Final answer:
The correlation coefficient between x and y is the same as between 2x and 3y + 2, which is y. Scaling by constants does not change the correlation, while adding or subtracting a constant has no effect.
Step-by-step explanation:
The question asks about the correlation coefficient between two pairs of variables. When you multiply one variable by a constant and add a constant to another variable (as in transforming x to 2x and y to 3y + 2), the correlation coefficient remains the same if you only multiply or divide the variables by constants. However, if you add or subtract a constant from either of the variables, such as adding 2 to 3y, it does not affect the correlation coefficient. Multiplying y by 3 scales the data but does not affect the direction or strength of the linear relationship; thus, the correlation coefficient remains y. The correct answer is (a) y. This demonstrates how correlation coefficients are robust to changes in scale and location of the variables involved.