Why the value of correlation coefficient is always between -1 and 1?"

Something can be anywhere from 100% correlated with another variable, to completely opposite at -100% correlated. 1 to -1 is a method to express coefficients in that range.

Indeed it is Elementary. But the sub-zero varient of zero is not always greater than the elevation.

Check on mc080401833

Actually it just represent relationship which is direct or positive, indirect or negative & No relation. If it is towards positive not perfect it is less than +1. If it is towards negative not perfect it is greater than -1. Hope that answers the question

Check on mc080401833

Actually it just represent relationship which is direct or positive, indirect or negative & No relation. If it is towards positive not perfect it is less than +1. If it is towards negative not perfect it is greater than -1. Hope that answers the question

It indicates the level of correlation between groups of data. If the number is positive, there is positive correlation; conversely, a negative value indicates a negative correlation. Positive values closer to 1 show strong positive correlation whereas positive values closer to 0 show weak positive correlation. This is the same with negative values closer to -1 and 0, they have stronger and weaker negative correlation respectively.

Elementary my dear. It is due to the fact the the sub-zero varient of zero is greater than the elevated sine wave of the gray matter between the sheets.