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The image asks two questions based on a correlation coefficient \( r \approx 0.812 \) for a bivariate data set:

1. **Is the correlation between the variables positive or negative? Explain your reasoning.**
   - Since \( r \approx 0.812 \) is a positive number, the correlation between the two variables is positive. A positive correlation indicates that as one variable increases, the other variable also tends to increase.

2. **Describe the strength of the correlation between the variables.**
   - The value of \( r = 0.812 \) suggests a strong positive correlation. Correlation coefficients close to 1 (either positive or negative) indicate strong relationships, while values near 0 indicate weak or no correlation. A value of 0.812 is considered to reflect a strong association between the two variables.

Do you need any further explanation or details on this?

Here are some follow-up questions to deepen your understanding:

1. What is the significance of a correlation coefficient being exactly 1 or -1?
2. How would you interpret a correlation coefficient of 0?
3. Can you describe how outliers might affect the correlation coefficient?
4. What is the difference between correlation and causation?
5. How can the strength of correlation impact predictions in a regression analysis?

**Tip:** Always remember that correlation does not imply causation. Just because two variables are correlated does not mean one causes the other to change.

The correlation coefficient for a bivariate data set is r ≈ 0.812. Is the correlation between the variables positive or negative? Describe the strength of the correlation between the variables.

Learn how to interpret a correlation coefficient of r ≈ 0.812 in a bivariate data set. This problem involves key statistical concepts such as correlation strength, direction, and the Pearson correlation formula. Suitable for high school students in Grades 10-12.

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