Improving multiple regression models log transformation and leverage points

[Nisha Arora]

Respected Neeraj Sir & group members,

Please bear with me, it's going to be little lengthy.

For 1 response and 6-7 predictors, I am playing around different models to improve my prediction. I managed to arrive at a model with around 56% adjusted r-squared.

I tried to look at the issues and found that there were three leverage points in the data (and thankfully no outliers), that were effecting my prediction accuracy badly.

When I removed those observations one by one, my adjusted r-squared increased to around 62 %.

Again in order to get even better model, looking carefully at the plots, I tried log transformation to one of my predictor and the results changed dramatically (adjusted r-squared 71%)

Feeling good about it but the output says "(42 observations deleted due to missingness)".

Probably R (I love R for regression modelling due to it's flexibility) removes observations with nearly zero values of that variable as log is not defined at zero.

Again to overcome this issue, I've applied log(x+x/2) or log(x+c); c being a small positive number. This further improved model accuracy and reduce the number of missing observations [but still there are some missing observations]

Now my concerns are:

• Should I report this regression model using log transformation (with around 75% adj R2 but ~20 missing obs) or the previous model without log transformation (with 62% R2, no missing obs)
• Do you suggest me to look for another transformation like beta, gamma or possion for that predictor
• It is ok to remove three obs with high leverage point, which effects the model badly
  

At last, I find the way to report regression redults as per APA style here, hope it will help other too: http://www.adart.myzen.co.uk/reporting-multiple-regressions-in-apa-format-part-two/

Thanks for being patient, please provide your valuable insights.

Thanks,

Nisha Arora 

 

[Neeraj Kaushik]

Dear Nisha

Are you just experimenting on Regression / Transformations etc or there is any requirements of such things in ur model?
Best wishes

Neeraj

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[Nisha Arora]

Dear sir,

I am trying to improve my regression model currently for a paper in which one of my objective is to build a model predicting academic grades on the basis of some variable.

Besides, I am learning Maching Learning using R/Python from last few months.

Thanks & Regards,

Nisha Arora 

[Neeraj Kaushik]

Dear Nisha

There is a difference between Data Analysis and Data Mining.

Data Analysis always works on fixed objectives and on the basis of No. of variables and the measurement of these variables, we decide for the tool/technique to be applied.

On the other hand, Data Mining is exploratory with no particular objective in mind.

What you are doing here seems like Data Mining.

Best wishes

Neeraj

[Nisha Arora]

Dear Sir, 

Thank you for your response. I agree that data analysis and data mining are different.

And my recent attraction for machine learning made me play with the model to further improve it.

This is my first paper that includes data analysis as my area of research was operations research modeling. 

That's why I am not sure where can we stop improving the model for the purpose of research paper's analysis part. I understand that we don't need to use cross validation techniques etc for this purpose. Researchers generally don't use R but it's just awesome.

Researchers generally prefer step wise method but it is criticized well by statisticians, so I am not directly using it.
Sorry if it is going out of the track.

[Neeraj Kaushik]

Actually its gud to know that you have learnt R.

If possible, plz plan to take some introductory classes for beginners of R.

As regard your work I shall suggest to work with Regression only and not the other things (until & unless you get some theory base for justifying why you are doing other things)

Best wishes

Neeraj

[Nisha Arora]

Thank you sir.

I would love to take class/ workshop for R. Please let me know, if there is an opportunity.

Regards,

Nisha Arora