Question 57

There is a weak positive correlation between the two variables.

The correlation coefficient r = 0.0964 indicates a weak positive relationship between the two variables. A value close to zero suggests that there is little to no linear correlation, but since it is slightly above zero, it reflects a weak positive correlation.

A) There is a strong negative correlation between the two variables.

This option is incorrect because a strong negative correlation would imply a correlation coefficient significantly less than zero, typically closer to -1. The given coefficient of r = 0.0964 does not support any negative correlation, strong or otherwise.

B) There is a strong positive correlation between the two variables.

This option is also incorrect. A strong positive correlation would require a correlation coefficient close to +1. The value of r = 0.0964 indicates a very weak positive correlation, not a strong one.

C) There is a weak negative correlation between the two variables.

This option is incorrect as well. A weak negative correlation would suggest a correlation coefficient slightly below zero. Since the given value is 0.0964, it does not indicate any negative correlation, weak or strong.

D) There is a weak positive correlation between the two variables.

This option is correct. The correlation coefficient of r = 0.0964 signifies a very weak positive correlation, indicating that as one variable increases, the other variable tends to do so slightly as well, although the relationship is not strong.

Conclusion

In summary, the correlation coefficient r = 0.0964 clearly represents a weak positive correlation between the two variables, as reflected in the correct answer choice D. The other options incorrectly interpret the nature of the correlation, either suggesting it is strong or negative, which is not supported by the numerical value provided.