Beta Coefficient

[Marco van de Ven]

Dear list,

I have rather simple question regarding the Beta coefficients in my linear regression analysis, and I hope anyone of you is willing to reply. For as far as I understand it, Beta coefficients reflect the percentage of explained variation of the dependent variable by the predictor, but during one of my recent analyses, the Beta coefficients of all variables in model 3 proposed by the stepwise linear regression procedure, I encountered a case where the total of Beta coefficients within a model is more than 1, hence explains more than 100%. Obviously this is nonsense, and therefore my understanding of the Beta coefficients is apparently incorrect. Could anyone explain how I should interpret this?

Let me describe the model: It contains three predictors. Predictor one has Beta = .666, predictor two has Beta = .323, and finally predictor three = .031. How should I interpret these values in term of the expanatoriness of this model?

Thanks in advance,

Marco


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[Hector Maletta]

Beta coefficients do not reflect what you say. Beta coefficients reflect the
expected increase in the dependent variable when the independent variable
increases by one unit. Raw betas (otherwise known as b coefficients) tell
this for the raw variables, and standardized betas (also known as beta
coefficients in the proper sense) tell this for the standardized or z-score
variables = raw variable minus mean divided standard deviation.
The story about explained variance refers to the squared correlation
coefficient, R square, which equals the proportion of total variance in the
dependent variable explained by the regression model.
At each step of your stepwise regression you will find the corresponding R
square and adjusted R square. Use the adjusted one for more conservative
assessment of the quality of your model.

Hector

-----Mensaje original-----
De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Marco
van de Ven
Enviado el: Saturday, August 05, 2006 5:38 AM
Para: [hidden email]
Asunto: Beta Coefficient

Dear list,

I have rather simple question regarding the Beta coefficients in my linear
regression analysis, and I hope anyone of you is willing to reply. For as
far as I understand it, Beta coefficients reflect the percentage of
explained variation of the dependent variable by the predictor, but during
one of my recent analyses, the Beta coefficients of all variables in model 3
proposed by the stepwise linear regression procedure, I encountered a case
where the total of Beta coefficients within a model is more than 1, hence
explains more than 100%. Obviously this is nonsense, and therefore my
understanding of the Beta coefficients is apparently incorrect. Could anyone
explain how I should interpret this?

Let me describe the model: It contains three predictors. Predictor one has
Beta = .666, predictor two has Beta = .323, and finally predictor three =
.031. How should I interpret these values in term of the expanatoriness of
this model?

Thanks in advance,

Marco


---------------------------------
 Try the all-new Yahoo! Mail . "The New Version is radically easier to use"
- The Wall Street Journal