Does the non-normality matter in using regression for prediction?
Hi all,
In the Q-Q plot of the residuals after linear regression, the residuals turned out to be highly non-Gaussian. Most of the points (95%) are below a 45º straight line. And those below the straight line are all on the lower side.
The shape of the curve looks like $f(x)=x^{1/5}$ for $x$ on $[0, 1]$. (The 5% points in the middle of this curve are above the 45º straight line).
It turns out that the dependent variable $y$ has data that are highly non-Gaussian. They are all in $[0, 1]$, but mostly clustered around $1$.
So I tried various ways of transforming $y$. The latest one I've found was to do $y_{new} = y^7$.
Using this transformation, the $y_{new}$ data become much more symmetrical than before, but they still in no way look Gaussian in a histogram.
Being very disappointed, I don't have any more weapons in my bag...Instead, I began to wonder, if my end goal is just to get the $\hat{y}$, i.e. the prediction of the data on a wider data-set, does the non-normality even matter, in terms of accuracy for prediction?
Please shed some light for me. Thank you!
The $y$ data looks very similar to the data generated using the following script:
mydata=rt(10000, df=5)
mydata=mydata[mydata<0.8]
mydata=(mydata-min(mydata))/(max(mydata)-min(mydata))
hist(mydata, 100)