Thread: Correlation and the SD line

This is a point of confusion for me...

When r = 1 or -1 for a set of bivariate data, does that mean that all the points must fall on the standard deviation line (which has a slope of + or -SDy/SDx and passes through the point of averages)? And conversely, when all points fall on the SD line does that mean that r is 1 or -1?

I'm just a little confused on how the SD line relates to correlation. Thanks!

Originally Posted by SwingingMonkey

This is a point of confusion for me...

When r = 1 or -1 for a set of bivariate data, does that mean that all the points must fall on the standard deviation line (which has a slope of + or -SDy/SDx and passes through the point of averages)? And conversely, when all points fall on the SD line does that mean that r is 1 or -1?

I'm just a little confused on how the SD line relates to correlation. Thanks!

There's no such thing as a standard deviation line. If you mean the regression line (which is likely a least squares line), then yes, a correlation coefficient of -1 or 1 means all points lie on the line, and vice versa.

Thanks! So when all points are perfectly correlated and we convert all x-values and y-values into standard units, then will all the x-values and y-values equal each other (ie (-1,-1) (-0.5,0.5) (0,0) (1,1) etc.?

What do you mean by standard units? To lie on a line, the y values don't need to equal the corresponding x values...

Conversion to standard units: (x-value - x-average)/SDx

So standard units is the number of standard deviations a particular value is above and below the average. To reword my question: if all points are perfectly correlated, then if one of the x-values is one SDx above the x-average, then its corresponding y-value is also one SDy above the y-average (and so on for every point). Is this true?

Sorry, my book must use different terminology