15 and strong correlation. How reliable is a prediction for x = 7?

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

  5. Question 5

    For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 2.7x. What does −2.7 tell you?

    • A. Each extra hour of screen time goes with about 2.7 fewer hours of sleep per week, on average
    • B. A teenager with no screen time sleeps 2.7 hours
    • C. The correlation coefficient is −2.7
    • D. Screen time causes 2.7 hours less sleep

  6. Question 6

    For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 12 + 3x. Predict the score for 5 hours of revision.

    Answer

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Answer key: Predict with a regression line and judge reliability

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

  2. 2. A. Each extra hour of screen time goes with about 2 fewer hours of sleep per week, on average

  3. 3. 42

  4. 4. A. Reliable: it is interpolation within the data

  5. 5. A. Each extra hour of screen time goes with about 2.7 fewer hours of sleep per week, on average

  6. 6. 27