What is the definition of the correlation coefficient?
Choose the correct answer below.
A. The correlation coefficient is a measure that describes the direction and strength of any relationship between two quantitative variables.
B. The correlation coefficient is a measure that describes the direction and strength of the linear relationship between two quantitative variables
C. The correlation coefficient is a measure that describes the direction and strength of any relationship between a qualitative variable and a quantitative variable.
D. The correlation coefficient is a measure that describes the direction and strength of the linear relationship between a qualitative variable and a quantitative variable.
E. The correlation coefficient is a measure that describes the direction and strength of the linear relationship between two qualitative variables.
The correct answer and explanation is:
The correct answer is B. The correlation coefficient is a measure that describes the direction and strength of the linear relationship between two quantitative variables.
Explanation:
The correlation coefficient, often denoted as r, is a statistical measure used to describe the relationship between two quantitative variables. It tells us both the direction and the strength of their linear relationship.
- Direction: The correlation coefficient can be positive or negative.
- A positive correlation (r > 0) means that as one variable increases, the other variable also tends to increase. For example, height and weight often show a positive correlation: as a person’s height increases, their weight may also increase.
- A negative correlation (r < 0) indicates that as one variable increases, the other tends to decrease. For example, the amount of time spent studying and the number of mistakes in a test may have a negative correlation: the more a student studies, the fewer mistakes they make.
- Strength: The magnitude of the correlation coefficient indicates how strongly the variables are related. The closer the correlation coefficient is to +1 or -1, the stronger the relationship between the variables.
- r = 1 or r = -1 indicates a perfect linear relationship, meaning every change in one variable corresponds to a predictable change in the other.
- r = 0 means no linear relationship between the variables, although other types of relationships may exist.
It is important to note that the correlation coefficient only measures the linear relationship between two variables. A strong correlation does not imply causation; it simply indicates that the variables tend to move together in a specific pattern, but it doesn’t explain why or how that relationship exists.
Options A, C, D, and E are incorrect because they either include qualitative variables or do not specifically mention the linear nature of the relationship.