Answer :
To determine what the "-" in the correlation coefficient -0.80 signifies, let's explore the concept of the correlation coefficient in detail.
The correlation coefficient, denoted as \( r \), measures the strength and direction of the linear relationship between two variables. The value of \( r \) ranges from -1 to 1.
Here's what the notation signifies:
1. Direction of the Relationship:
- If \( r \) is positive, it indicates a positive relationship between the variables, meaning that as one variable increases, the other variable also increases.
- If \( r \) is negative, it signifies a negative relationship between the variables, meaning that as one variable increases, the other variable decreases.
2. Strength of the Relationship:
- The closer the value of \( r \) is to 1 or -1, the stronger the relationship.
- A value of \( r \) close to 0 indicates little to no linear relationship.
Given the correlation coefficient of -0.80, here's what we can infer:
- The "-" sign indicates the direction of the relationship. Specifically, it tells us that the relationship between the two variables is inverse; as one variable increases, the other one decreases.
Based on these insights:
- a The strength of the relationship: While the value 0.80 indicates the strength, the "-" itself does not. So this is incorrect.
- b The direction of the relationship: The "-" sign indicates that the relationship is negative.
- c That when one variable increases the other variable increases: This is incorrect because the "-" indicates a negative relationship, meaning when one increases, the other decreases.
- d That when one variable increases the other variable decreases: This correctly interprets the meaning of the "-" sign.
Thus, the correct answers are:
- b The direction of the relationship
- d That when one variable increases the other variable decreases
Therefore, the final selected answers are:
[2, 4]
The correlation coefficient, denoted as \( r \), measures the strength and direction of the linear relationship between two variables. The value of \( r \) ranges from -1 to 1.
Here's what the notation signifies:
1. Direction of the Relationship:
- If \( r \) is positive, it indicates a positive relationship between the variables, meaning that as one variable increases, the other variable also increases.
- If \( r \) is negative, it signifies a negative relationship between the variables, meaning that as one variable increases, the other variable decreases.
2. Strength of the Relationship:
- The closer the value of \( r \) is to 1 or -1, the stronger the relationship.
- A value of \( r \) close to 0 indicates little to no linear relationship.
Given the correlation coefficient of -0.80, here's what we can infer:
- The "-" sign indicates the direction of the relationship. Specifically, it tells us that the relationship between the two variables is inverse; as one variable increases, the other one decreases.
Based on these insights:
- a The strength of the relationship: While the value 0.80 indicates the strength, the "-" itself does not. So this is incorrect.
- b The direction of the relationship: The "-" sign indicates that the relationship is negative.
- c That when one variable increases the other variable increases: This is incorrect because the "-" indicates a negative relationship, meaning when one increases, the other decreases.
- d That when one variable increases the other variable decreases: This correctly interprets the meaning of the "-" sign.
Thus, the correct answers are:
- b The direction of the relationship
- d That when one variable increases the other variable decreases
Therefore, the final selected answers are:
[2, 4]
