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The question asks you to describe the slope of the least squares regression line given four options based on the correlation coefficient \( r \). The information provided includes:

- \( r = 0.6 \)
- \( r = -0.6 \)
- \( r = 0 \)
- \( r^2 = 0.49 \)

### Step-by-Step Explanation:
1. **Interpretation of \( r \):** The correlation coefficient \( r \) represents the strength and direction of the linear relationship between two variables. 
    - If \( r > 0 \), the slope of the regression line is **positive**.
    - If \( r < 0 \), the slope of the regression line is **negative**.
    - If \( r = 0 \), there is no linear relationship, and the slope of the line would be **0**.

2. **Interpretation of \( r^2 \):** The coefficient of determination, \( r^2 \), shows how much of the variance in the dependent variable is explained by the independent variable. In this case:
   - \( r^2 = 0.49 \), so \( r \) could be either \( +0.7 \) or \( -0.7 \), since \( r^2 \) is the square of the correlation coefficient \( r \). This means that 49% of the variance is explained by the model.

### Answers Analysis:
- **Option A: \( r = 0.6 \):** A positive correlation, so the slope is **positive**.
- **Option B: \( r = -0.6 \):** A negative correlation, so the slope is **negative**.
- **Option C: \( r = 0 \):** No correlation, so the slope is **0**.
- **Option D: \( r^2 = 0.49 \):** This suggests \( r \) is either \( +0.7 \) or \( -0.7 \), which doesn't tell the exact sign of \( r \), but either way, the slope is nonzero.

### Conclusion:
The correct interpretation depends on the value of \( r \). If you select a specific \( r \) value, the slope is either positive, negative, or zero.

Let me know if you'd like further clarification or more details! Here are 5 relative questions to think about:
1. How is the correlation coefficient \( r \) related to the slope of a regression line?
2. What does it mean if \( r = 0 \) in terms of the relationship between variables?
3. Can \( r^2 \) ever be negative?
4. How does a high \( r^2 \) value affect the accuracy of predictions?
5. What is the difference between correlation and causation in regression analysis?

**Tip:** The sign of the correlation coefficient \( r \) directly indicates the direction of the regression line's slope.

Describe the slope of the least squares regression line for the given information. Options:
A. The slope of the line is negative.
B. The slope of the line is positive.
C. The slope of the line is 0.
D. The slope of the line can be positive or negative.
Information provided:
a. r = 0.6
b. r = -0.6
c. r = 0
d. r^2 = 0.49

Explore how to interpret the slope of a least squares regression line using correlation coefficient values such as r = 0.6, r = -0.6, r = 0, and r^2 = 0.49. Learn the relationship between the slope and the value of r. Suitable for students in Grades 10-12 studying statistics and linear regression.

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