After a bidirectional step wise, I have the following generalized linear model:

Y = -8.18 + 1.18 v1 - 7.32 v2

In a simple linear model (with one explanatory variable), the coefficient of my variable corresponds to the slope of my line. If the coefficient is positive, the line goes up, if it is negative, goes down. If it's positive there is a positive relation between my explanatory variable and my dependent variable and if it's negative the relation too.

In a generalized linear model it is the same? In the example I give, v2 has a negative relation with my dependent variable? if there's more of v2 less of Y?

I think is a silly question, but I don't get it, I appreciate the help understanding this.


No such thing as a silly question. The simple answer is yes, you are correct.

More nuanced answer - Y is negatively related to v2, after controlling for v1. That is, for any given level of v1 and keeping v1 constant, an increase in v2 means a decrease in Y. Note that the intepretation starts to get complex if v1 and v2 are correlated (positively or negatively).

Additional observations, not directly related to answering your question:

  1. Terminology can be confusing. "General linear model", a term used by SPSS and in some other quarters, should not be confused with "generalized linear model". The "general linear model" refers to just an multivariable regression with a Normally distributed response and a combination of categorical and continuous explanatory variables. A generalized linear model is a further generalization to allow the response to have a distribution other than Normal, so long as it is in the exponential family; and a non linear "link" to the linear predictor.

  2. You might want to read some of the wisdom on Cross-Validated and elsewhere about issues with building a model by step-wise selection of variables.


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