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I have a model needs to transform to log function to perform a linear model, how can I move from $\log(E(Y))= -1.146 + 0.747x$ to get $\hat y = 0.318(1.0776)^x$?

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    $\begingroup$ Could you clarify please, which three null hypotheses you mean, and what you mean by "the initial hypothesis"? When you say 'solving the problem', which problem do you mean? $\endgroup$
    – Glen_b
    Feb 22, 2013 at 23:12
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    $\begingroup$ Welcome to the site, @jimmy. Could you please provide more details about your situation, your data & your goals. Trying to reformulate your question so that it addresses Glen_b's requests would be helpful, eg. As it is, it's still hard to know how to answer it, or if GregSnow's post does (if so, please accept it). I appreciate that you read our about page, our FAQ might also be helpful, as might this blog post: how to ask a statistics question. $\endgroup$ Feb 23, 2013 at 22:19

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This really depends on what question(s) you are trying to answer with this analysis.

Some things to consider:

Does it make sense to test H01 and H02 if H03 is not true? In most cases it does not.

If you test H03 and don't have the evidence to reject H03 that does not mean that H03 is true. Studies generally have lower power to detect interactions than main effects. And if you don't know whether H03 is true or not you need to refer back to the former question.

What does the science behind your data suggest about how likely there is to be an interaction? What does the science suggest is the most interesting question to answer?

It may be more interesting to look at predictions from the model and how much the predictions change going between different conditions.

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