Question

the correlation coefficient between two observed variables is -.84. from this it can be concluded that:

one variable causes the other variable to occur

the two variables are unrelated.

as one variable increase, the other is likely to decrease, showing an inverse relationship.

as one variable increases, the other is likely to increase, showing a direct relationship.

Explanation:

1. Recall the concept of correlation coefficient: A negative correlation coefficient (here, -0.84) indicates an inverse relationship. A correlation coefficient close to -1 or 1 shows a strong relationship, and the sign (negative here) shows the direction.
2. Analyze each option:

• "One variable causes the other" is wrong because correlation does not imply causation.
• "The two variables are unrelated" is wrong as -0.84 is a strong (negative) correlation, so they are related.
• "As one variable increase, the other is likely to decrease, showing an inverse relationship" matches the negative correlation: negative sign means as one increases, the other tends to decrease.
• "As one variable increases, the other is likely to increase" is for positive correlation, but here the coefficient is negative, so this is wrong.

Answer:

C. As one variable increase, the other is likely to decrease, showing an inverse relationship.