Math lesson plan · 12th grade (Year 13 in England) · 30 minutes
Linear regression and correlation coefficient
Statistics and probability
CCSS HSS.ID.B.6CCSS HSS.ID.C.7CCSS HSS.ID.C.8
Objective and success criteria
Students will: Linear regression and correlation coefficient.
- 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: Scatter graphs and correlation; Find the equation of a line
Leads to: Predict with a regression line and judge reliability
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 (Scatter graphs and correlation; Find the equation of a line). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A line has slope 1 and crosses the y-axis at −2. Write its equation as y = … (type the right-hand side). → x-2Prompt: Use y = mx + b.
- A line has slope −2 and crosses the y-axis at −6. Write its equation as y = … (type the right-hand side). → -2x-6Prompt: Use y = mx + b.
- A line has slope −4 and crosses the y-axis at 0. Write its equation as y = … (type the right-hand side). → -4xPrompt: Use y = mx + b.
Hook · 3 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Linear regression and correlation coefficient. 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: A correlation coefficient is r = 0.02. How would you describe the correlation?
- Step 1: r = 0.02: no linear correlation.
- Answer: no linear correlation
- 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.
- 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.
- The regression line is ŷ = 9x + 26. A data point is (15, 164). What is its residual (actual − predicted)? → 3Prompt: Find the predicted value ŷ at this x.
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.
- The regression line is ŷ = 4x + 14. A data point is (19, 85). What is its residual (actual − predicted)? → -5Prompt: Find the predicted value ŷ at this x.
- 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.
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: Scatter graphs and correlation.
- 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
- Move on to: Predict with a regression line and judge reliability.
- 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