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Grade 9 / Middle 3 (age 14-15)

Correlation

Correlation

Correlation is how two quantities move together. Study hours rising with scores is positive; one dropping as the other rises is negative; no clear trend means none. But ice cream and drownings rising together does not prove one causes the other; the hidden cause may simply be summer. Slide the strength control and watch the points line up.

Intuition — Study Hours vs Test Score
0.7
👀 Reading a Scatter Plot
①Each point = one student (hours, score)
②Points trending up-right → positive correlation
③Trending down-right → negative correlation
④Spread out randomly → no correlation
⑤Move the slider; watch how points cluster along a line!
Three Types of Correlation
Positive Correlation
x ↑ → y ↑
Points trend up-right. e.g., height vs weight, study hours vs grade
Negative Correlation
x ↑ → y ↓
Points trend down-right. e.g., absences vs grade, temperature vs heating cost
No Correlation
No trend between x and y
Points scattered randomly. e.g., shoe size vs math score
💡 Strong vs Weak Correlation
①The closer points cluster to a line, the 'stronger' the correlation
②More spread → 'weaker'
③r near +1 → strong positive; r near −1 → strong negative
④r near 0 → little correlation
Correlation ≠ Causation!
⚠️ The Most Important Distinction!
①On days ice-cream sales are high, drownings are also high → positive correlation
②Does that mean ice cream causes drowning? No!
③The real cause is 'summer' — both rise because it's hot
④Correlation does NOT imply causation
⑤A common essay-question topic!
Practice Reading Scatter Plots
📊 Real-life Examples
①Positive: height-weight, exercise-strength, temperature-AC use
②Negative: exercise-body fat, temperature-heating cost, car age-price
③None: height-IQ, blood type-grade, birthday-math score
💡 Three Steps to Read a Scatter Plot
①Step 1: Overall trend (up-right? down-right? random?)
②Step 2: Tightness (strong? weak?)
③Step 3: Are there outliers?
Work It Out
Example 1
Taller people tend to weigh more. State the correlation between the two variables.
1
Check whether one variable grows as the other grows.
height ↑ → weight ↑
2
They increase together, so it is a positive correlation.
positive correlation
▸ Positive correlation
Points trending up-right on a scatter plot mean a positive correlation.
Example 2
In winter, the lower the temperature, the higher the heating cost. State the correlation.
1
See how the heating cost changes as the temperature rises.
temperature ↑ → heating cost ↓
2
One rises as the other falls, so it is a negative correlation.
negative correlation
▸ Negative correlation
Points trending down-right on a scatter plot mean a negative correlation.
Exam Wrap-up
Core of Correlation
Judge from the direction and tightness of points on a scatter plot
Positive/negative/none + strong/weak
G9 school-exam type
Over the same distance, which describes the correlation between a car's speed and its travel time?
①Strong positive correlation
②Weak positive correlation
③Negative correlation
④No correlation
⑤Cannot tell
▸ ③ Negative correlation
1
As speed increases, the time to cover the same distance decreases.
speed ↑ → time ↓
2
One rises while the other falls, so it is a negative correlation.
negative correlation
🎯 Exam Points
①Up-right vs down-right tells positive vs negative
②Closer to a line = stronger correlation
③Correlation ≠ causation — classic essay topic
④Extreme outliers stand apart on a scatter plot
⑤A correlation table summarizes the relation in tabular form
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