The question is asking about the correlation coefficient $r$ and which statement is not true.

Here is an analysis of each option:

1. $-1 \leq r \leq 1$

   • This is true. The correlation coefficient $r$ always lies between $-1$ and $1$.

2. The closer $r$ is to ±1, the more closely the scattered points line up.

   • This is also true. When $r$ is close to $+1$ or $-1$, the data points lie closer to a straight line.

3. $r > 0$ when scatter plot shows a rising trend.

   • This is true. A positive $r$ indicates a positive correlation, meaning a rising trend in the data.

4. $r$ is the slope of the best-fit line.

   • This is not true. The correlation coefficient $r$ measures the strength and direction of the linear relationship between variables, but it is not the slope of the line of best fit. The slope is a separate value.

5. $r < 0$ when scatter plot shows a falling trend.

   • This is true. A negative $r$ indicates a negative correlation, meaning a downward trend.

Correct Answer:

"$r$ is the slope of the best-fit line."

Would you like me to explain correlation coefficients further or break down other concepts related to this question?

Related Questions:

1. What is the significance of a correlation coefficient $r = 0$?
2. How does $r$ differ from the slope of a regression line?
3. How is the correlation coefficient $r$ calculated mathematically?
4. Can the correlation coefficient indicate causation? Why or why not?
5. What does a perfect positive correlation ($r = 1$) look like on a scatter plot?

Tip: Remember, the correlation coefficient $r$ describes association, not the actual slope of a line.