Define and distinguish among positive correlation, negative correlation, and no correlation. Give an example of each type of correlation. B. Positive correlation means that two variables tend to change in opposite directions, with one increasing while the other decreases. An example might be age and vision. be the diameter of a circle and its circumference. Dositive correlation means that both variables tend to increase (or decrease) together. An example might be shoe size and height. might be hair color and weight. Define negative correlation. Choose the correct answer below. A. Negative correlation means that both variables tend to increase (or decrease) together. An example might be shoe size and height.

**Step 1. Define Positive, Negative, and No Correlation** - **Positive correlation:** Two variables exhibit a positive correlation if, when one variable increases, the other variable tends to increase as well, and vice versa. *Example:* The diameter \( d \) and the circumference \( C \) of a circle are positively correlated because \( C = \pi d \); as the diameter increases, the circumference increases too. - **Negative correlation:** Two variables have a negative correlation if, when one variable increases, the other variable tends to decrease, and vice versa. *Example:* Consider age and vision quality. As age increases, vision quality tends to decline, thus exhibiting a negative correlation. - **No correlation:** Two variables have no correlation if changes in one variable do not predict any specific changes in the other. *Example:* Hair color and weight have no systematic relationship, so they are uncorrelated. **Step 2. Correcting the Misconception** In the provided statements, there is a mix-up: - The statement “Positive correlation means that two variables tend to change in opposite directions” is incorrect. In fact, positive correlation means that the variables increase (or decrease) together. - The correct definition of negative correlation is that as one variable increases, the other decreases. **Step 3. Answer the Specific Question on Negative Correlation** The correct answer for defining negative correlation is: - **Negative correlation means that as one variable increases, the other variable tends to decrease (and vice versa).** Thus, the statement “Negative correlation means that both variables tend to increase (or decrease) together” is incorrect.