Define and distinguish among positive correlation, negative correlation, and no correlation. Give an example of each type of correlation. Define positive correlation. Choose the correct answer below. A. Positive correlation means that there is a good relationship between the two variables. An example might be the diameter of a circle and its circumference. 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. C. Positive correlation means that both variables tend to increase (or decrease) together. An example might be shoe size and height. D. Positive correlation means that there is no apparent relationship between the two variables. An example might be hair color and weight.

**Step 1: Define Positive Correlation** Positive correlation means that when one variable increases, the other variable also tends to increase, and when one variable decreases, the other variable tends to decrease. In other words, the two variables move in the same direction. For example, as shoe size increases, height tends to increase. **Step 2: Examine Each Option** - **Option A:** States: "Positive correlation means that there is a good relationship between the two variables." This definition is vague and the example of the diameter of a circle and its circumference does show a positive relationship but the reasoning provided does not clearly explain the concept of both variables moving together. - **Option B:** States: "Positive correlation means that two variables tend to change in opposite directions, with one increasing while the other decreases." This is actually the definition of negative correlation, not positive correlation. - **Option C:** States: "Positive correlation means that both variables tend to increase (or decrease) together." This precisely captures the definition of positive correlation. The example given, "shoe size and height," is appropriate since typically, as one increases, the other increases as well. - **Option D:** States: "Positive correlation means that there is no apparent relationship between the two variables." This describes no correlation, not positive correlation. **Step 3: Correct Answer Selection** The correct answer is **Option C**: \( \textbf{C. Positive correlation means that both variables tend to increase (or decrease) together. An example might be shoe size and height.} \)