grade 9 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. Change the strength and the scatter points line up closer to a straight line.

Intuition — Study Hours vs Test Score

Correlation r0.7

👀 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! Default r=0.7 is visual strength. The 25 points are scattered, so Pearson is not 0.7. Axes 0~5 and 40~100 are sample ticks. Grade 9 does not compute r. A correlation table puts two variables in cells

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.

Check whether one variable grows as the other grows.

height ↑ → weight ↑

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.

See how the heating cost changes as the temperature rises.

temperature ↑ → heating cost ↓

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

As speed increases, the time to cover the same distance decreases.

speed ↑ → time ↓

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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Representative Values & Spread

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