To address the question, let's analyze the statements about the "best-fit line" (also called the regression line or line of best fit) and determine which are true.

True Statements About the Best-Fit Line:

1. "It makes the least distance from every point."
   This is partially misleading. The best-fit line minimizes the sum of squared vertical distances between the data points and the line, not the distance in every direction.
   FALSE.

2. "The slope is the correlation coefficient."
   This is not true. The slope of the best-fit line depends on the standard deviations and the correlation coefficient $r$, but the slope itself is not equal to $r$.
   FALSE.

3. "It must contain all scattered points."
   The best-fit line does not need to pass through all points. Instead, it minimizes the errors (vertical residuals) overall.
   FALSE.

4. "The line is horizontal when the correlation coefficient is 0."
   This is TRUE. When the correlation coefficient $r = 0$, there is no linear relationship between the variables, so the best-fit line will be horizontal, corresponding to the mean of $y$-values.

5. "It is used to predict values that are not in the data."
   This is TRUE. One purpose of the best-fit line is to make predictions, even for $x$-values outside the observed range (called extrapolation).

Final Answer:

The correct statements are:

• "The line is horizontal when the correlation coefficient is 0."
• "It is used to predict values that are not in the data."

Would you like more explanation on any of these points?

Related Questions:

1. What is the role of residuals in determining the best-fit line?
2. How is the slope of the best-fit line calculated?
3. Why does the best-fit line minimize squared errors instead of absolute errors?
4. What happens when the correlation coefficient is close to $-1$ or $1$?
5. What is the difference between interpolation and extrapolation when using the best-fit line?

Tip: The least-squares regression method minimizes the sum of the squared vertical distances (residuals) from the data points to the line, not the perpendicular distances.