What is the relationship between the slope of the least squares regression line and the correlation coefficient?
1 Answer
Actually there isn't much relation between the two, except for the direction of the slope
Let's do a few examples:
If you correlate Hours of couch-surfing with Weight you may find a regression line that slopes up from left to right. The correlation coëfficient can still be anywhere between 0 and 1, meaning couch surfing is less or more related to weight. This would be called positive correlation.
If you do the same with Hours working out, you may find a line that slopes down. Again correlation coefficients can go anywhere, but it is called negative correlation (=the higher the one, the lower the other).
There are rules for what correlation coefficients may be considered significant, depending on sample size and desired degree of significance.
Warning: NEVER draw conclusions about cause and effect!
In some town they had yearly records about the number of births and the number of stork nests kept for over 60 years.
Guess what?
0.9 correlation, which is extremely significant by any measure!
