# How are the correlation coefficient and regression line coefficients related?

#### mathprof

##### New Member
For a given r value, say r=0.8:
for the regression line equation y=mx+b

a) given the value of the slope (m) in the regression line, can the y-intercept (b) be calculated?

b) given the value of the y-intercept (b) in the regression line, can the slope (m) be calculated?

#### Marc_Berlin1

##### New Member
for a and b: no, you would need the exact covariances

#### Dragan

##### Super Moderator
For a given r value, say r=0.8:
for the regression line equation y=mx+b

a) given the value of the slope (m) in the regression line, can the y-intercept (b) be calculated?

b) given the value of the y-intercept (b) in the regression line, can the slope (m) be calculated?
Well, mathprof, the slope (m) is equal to m = r*(sy/sx),
the y-intercept (b) is equal to b = ybar - m*xbar,
where sy, sx, xbar, and ybar are the standard deviations and means associated with y and x, respectively.

So, what do you think?