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I need to create a Multiple Linear regression model on those data explaining max03 T9 T12 T15 Ne9 Ne12 Ne15 Vx9 Vx12 Vx15 maxO3v

!My data 1

My first intuition was to make a backward selection :

attach(ozone)
res <- lm(maxO3~T9+T12+T15+Ne9+Ne12+Ne15+Vx9+Vx12+Vx15+maxO3v)
shapiro.test(res$residuals)

data: res$residuals

W = 0.9682, p-value = 0.008945

But the first full model return non-normal residuals.

Is it okay to continue doing a backward selection (AIC criterion)?

I don't think it [non-normal residuals] has an impact on that sort of selection, but I can't find a definite answer to that question.

If I keep doing the backward selection process

[...]
res <- lm(maxO3~T12+Ne9+Vx15+maxO3v)
drop1(res)

summary(res)
shapiro.test(res$residuals)

Shapiro-Wilk normality test

data: res$residuals W = 0.9622, p-value = 0.002946

My residuals aren't normal at the end ...

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Normality is relevant only when you do inference. Using AIC as a criteria does not require normality. Saying that I think it is better you transform the dependent variable using e.g. BoxCox transformations to get normality before proceeding with any kind of variable selection methods

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    $\begingroup$ Information criteria are not sensitive to distributional assumptions, but linear regression is... $\endgroup$
    – katya
    Nov 11 '14 at 17:08
  • $\begingroup$ Thanks for this answer, but does that mean my final regression linear model worth nothing ? If so, what can I do ? $\endgroup$
    – Boo
    Nov 11 '14 at 17:10
  • $\begingroup$ OK i just plot my residuals and there's 4 extreme data that skew my normality. If i delete them the shapiro test shows a normal distribution >> Can i do that ? or should I transform the dependent variable beforehand ? $\endgroup$
    – Boo
    Nov 11 '14 at 17:37
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Be careful of using only the Shapiro test for determining if the error follow a normal distribution. I led to bad results. Here is a full explanation of this point.

When I see errors, I always plot an histogram and perform a Q-Q plot. Basically Q-Q plot shows how a distribution would be against what you have, if the theoretical dist is far away from what you have, it don't follow the distribution you are testing.

You can use Q-Q plot for testing several distributions, one of them could be the "normal"

Q-Q plot example, when your data is very likely of been the same distribution of your test

More points are around the line, more likely is your data normal (in this case)

Here is the R code for plotting this curve:

qqplot(res$residuals) # Following your example

Produces a plot like this one:

qqplot example

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