If the correlation between x and y is r = 0.35 and we double each x value, decrease each y by 0.20, and interchange the variables, what is the new correlation?

To determine the new correlation after the transformations applied to the variables (x) and (y), it's essential to understand the effects of these modifications on correlation.

The original correlation between the variables is (r = 0.35). Correlation is a measure of the strength and direction of a linear relationship between two variables, with possible values ranging from -1 to 1. Importantly, correlation is invariant under linear transformations of the form (y = ax + b) (where (a) and (b) are constants). This means that if we multiply or add constants to one variable, the correlation remains unchanged.

In the scenario given, the transformations involve:

1. Doubling each (x) value. This is a linear transformation (multiplying by 2) which does not affect the correlation.

2. Decreasing each (y) value by 0.20. This is another linear transformation (adding a negative constant), which also does not impact the correlation.

Next, we interchange (x) and (y). The correlation between two variables (x) and (y) is the same as the correlation between (y) and (x). Thus, inter