State whether the following statement is True or False and also give the reason in support of your answer.
c) The correlation coefficient between \(\mathrm{x}\) and \((a-\mathrm{x})\) is \(-1\).
Solution
c) True.
The correlation coefficient between x and (a – x) is –1.
The correlation coefficient measures the strength and direction of the linear relationship between two variables. If x and (a – x) are perfectly negatively correlated, meaning that as x increases, (a – x) decreases and vice versa, then the correlation coefficient between the two variables will be equal to –1.
A correlation coefficient of –1 indicates a perfect negative linear relationship, where the variables are perfectly inversely proportional to each other. In this case, the variables x and (a – x) have a strong and perfect negative linear relationship, so the correlation coefficient between the two is –1.
Hence given statement is true.