is a measure of the correlation between the observed value and the predicted**r**

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.To index

## Sunday, March 27, 2011

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

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## 5 comments:

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

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.

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

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

I get a positive r when undertaking spearkman correlation analysis looking at correlation between two variables but I undertake a multiple regression analysis I get a negative beta for the same variable, how do I interpret this?

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