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I recently used multiple linear regression to model monthly species abundance (y) and environmental variables (x) 2005-2016.

To ensure assumptions were satisfied for multiple linear regression I had to apply a transformation (abs(y-mean(y))) to the response variable. Having completed model selection, I wanted to see how well it was able to predict y using x from 2017 so I used the predict() function. The result was returned in its transformed state which is no use to me so, I have removed the transformation and used the following script.

mod1<-lm(y~x1+x2, data=mydata)
new.df <- data.frame(x1=c(),
                     (x2=c()))
predict(mod1, new.df)

I compared the result to the actual monthly species abundance data for 2017, and the predictions were very accurate.

I have two questions,

1) Can I report the prediction when this MLR model does not satisfy assumptions?

2) As the initial model selection was based on models with a transformed data is it suitable for me to report predictions from the model without transformation?

I have seen many answers to questions that may appear similar to this that seem suggest assumptions do not need to be satisfied for making predictions, however, I have been unable to find any reference for this in published literature.

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    $\begingroup$ I had to apply a transformation (abs(x-mean(x))) to the response variable Can you clarify this point? Response variable is usually used to describe y, the dependent variable. $\endgroup$ Apr 24, 2018 at 15:13
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    $\begingroup$ By applying that transformation you guaranteed that one important assumption (at least) is not satisfied: all your responses are now associated with one another, perhaps strongly so, through the incorporation of their mean within every one of the transformed values. That is the very opposite of the independence that is assumed. Moreover, you have no way of inverting that "transformation," so of what use would it be? In what sense were you able to "remove" it? $\endgroup$
    – whuber
    Apr 24, 2018 at 15:14
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    $\begingroup$ I'm sorry that you got bad advice, but you cannot justify an improper analysis with a citation. Even if such a citation did exist, it would be wrong - plenty of incorrect things get published, after all. But the fact of their having escaped close scrutiny during peer review does not make them correct, or a valid basis for action. $\endgroup$
    – mkt
    Apr 24, 2018 at 15:22
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    $\begingroup$ Of course you can use predict: like the sorcerer's apprentice, it will perform exactly the computation you require, whether or not it makes any sense or has any justification. A thesis is supposed to be published, so you need to apply publication standards to its preparation. That would include, at the very minimum, eliminating--or at least clearly and explicitly acknowledging--any elements you believe could be incorrect or misleading. $\endgroup$
    – whuber
    Apr 24, 2018 at 15:23
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    $\begingroup$ This is not a "transformation" in the sense you probably intended because (1) it is not invertible and (2) it depends on all the data at once rather than on just a single number at a time. Although there's nothing mathematically wrong with it, in most statistical applications it likely would not give rise to a useful model. $\endgroup$
    – whuber
    Apr 24, 2018 at 16:06

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