What will be the value of the correlation coefficients for each of the two cases?0.5 and 0.50.5 and 11 and 0.51 and 1

The correlation coefficient, often denoted by r, is a measure of the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative linear relationship, 1 indicating a perfect positive linear relationship, and 0 indicating no linear relationship.

1. For the case of 0.5 and 0.5, the correlation coefficient is 1. This is because the two variables increase at the same rate, indicating a perfect positive linear relationship.

2. For the case of 0.5 and 1, the correlation coefficient is also 1. This is because as one variable increases, the other also increases, indicating a perfect positive linear relationship.

3. For the case of 1 and 0.5, the correlation coefficient is -1. This is because as one variable increases, the other decreases, indicating a perfect negative linear relationship.

4. For the case of 1 and 1, the correlation coefficient is 1. This is because the two variables increase at the same rate, indicating a perfect positive linear relationship.