Linear Scatter Plots Notes Worksheet

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

We are given definitions with blanks to fill in:

1. Correlation – the relationship between two variables in a data set
*(Note: "relationship" is the correct term here — it describes how two variables are connected.)*

2. Correlation coefficient (r) – measures the strength and direction of the relationship between two variables in a data set
✔ *This is standard: r tells us both how strong and in which direction the relationship is.*

3. r must be between -1 and 1

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🔹 Step 2: Understanding the Three Types of Correlation

| Type | Description |
|------|-------------|
| Positive Correlation | Points trend upward from left to right. r > 0, closer to 1 = stronger correlation |
| Negative Correlation | Points trend downward from left to right. r < 0, closer to -1 = stronger correlation |
| No Correlation | No clear pattern; points scattered randomly. r ≈ 0 |

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🔹 Step 3: Analyze Each Example Scatter Plot

Now, we’ll analyze each of the four scatter plots and estimate the type of correlation and an approximate r value.

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#### Example 1

- Pattern: Points generally trend upward from left to right.
- Strength: Moderate to strong — not perfectly linear, but there’s a clear positive trend.
- Direction: Positive
- ✔ Correlation: Positive
- ✔ Estimated r value: Around 0.7 to 0.8

> ✔️ Reasoning: The points follow a clear upward trend but have some scatter.

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#### Example 2

- Pattern: Points appear randomly scattered with no clear trend.
- Direction: None
- Strength: Very weak or none
- ✔ Correlation: No correlation
- ✔ Estimated r value: Close to 0, maybe ±0.1

> ✔️ Reasoning: There's no consistent pattern — points are spread out evenly.

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#### Example 3

- Pattern: Points form a very clear downward trend from left to right.
- Strength: Very strong — nearly all points lie along a straight line.
- Direction: Negative
- ✔ Correlation: Negative
- ✔ Estimated r value: Around -0.9 to -0.95

> ✔️ Reasoning: Almost perfectly linear negative slope — very strong negative correlation.

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#### Example 4

- Pattern: Points trend upward from left to right.
- Strength: Strong — points are tightly clustered around a line.
- Direction: Positive
- ✔ Correlation: Positive
- ✔ Estimated r value: Around 0.9 to 0.95

> ✔️ Reasoning: Strong positive trend with minimal scatter.

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✔ Final Answers for Examples:

| Example | Correlation Type | Estimated r Value |
|--------|------------------|-------------------|
| 1 | Positive | ~0.7–0.8 |
| 2 | No correlation | ~0 |
| 3 | Negative | ~-0.9 to -0.95 |
| 4 | Positive | ~0.9 to 0.95 |

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📌 Summary of Key Concepts:

- Correlation: The relationship between two variables.
- Correlation coefficient (r): Measures the strength and direction of the relationship.
- Range of r: Always between -1 and 1.
- r = 1 → perfect positive correlation
- r = -1 → perfect negative correlation
- r = 0 → no linear correlation

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✔ Completed Worksheet (Blanks Filled):

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

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