The question asks for an estimate of the correlation coefficient $r$ for the scatter plot provided. The options for $r$ are:

• $a. -2.50$
• $b. -1.00$
• $c. 2.50$
• $d. 1.00$

Observations:

The scatter plot shows a negative linear trend, as $x$ increases, $y$ decreases. This indicates that $r$ must be a negative value. The points align relatively well, suggesting a strong correlation.

Evaluation:

1. The correlation coefficient $r$ always falls between $-1$ and $1$. Hence, options $-2.50$ and $2.50$ are invalid because they are out of this range.
2. A perfect negative correlation ($r = -1$) occurs when all points lie exactly on a straight descending line. Since the points in this scatter plot are close to a line but not perfectly aligned, $r$ is likely close to $-1$, but not exactly $-1$.

Conclusion:

The best estimate for $r$ is $b. -1.00$. However, if exact values aren't required, the correlation is close to $-1$, indicating a strong negative relationship.

Would you like a more detailed explanation about correlation or scatter plots?

Related Questions:

1. What is the mathematical formula to calculate the correlation coefficient $r$?
2. How does $r$ differ between strong and weak correlations?
3. Why can't $r$ exceed the range of $[-1, 1]$?
4. What real-world scenarios might produce strong negative correlations?
5. How does the scatter plot's density affect the estimated value of $r$?

Tip:

When estimating $r$ visually, focus on both the direction and how tightly the points cluster around an imaginary line.