Can we back up a little? The questions seem a little odd, and I just want to make sure that I am understanding the problem.

Why are you using standardized regression coefficients? What is the context of the problem (is this biology, medicine, sociology, ecology)?

Without further information I would answer as follows:

I interpret your last question to be if the total of the regression coefficients should equal the Pearson correlation coefficient (R). The answer is No. R is an estimate of the proportion of variability in the dependent variable that is explained by the independent variables. The coefficients are numbers that convert a value of the independent variable into the expected value for the dependent variable.

The answer to the second question is no. R is bounded -1 to 1. A value outside these limits indicates an error. The standardized coefficients are the regression coefficients multiplied by the standard deviation in the independent variable divided by the standard deviation of the dependent variable. Depending on your data, this may give a value close to 1. However, there is no cause-effect relationship between this value and R, so the answer is no.

The values for individual betas are not bounded. So the standardized regression coefficient can take any value. It may be greater than or less than the untransformed beta depending on the variance structure of the independent and dependent variables.

The formulae for making the calculations can be found in many introductory statistics books.

Can we back up a little? The questions seem a little odd, and I just want to make sure that I am understanding the problem.

Why are you using standardized regression coefficients? What is the context of the problem (is this biology, medicine, sociology, ecology)?

Without further information I would answer as follows:

I interpret your last question to be if the total of the regression coefficients should equal the Pearson correlation coefficient (R). The answer is No. R is an estimate of the proportion of variability in the dependent variable that is explained by the independent variables. The coefficients are numbers that convert a value of the independent variable into the expected value for the dependent variable.

The answer to the second question is no. R is bounded -1 to 1. A value outside these limits indicates an error. The standardized coefficients are the regression coefficients multiplied by the standard deviation in the independent variable divided by the standard deviation of the dependent variable. Depending on your data, this may give a value close to 1. However, there is no cause-effect relationship between this value and R, so the answer is no.

The values for individual betas are not bounded. So the standardized regression coefficient can take any value. It may be greater than or less than the untransformed beta depending on the variance structure of the independent and dependent variables.

The formulae for making the calculations can be found in many introductory statistics books.

Hi Japnet

timothy put it nicely. standardised regression coefficient can take any value.

you may want to have a look at this article:

http://www.ssicentral.com/lisrel/techdocs/HowLargeCanaStandardizedCoefficientbe.pdf

Cheers.

saiyidi

Thanks Timothy, that was a helpful reply. 

The problem was in reference to social sciences research, and i had read some where that in case of  linear regression the value of beta is exactly equal to R. So was confused if the cumulative effect of betas' as in case of multiple regression would also lead to total value of R, which is not the case, as explained by you so well. And yes know its clear that the individual beta values can be greater than 1.

Thanks Saiyidi for the reference link

I notice this is a question dated back to a fairly long time ago, yet I still want to add a few words here just in case someone else (like me) comes across the thread :-)

Let's say the multi-regression equation is as follows:

Y = c1 + c2*X1 + c3*X2 + c4*X3

Y is the response variable, X1-X3 are predictors, c1-c4 are the coefficients.

Whether your multi-regression coefficients c1-c4 exceeds [-1 1] or just within [-1 1] depends on whether you standardize Y and X1-X3, or you just standardize X1-X3.

If say you just standardize X1-X3, then your coefficients can be any value, while if you standardize Y & X1-X3, then your coefficients can not be beyond [-1 1].

Cheers

Thanks Wong,

Although the question was posted alot earlier but a insightful reply is always awaited and welcomed.

In my future research I'll surely keep the standardizing aspect in mind.

Dear Hailong,

sorry, but I have to disagree. The standardized regression coefficients (which equal the coefficients of a regression from your standardized dependent variable on the standardized explanatory variables) are not bounded between [-1;1]. If you use google, you can quickly find the answer why...

Best regards,

Florian

Collinearity is the culprit. In it's presence, regression weights are not bounded, even given standardization.