(1 point) Match the following sample correlation coefficients with the explanation of what that correlation coefficient means. Type the correct letter in each box. 1. $r=0$ 2. $r=1$ 3. $r=-.97$ 4. $r=-.15$ A. a weak negative relationship between $x$ and $y$ B. a strong negative relationship between $x$ and $y$ C. no relationship between $x$ and $y$ D. a perfect positive relationship between $x$ and $y$

Step 1 ：The correlation coefficient, often denoted by r, is a measure of the strength and direction of a linear relationship between two variables. The value of r is always between -1 and 1 inclusive. A positive r indicates a positive relationship between the variables, while a negative r indicates a negative relationship. The closer r is to 1 or -1, the stronger the relationship. An r of 0 indicates no linear relationship.

Step 2 ：Match the given correlation coefficients with their meanings:

Step 3 ：\(r=0\) corresponds to no relationship between \(x\) and \(y\).

Step 4 ：\(r=1\) corresponds to a perfect positive relationship between \(x\) and \(y\).

Step 5 ：\(r=-.97\) corresponds to a strong negative relationship between \(x\) and \(y\).

Step 6 ：\(r=-.15\) corresponds to a weak negative relationship between \(x\) and \(y\).

Step 7 ：Final Answer:

Step 8 ：\(\boxed{r=0}\) corresponds to \(\boxed{C.}\) no relationship between \(x\) and \(y\).

Step 9 ：\(\boxed{r=1}\) corresponds to \(\boxed{D.}\) a perfect positive relationship between \(x\) and \(y\).

Step 10 ：\(\boxed{r=-.97}\) corresponds to \(\boxed{B.}\) a strong negative relationship between \(x\) and \(y\).

Step 11 ：\(\boxed{r=-.15}\) corresponds to \(\boxed{A.}\) a weak negative relationship between \(x\) and \(y\).