Paste two columns and get Pearson’s r, r squared, and the least squares line. Says what r cannot tell you: a perfect curve scores near zero.
What counts as a strong correlation?
There is no statutory answer, and anyone who gives you one is quoting a convention. This page uses the common bands - below 0.2 nothing worth reading, to 0.4 weak, to 0.7 moderate, above that strong - and they are conventions rather than facts about your data. What matters far more is the size of your sample and what the scatter looks like: r = 0.8 on four points is much weaker evidence than r = 0.4 on four hundred.
My r is almost zero. Does that mean the columns are unrelated?
No. It means they are not related in a STRAIGHT LINE. r measures linear association and nothing else, so a perfect parabola scores about zero: as x goes from -3 to 3 and y follows x squared, every point sits exactly on a curve and r cannot see it. Plot the two columns before concluding there is nothing there. A near-zero r rules out a line, not a relationship.
Does a high r mean one column causes the other?
No, and this is the mistake the figure is most often used to make. Two things can move together because one drives the other, because a third thing drives both, or because the sample happens to line up. Nothing in the arithmetic can tell those apart, and no amount of extra data will - separating them takes an experiment or an argument about the world, not a calculator.
Why does swapping the columns change the slope but not r?
Because least squares minimises the vertical distance from each point to the line, and vertical means "in the y direction". Swap which column is y and you are minimising a different set of distances, so you get a different line. r has no such asymmetry: it is symmetric in x and y by construction, so it comes back identical. If the two slopes matter to you, the question you are asking is probably which column you would be predicting from which.
What does r squared actually mean?
It is the share of the variation in y that the line accounts for. r squared of 0.9 means the line accounts for about 90% of how much y moves around its own mean, and the remaining 10% is everything the line does not capture. It is not the share of points near the line, and it is not a probability that the relationship is real.