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Hi Mario! Would .010 or .007 be the weakest correlation coefficient?I’m having trouble understanding how the zeros factor in and when that would mean that there is simply no association at all.
I know I'm 10 months too late, but I had the same question! And turns out, yes, it would be zero. Intuitively, this is because if you have a horizontal line, then y does not change with x. In other words, y is independent from x and there is no correlation. If you were to derive the formula, it would simply be y = b. No x. Regardless of how spread out the data is along the y-axis, while there is no correlation, the line will be horizontal. If you were to create a vertical line, any data point not on the line would have infinite vertical distance from the line. So a line of best fit will tend to a horizontal line instead of a vertical line. Even if every point was on the same x value, you would still have a horizontal line. After all, there is no formula for a vertical line. Well, you could say x = b, but that's independent from y (no correlation), and you've inverted the axes.