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
✔ *Explanation:* Correlation describes how two variables are related—whether they tend to increase or decrease together.

#### Correlation coefficient (r) – measures the strength and direction of the relationship between two variables in a data set
✔ *Explanation:*
- Strength: How closely the points follow a straight line.
- Direction: Whether the relationship is positive or negative.

> ✔ *r must be between* -1 and 1

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🔹 Step 2: Analyze Each Scatter Plot (Examples 1–4)

We need to:
1. Determine the type of correlation (positive, negative, or no correlation).
2. Estimate the correlation coefficient (*r*) value.

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#### Example 1

🔹 Scatter Plot Analysis:
- Points trend upward from left to right.
- The pattern is somewhat tight but not perfectly linear.
- There’s a positive correlation, but some spread.

✔ Correlation: Positive
✔ Estimated r value: Around 0.7
> Reasoning: It’s strong but not perfect. Since it’s not perfectly aligned, it's less than 1. A good estimate for this level of clustering is around 0.7.

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#### Example 2

🔹 Scatter Plot Analysis:
- Points appear randomly scattered with no clear pattern.
- No upward or downward trend.

✔ Correlation: No correlation
✔ Estimated r value: 0
> Reasoning: The points don’t show any consistent direction. This matches "no correlation" where $ r \approx 0 $.

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#### Example 3

🔹 Scatter Plot Analysis:
- Points form a clear downward trend from left to right.
- The points are tightly clustered along a straight line.

✔ Correlation: Negative
✔ Estimated r value: Around -0.9
> Reasoning: Strong negative correlation. Very close to a straight line going down, so very close to -1. But not perfect, so we estimate -0.9.

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#### Example 4

🔹 Scatter Plot Analysis:
- Points trend upward from left to right.
- The pattern is very tight and nearly forms a straight line.

✔ Correlation: Positive
✔ Estimated r value: Around 0.95
> Reasoning: Almost all points lie on a straight line with a positive slope. This indicates a very strong positive correlation, so $ r \approx 0.95 $.

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✔ Final Answers:

| Example | Correlation Type | Estimated r Value |
|--------|------------------|-------------------|
| 1 | Positive | ~0.7 |
| 2 | No correlation | ~0 |
| 3 | Negative | ~-0.9 |
| 4 | Positive | ~0.95 |

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📝 Summary Notes:

- Positive correlation: As x increases, y increases → $ r > 0 $
- Negative correlation: As x increases, y decreases → $ r < 0 $
- No correlation: No pattern → $ r \approx 0 $
- Stronger correlation = closer to 1 or -1
- Weaker correlation = closer to 0

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✔ Final Answer (for the blanks):

- Correlation – the relationship between two variables in a data set
- Correlation coefficient (r) – measures the strength and direction of the relationship
- $ r $ must be between -1 and 1

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