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

When a scatter plot shows points that are **closely clustered together**, it suggests a **strong correlation** between the two variables being analyzed. Here's what this generally indicates: 1. **Strong Positive Correlation**: - **Appearance**: Points tightly clustering along an upward-sloping line. - **Interpretation**: As one variable increases, the other variable tends to also increase consistently. 2. **Strong Negative Correlation**: - **Appearance**: Points tightly clustering along a downward-sloping line. - **Interpretation**: As one variable increases, the other variable tends to decrease consistently. 3. **Type of Correlation**: - The tight clustering indicates a **linear relationship**, meaning the variables change in a predictable, straight-line manner relative to each other. - It's important to note that tight clustering doesn't inherently specify whether the correlation is positive or negative; the direction of the slope determines this. **Key Takeaway**: - **Tight Clustering** ➔ **Strong Correlation** (either positive or negative) - **Loose Clustering** ➔ **Weak or No Correlation** **Example**: - If you're plotting hours studied vs. exam scores and the points are tightly aligned along an upward slope, this indicates a strong positive correlation: more hours studied generally lead to higher exam scores. **Caveat**: - While tight clustering suggests a strong linear relationship, it's essential to consider other factors and perform statistical tests (like calculating the Pearson correlation coefficient) to quantify the strength and significance of the correlation. **Summary**: Closely clustered points in a scatter plot indicate that the two variables have a strong linear relationship, showing a strong positive or negative correlation.