1. ## Correlation coefficient

I don't understand correlation coefficient well and I have few questions related to it.

1)Can I say that correlation is based on slope concept?
2)Does the correlation coefficient show how much are data points scattered on the plane?
3)Correlation varies between -1 and 1. Does this mean that the line with a slope larger than 1 or smaller than -1 (e.g. 1000, -320) will have correlation of 1 or -1?
4)What if I have a line y=5 (slope of which is zero) or x=5 (with undefined slope)?
5)If I have data points very near to each other but they don't form any specific line, does this mean that the scatter plot will have correlation coefficient of zero?

2. ## Re: Correlation coefficient

1. No, correlation is not based on slope. The correlation coefficient r lies between -1 and 1. If r=1 then the points on the scatterplot lie in a perfect upward sloping straight line. If r is say 0.9 the points would lie roughly in an upward sloping straight line, but not perfectly. The closer r gets to 0 the more "scattered" the points are ie they'll be a bit all over the place.
If r=-1 the points will lie in a perfect downward sloping straight line
2. Yes, see comment for 1
3. No, the slope of the regression line has nothing to do with r. r is a measure of how well the regression line fits the points.
4. Won't happen with useful data.
5. No if you increase the scale on your axes ie zoom in you may or may not see the points lying along or close to a straight line.

Best thing for you to do is to google Pearson's correlation coefficient - there are some excellent explanations out there. eg https://www.spss-tutorials.com/pears...n-coefficient/