If a scatter plot shows points that are closely clustered together, what can you infer about the correlation between the variables?

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If a scatter plot shows points that are closely clustered together, it typically indicates a strong correlation between the two variables being plotted. Here's how to interpret the nature of that correlation:

1. **Positive Correlation**: If the clustered points trend upward from left to right, it suggests a strong positive correlation. This means that as one variable increases, the other variable also tends to increase.

2. **Negative Correlation**: If the clustered points trend downward from left to right, it indicates a strong negative correlation. In this case, as one variable increases, the other variable tends to decrease.

3. **No Correlation**: If the points are closely clustered but show no clear upward or downward trend, it may suggest little to no linear correlation between the variables. However, there might still be a nonlinear relationship that the scatter plot isn't capturing.

**Key Takeaway**: Closeness of the cluster indicates the strength of the relationship, while the direction of the trend (upward or downward) indicates whether the correlation is positive or negative.

**Example Visualization:**

- **Strong Positive Correlation**:
  
  ![Positive Correlation](https://i.imgur.com/positive_correlation.png)

- **Strong Negative Correlation**:
  
  ![Negative Correlation](https://i.imgur.com/negative_correlation.png)

- **No Clear Correlation**:
  
  ![No Correlation](https://i.imgur.com/no_correlation.png)

Understanding the pattern and tightness of the clustering in a scatter plot is crucial for determining the nature and strength of the relationship between variables.

**References:**
- [Correlation and Scatter Plots - Khan Academy](https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitative-data)
- [Understanding Correlation Coefficients](https://statisticsbyjim.com/basics/correlation-coefficient-formula/)
If a scatter plot shows points closely clustered together, it means there is a strong correlation between the variables. If the points trend upward, it's a strong positive correlation; if they trend downward, it's a strong negative correlation. If there's no clear trend, there's little to no linear correlation.

If a scatter plot shows points that are closely clustered together, what can you infer about the correlation between the variables?

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