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If the correlation coefficient is 0, then the two tings vary separately. They are not related.
"If coefficient of correlation, "r" between two variables is zero, does it mean that there is no relationship between the variables? Justify your answer".
No. If the correlation coefficient is close to 1 or -1, then the two variables have a high degree of statistical linear correlation. See the related link, particularly the graphs which illustrate correlation.
A coefficient of zero means there is no correlation between two variables. A coefficient of -1 indicates strong negative correlation, while +1 suggests strong positive correlation.
Correlation Coefficient.