Which of the following correlation coefficients may represent a strong correlation?
a) +0.30 b) +0.75 c) +1.3 d) -0.85 e) -0.05

Solution:

Correlation coefficients are used to measure how strong a relationship is between two variables. There are several types of correlation coefficients, but the most popular is Pearson’s. Pearson’s correlation is a correlation coefficient commonly used in linear regression. Generally, correlation coefficients range between -1.00 to +1.00.

According to the rule of correlation coefficients, the strongest correlation is considered when the value is closest to +1 (positive correlation) or -1 (negative correlation). 

A positive correlation coefficient indicates that the value of one variable depends on the other variable directly.

A zero-correlation coefficient indicates that there is no correlation between both variables.

A negative correlation coefficient indicates that the value of one variable depends on the other variable inversely.

Hence, according to the options, we know that -0.85 is the closest to -1, and none of the values is closer than that to either of -1 or +1. Hence, it is more negatively correlated.

Hence, -0.85 (Option d) is the strongest correlation coefficient which represents the strongest correlation as compared to others.

Which of the following correlation coefficients may represent a strong correlation?

Summary:

-0.85 (Option d) is the strongest correlation coefficient which represents the strongest correlation as compared to others.