Question

Prove that coefficient of correlation always lies between -1 to +1

Answer 1

Coefficient of correlation is the degree of relationship between two variables. Positive correlation:- By increasing a variable, if there's increase in other variable, then these two variables are positively correlated. Negative correlation:- By increasing a variable if there is decrease in other variable, then these two variables are negatively correlated. No Correlation:- If either by increasing or by decreasing a variable, if there is no change in other variable, then there is no correlation between these two variables. The maximum positive relationship between two variables can be +1 meaning 100% positive correlation. The maximum negative relationship between two variables can only be -1 meaning 100% negative correlation. Third probability may be no relationship between two variables. In this case the coefficient of correlation can only be zero (0) As there can either be perfect correlation +1 or -1 or be no correlation,the coefficient will be zero (0) Correlation between any two variables can't be more than +1 or less than -1 so the coefficient of correlation always lies between -1 to +1.