Scatter Plots Notes and Worksheets - Lindsay Bowden - Free Printable

Let's solve the problem step by step based on the image you provided. This worksheet is about linear scatter plots and understanding correlation and the correlation coefficient (r).

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🔹 Step 1: Fill in the Blanks

#### Correlation – the relationship between two variables in a data set
> ✔ *This describes how two variables are related — whether they increase or decrease together.*

#### Correlation Coefficient (r) – measures the strength and direction of the relationship between two variables in a data set
> ✔ *Strength*: How closely the points follow a line.
> ✔ *Direction*: Whether it's positive or negative.

> ✔ *r must be between* -1 and 1

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🔹 Step 2: Understand the Three Types of Correlation

| Type | r Value Range | Description |
|------|----------------|-------------|
| Positive Correlation | $0 < r \leq 1$ | As x increases, y increases |
| Negative Correlation | $-1 \leq r < 0$ | As x increases, y decreases |
| No Correlation | $r = 0$ | No clear pattern |

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🔹 Step 3: Analyze Each Example Scatter Plot

We are to determine the type of correlation and estimate the r value for each of the four scatter plots.

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#### Example 1:
- Points trend upward from left to right → Positive correlation
- Points are somewhat scattered but generally follow a line
- Not perfectly linear, but fairly strong

✔ Correlation: Positive
✔ Estimated r value: Around 0.7
> (Because it’s not perfect, so less than 1; but clearly trending)

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#### Example 2:
- Points appear randomly scattered with no clear trend
- No consistent increase or decrease

✔ Correlation: No correlation
✔ Estimated r value: 0
> (Points are spread out with no pattern)

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#### Example 3:
- Points form a very clear downward trend from left to right
- Very tight clustering around a straight line

✔ Correlation: Negative
✔ Estimated r value: Around -0.95
> (Very close to -1, indicating a strong negative correlation)

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#### Example 4:
- Points form a clear upward trend from left to right
- Very tightly clustered along a straight line

✔ Correlation: Positive
✔ Estimated r value: Around 0.98
> (Almost perfect positive correlation)

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✔ Final Answers:

| Example | Correlation | Estimated r Value |
|--------|-------------|-------------------|
| 1 | Positive | ~0.7 |
| 2 | No | 0 |
| 3 | Negative | ~-0.95 |
| 4 | Positive | ~0.98 |

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📌 Summary Explanation:

- The correlation coefficient (r) tells us:
- Direction: Positive (+), Negative (–), or None (0)
- Strength: How close the points are to a straight line
- Values range from -1 to 1:
- $r = 1$: Perfect positive linear relationship
- $r = -1$: Perfect negative linear relationship
- $r = 0$: No linear relationship

By visually inspecting the scatter plots, we estimate r based on:
- Trend direction
- How tightly the points cluster around an imaginary line

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