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Question 8

Examining the correlation coefficient \(-0.80\), what does the "-" tell you? Select all that apply.

A. The strength of the relationship
B. The direction of the relationship
C. That when one variable increases the other variable increases
D. That when one variable decreases the other variable increases

Sagot :

GinnyAnswer
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]
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