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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 = −0.92. How would you describe the correlation? (strong positive / strong negative / weak positive / weak negative / no linear correlation) → strong negativePrompt: The sign gives the direction.
  2. The regression line is ŷ = 5x + 22. By how much does the predicted y change when x increases by 1? → 5Prompt: That is the meaning of the slope.
  3. The regression line is ŷ = 1.5x + 13. A data point is (10, 27). What is its residual (actual − predicted)? → -1Prompt: 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 = 7 + 4x. Predict the score for 11 hours of revision. → 51Prompt: Substitute the x-value into the equation.
  2. A regression line was found from data with x between 1 and 11 and strong correlation. How reliable is a prediction for x = 9? (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. A regression line was found from data with x between 5 and 19 and strong correlation. How reliable is a prediction for x = 29? (Reliable: it is interpolation within the data / Unreliable: it is extrapolation beyond the data) → Unreliable: it is extrapolation beyond the dataPrompt: Is the x-value inside the range of the data?
  2. For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 2.5x. What does −2.5 tell you? (A teenager with no screen time sleeps 2.5 hours / Screen time causes 2.5 hours less sleep / Each extra hour of screen time goes with about 2.5 fewer hours of sleep per week, on average / The correlation coefficient is −2.5) → Each extra hour of screen time goes with about 2.5 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

    For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 18 + 1x. Predict the score for 3 hours of revision.

    Answer

  2. Question 2

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

  3. Question 3

    A regression line was found from data with x between 3 and 15 and strong correlation. How reliable is a prediction for x = 4?

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

  4. Question 4

    For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 23 + 1x. Predict the score for 9 hours of revision.

    Answer

  5. Question 5

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

  6. Question 6

    A regression line was found from data with x between 5 and 17 and strong correlation. How reliable is a prediction for x = 15?

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

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Answer key: Predict with a regression line and judge reliability

  1. 1. 21

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

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

  4. 4. 32

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

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