## **Core Concept**
The coefficient of correlation, often denoted as (r), measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of (r) ranges from -1 to 1. A value of 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.

## **Why the Correct Answer is Right**
When the height and weight are perfectly correlated, it implies that as one variable increases, the other variable increases in a perfectly predictable manner. This situation represents a perfect positive linear relationship. Therefore, the coefficient of correlation (r) would be 1, indicating that the variables are perfectly correlated in a positive direction.

## **Why Each Wrong Option is Incorrect**
- **Option A:** (-infty) is incorrect because the coefficient of correlation cannot be infinite; it must be within the range of -1 to 1.
- **Option B:** (-1) is incorrect because it represents a perfect negative correlation, which is the opposite of what the question describes.
- **Option C:** (0) is incorrect because it indicates no linear relationship between the variables, which does not match the scenario of a perfect correlation.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that correlation does not imply causation. Even if height and weight are perfectly correlated, it doesn't mean that one causes the other; they could both be influenced by a third factor, such as genetics or nutrition.

## **Correct Answer:** . **1**