Which of the following statements about correlation is​ true?

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Part 1

Choose the correct answer below.

A.

We say that there is a positive correlation between x and y if there is no distinct pattern in the scatterplot.

B.

We say that there is a positive correlation between x and y if the​ x-values increase as the corresponding​ y-values decrease.

C.

We say that there is a negative correlation between x and y if the​ x-values increase as the corresponding​ y-values increase.

D.

We say that there is a positive correlation between x and y if the​ x-values increase as the corresponding​ y-values increase.

The correct statement about correlation is:

**D. We say that there is a positive correlation between x and y if the x-values increase as the corresponding y-values increase.**

### Explanation:
- **Positive Correlation:** Occurs when both variables move in the same direction. As one variable increases, the other also increases.
- **Negative Correlation:** Occurs when the variables move in opposite directions. As one variable increases, the other decreases.

### Review of Other Options:
- **A.** Incorrect, because a positive correlation is characterized by a clear upward trend, not a lack of pattern.
- **B.** Incorrect, as this describes a negative correlation.
- **C.** Incorrect, as this also describes a positive correlation, but the description given is for negative correlation.

Would you like further details or have any questions?

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### 8 Relative Questions:
1. How is the correlation coefficient interpreted?
2. What is the range of the correlation coefficient?
3. How can you visually identify a positive correlation on a scatterplot?
4. What does a correlation coefficient of 0 indicate?
5. How does correlation differ from causation?
6. What factors can affect the strength of a correlation?
7. Can a correlation coefficient be greater than 1?
8. What methods can be used to calculate the correlation coefficient?

**Tip:** Always check the direction and strength of the correlation when interpreting data. It helps to visualize the relationship using a scatterplot.

Explore the concept of positive correlation in statistics with detailed explanations and examples. Learn how to interpret scatterplots and understand the relationship between variables. Ideal for high school students studying statistics.

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