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If variables have zero correlation, they do not have a linear relationship. Zero correlation shows that two things were not found to be related.
If measurements are taken for two (or more) variable for a sample , then the correlation between the variables are the sample correlation. If the sample is representative then the sample correlation will be a good estimate of the true population correlation.
Evidence that there is no correlation.
They can be positive correlation, negative correlation or no correlation depending on 'line of best fit'
Yes it can be a correlation coefficient.