In a multiple regression with 16k cases 2 IV (non-normally distributed) and one dependent variable that is also not normally distributed. DV see below:

![enter image description here][1]![enter image description here][2]

I've tried three ways of transforming the DV (sqrt/ln/log) to normal but the K-S statistic reports it clearly as non-normal . 

![enter image description here][3]

The best I could come up with was the ln or log transformation, which clearly shows a trend in the detrended qq plot. Any ideas how to "fine-tune" the ln transformation to remove that trend?

![enter image description here][4]


![enter image description here][5]

Now I've performed the same ln-transformation which on both the IV which were also not normally distributed. The result of the transformation is shown below: 

![enter image description here][6]
![enter image description here][7]
![enter image description here][8]
![enter image description here][9]

My approach was instead of trying harder to better transform the IV and DV, to bootstrap the regression in spss and and use the ln_RT_vol_in as the DV and ln_AT_vol_in and ln_FF_vol_in as the predictors. The residuals look fine at least the histogram.

The regression without bootstrapping:

    REGRESSION 
    /MISSING LISTWISE 
    /STATISTICS COEFF OUTS CI(95) R ANOVA COLLIN TOL 
    /CRITERIA=PIN(.05) POUT(.10) 
    /NOORIGIN 
    /DEPENDENT LN_RT_vol_in 
    /METHOD=ENTER LN_AT_vol_in LN_AT_bin_in_deg 
    /PARTIALPLOT ALL 
    /SCATTERPLOT=(*ZRESID ,*ZPRED) 
    /RESIDUALS DURBIN HISTOGRAM(ZRESID) NORMPROB(ZRESID).

![enter image description here][10]
![enter image description here][11]

And with bootstrapping. I have the same B values but slightly bigger confidence intervals for the bootstrapped version and a slightly less see below. 

    BOOTSTRAP 
    /SAMPLING METHOD=SIMPLE 
    /VARIABLES TARGET=LN_RT_vol_in INPUT=  LN_AT_vol_in LN_AT_bin_in_deg 
    /CRITERIA CILEVEL=95 CITYPE=PERCENTILE  NSAMPLES=1000 
    /MISSING USERMISSING=EXCLUDE.

![enter image description here][12]

What do you think of this approach?  Do you have any comments on how to improve the transformation in order to maybe get rid of the trend in the de-trended versions of the qqplots? 

Another problem is that the bootstrapping doesnt seem to fit the 1000 samples in my memory instead only 49 see below. What can I do about it apart from increasing my mem?

 


  [1]: https://i.sstatic.net/zQ524.png
  [2]: https://i.sstatic.net/tOYbl.png
  [3]: https://i.sstatic.net/TffAZ.png
  [4]: https://i.sstatic.net/UIPzZ.png
  [5]: https://i.sstatic.net/yi5YS.png
  [6]: https://i.sstatic.net/5vnvU.png
  [7]: https://i.sstatic.net/rCgw5.png
  [8]: https://i.sstatic.net/ZdSA2.png
  [9]: https://i.sstatic.net/MoraJ.png
  [10]: https://i.sstatic.net/uAu05.png
  [11]: https://i.sstatic.net/9d28b.png
  [12]: https://i.sstatic.net/mIQz1.png