The Pearson correlation coefficient between two variables, x and y, based on a random sample, is found to be -0.6.Question 15Which one of the following is always correct?For each increase in x of 10 units, y will reduce by 6 unitsFor each increase in y of 10 units, x will decrease by 6 unitsThere must be some causal factor between x and yIf 10 units were added to each y value the correlation coefficient would not change

The correct statement is: "If 10 units were added to each y value the correlation coefficient would not change".

The Pearson correlation coefficient measures the linear relationship between two datasets. The sign of the coefficient indicates the direction of the relationship. If it's negative, as in this case, it means that as one variable increases, the other decreases. However, it does not specify by how much one variable will change if the other one increases by a certain amount.

The correlation coefficient is also not a measure of causality, so we cannot infer that there is a causal factor between x and y just based on the correlation coefficient.

Finally, adding a constant to each y value (or each x value) does not change the correlation coefficient. This is because the correlation coefficient only measures the strength and direction of the linear relationship, and adding a constant does not change this relationship.