Question 13

0.998 represents a strong direct relationship.

A correlation coefficient of 0.998 indicates a very strong positive correlation between two variables, suggesting that as one variable increases, the other variable also tends to increase in a nearly linear manner.

A) Strong direct relationship

This option accurately describes the meaning of a correlation coefficient of 0.998. A value so close to 1 signifies a strong positive relationship, where the two variables move in the same direction.

B) Strong inverse relationship

This option is incorrect because a strong inverse relationship would be represented by a correlation coefficient close to -1. Since 0.998 is a positive value, it indicates a direct, not inverse, relationship.

C) Weak direct relationship

This option is incorrect as well. A correlation coefficient of 0.998 does not indicate a weak relationship; rather, it signifies a very strong relationship. A weak direct relationship would be represented by a value significantly closer to 0.

D) Weak inverse relationship

This option is also incorrect. A weak inverse relationship would suggest a negative correlation that is weak, typically indicated by a correlation coefficient that is close to 0 but negative. The value of 0.998 does not support this interpretation.

Conclusion

The interpretation of 0.998 as a correlation coefficient clearly indicates a strong direct relationship between the two variables. All other options fail to accurately represent the strength and direction of the correlation, demonstrating a misunderstanding of correlation coefficients and their implications in statistical analysis.