Correlation and regression coefficient

Question

Hi,

Does correlation coefficient decide regression coefficient?

For example, if I'm trying to figure out the relationship between hours exercising and GPA between male and female students. Suppose I know from the Pearsonian correlation that the correlation for male students is 0.4 and for female it is 0.7. Does that always make the b coefficient of my regression line different? Why or why not?

 

Thank you so much!

Answer 1

Hi Keisha,

        The correlation coefficient is a measure of how much of the deviation is explained by the model. So the .7 would generally appear as a "tighter" fit of the data around a plot of the regression line than the R² of .4. The b coefficient of each line could be totally different or they could be the same. b is an estimate of how much GPA increases or decreases for each exercising hour increase.

 

Hope this helps.

 

Jim