## Sunday, March 27, 2011

### Correlation Coefficient r and Beta (standardised regression coefficients)

• r is  a  measure  of  the  correlation  between  the  observed  value  and  the  predicted
value of the criterion variable.
• When you have only one predictor variable in your model, then beta is equivalent to
the  correlation coefficient (r) between  the  predictor  and  the  criterion  variable.
• When  you  have  more  than  one  predictor  variable,  you  cannot  compare  the
contribution  of  each  predictor  variable  by  simply  comparing  the  correlation
coefficients. The beta (B) regression coefficient is computed to allow you to make such
comparisons  and  to  assess  the  strength  of  the  relationship  between  each  predictor variable to the criterion variable.
• Beta (standardised regression coefficients)  --- The beta value is a measure of how strongly each predictor variable influences the criterion (dependent) variable. The beta is measured in units of standard deviation. For example,  a beta value of 2.5 indicates that a change of one standard deviation in the predictor  variable will result in a change of 2.5 standard deviations in the criterion variable. Thus, the higher the beta value the greater the impact of the predictor variable on the criterion variable.
• In multiple regression, to interpret the direction of the relationship between variables, look at the signs (plus or minus) of the B coefficients. If a B coefficient is positive, then the relationship of this variable with the dependent variable is positive (e.g., the greater the IQ the better the grade point average); if the B coefficient is negative then the relationship is negative (e.g., the lower the class size the better the average test scores). Of course, if the B coefficient is equal to 0 then there is no relationship between the variables.

Missy said...

Hey - Quick (and most likely simple) question regarding betas and r. I have many models with betas, and am hoping to compare these results with some models that present R-squared statistics, as well as partial-R-squared statistics. If I want to convert the R-square coefficient to an r-coefficient, I only need to take its' square root, correct?

Thanks!

--Melissa

Anonymous said...

There is a difference between
a zero order correlation and
a partial correlation.
with the zero order correlation you take zero other variables into account, with the partial correlation you take other factors into account.
If you do a partial correlation you will get a R-square for the model, in that case squaring the r will not give r2. You can test it out by trying.

Anonymous said...

How to convert a standardised beta value into r coefficient? THX

kiran kumar said...

Can any one please tell me "How to calculate Standard error (SE) if beta coefficient and 95% CI are given"