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My binary logistic regression analysis (method=ENTER) model has all beta values are statistically non-significant.

Should I include these predictors in the final binary logistic regression equation?

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This is a very broad question about variable selection. It would be helpful if you asked a more specific question. Or, you can see one of the many other questions on this site concerning the topic of model selection - stats.stackexchange.com/questions/tagged/… – Macro Jul 16 '12 at 15:43
@Macro You are correct that the question can be interpreted broadly and therefore can be improved. However, Michael Chernick has argued, with some merit it seems to me, that this is a natural question with a natural interpretation. As such I would like to suggest it deserves a warmer welcome and more constructive guidance for eliciting the information needed to narrow it down. (Such as--Ann--indicating the purpose of this analysis, what diagnostic plots and tests you have considered, how much data and how many variables you have, and more.) Could you and Michael cooperate in doing this? – whuber♦ Jul 16 '12 at 19:29
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In SPSS Method=ENTER means that all variables specified are considered simultaneously, so no variable selection. See e.g. ats.ucla.edu/stat/spss/output/reg_spss.htm – Momo Jul 16 '12 at 19:29
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@Ann This question has been downvoted because it lacks critical information to elicit unchallengeable answers. Often times, negative votes are a way to indicate to the OP that the question might be improved in many ways, and they can be removed upon clarification. Some suggestions were offered to you, and I do hope you will consider them. (Also, please make sure to register your account on this site.) – chl♦ Jul 17 '12 at 8:25

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In general if a test for the regression coefficient being statistically significantly different from 0 cannot be rejected it suggests that the variable has little influence on the outcome and hence should not be included. However, it could be that the sample size is small and hence the variance of the estimate of the regression coefficient is too large to exclude the possiblity that it is zero. So the question then becomes how much bigger than 0 do I need the coefficient to be for me to want to include it in the model. Then figure out how large a sample size you need to detect a difference from 0 of at least that magnitude. If the sample size is large and all the estimates are close to 0 then exclude them and look for other predictors that might be better. But if the sample size is small and say a 95% confidence interval for a predictor is wide enough to include 0 and your significantly high slope parameter then consider increasing the sample size before you decide.

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Michael, this question is so broad (and probably a duplicate), it's hard to say whether this (or any answer) answers the question at all. I wish you'd use your high rep status to help us clean up low quality, possibly duplicate, questions like this by casting close votes(or explaining why you think the close votes are misguided) rather than just posting a response that may or may not answer the question. Since you have the expertise to tell when a question is overly broad and you are on the site so frequently, your help could really be valuable. – Macro Jul 16 '12 at 16:14
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The shortage of action like this by high rep users (there may be a grand total of 10 users I've ever seen cast a close vote in my time here) is the reason that there are many low quality answers that are never removed. The moderators aren't omniscient and seem hesitant to act unilaterally on these matters. – Macro Jul 16 '12 at 16:15
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@Macro I answered because I disagree with you. I am not sure whether or not this duplicates other past questions but i think the question is very clear and that is why i replied. The OP ran a logistic regression analysis with a group of variables that all turned out to have statistically insignificant coefficients. She simply asked whether or not to exclude them all from the model based on the significance tests. That is a simple straightforward question that does not require a complicated answer nor does it require a discussion of variable selection techniques. – Michael Chernick Jul 16 '12 at 16:33
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More importantly than the unclear aspects I just pointed out is what is the point of this endeavor? Is it to figure out what individual predictors are important? If so, some thought about collinearity would have to be given if they are all entered into the same model. Is it to figure out whether the variables as a group are important? If so, we have a simple $\chi^2$ test and we're done. The point is that two rational people could interpret this question in very different ways, which is part of the definition of the 'Not a real question' close vote reason, which is my entire point. – Macro Jul 16 '12 at 16:45
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Please see my blog post: How to ask a statistics question – Peter Flom Jul 16 '12 at 18:17
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