What Does a Correlation Coefficient of Zero indicate?

In the field of statistics, the correlation coefficient is a means to measure how much do two variables move together. It is a measure to indicate that how good is the association between two variables. But it is at the same time not necessary that it would show whether one is causing a change in the other. The correlation coefficient is zero; it means that there is not a correlation association of any types.

The co variance  in a pair of variables is a very useful metric for the purpose of comparison; it is a measure to understand the way in which the two variables move together. When the co-variance is negative it implies that two variables are related inversely and on the other hand a positive co-variance means that there is a positive correlation between two variables. It further means that they go up and down at the same time.  The correlation coefficient is dependent upon the co-variance.

When we take out the co-variance of two variables, it also helps in the interpretation. When the researcher has to take out the correlated coefficient, the co-variance of the variables under study should be divided by the product of the standard deviation of the two respective variables.

It is mandatory for the correlation coefficient to be between -1 and 1.  When the value of the correlation coefficient is close to -1, it indicates that these two move in the opposite direction. This means that when one goes up the other one comes down, there is a negative correlation between them. On the other hand, if the value is close to 1, the implication is the opposite. However, when the value is closer to zero or it is zero, it indicates that there is no correlation between the variables and in either of the two direction there isn’t any strong correlation.

The correlation coefficient will always be between -1 and 1. A correlation coefficient close to -1 implies that the two variables move in opposite directions. When one goes up, the other goes down. They are negatively correlated. A value close to 1 implies the opposite. If the value is zero, or close to zero, that means that the two variables do not share any particular correlation. There is no strong correlation relationship in one direction or the other.