A correlation coefficient of 0 signifies that there is no linear relationship between the two variables being analyzed. This means that changes in one variable do not predict changes in the other variable at all. In simple terms, a correlation of 0 indicates that knowing the value of one variable provides no information about the value of the other variable. However, it's important to note that a correlation coefficient of 0 does not imply that there is no relationship whatsoever; there could still be a non-linear relationship that the correlation coefficient does not capture.