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.