Correlation with Same Standard Deviation

One easy way to ensure the standard deviation for X and Y are the same is to use the same values! Here, you can adjust the values by dragging the blue circles along the x-axis, which will adjust the corresponding red circle on the y-axis. Drag the green points up or down to select which y-value they should be connected with. When each y-value has a point on it, the best-fitting line will appear and you can examine the correlation. The "Mixed Products" represent the numerator for the formula for r: Keeping the x and y values constant, and simply changing the order they are paired with each other, will only effect the numerator of this equation. Therefore, the closer to zero you can get the "Mixed Products", the worse your correlation will be.
What is the smallest correlation you can find? What algorithm can you follow to create the maximum correlation? How about the minimum correlation?