R help - Feb 2018 - questions about performing Robust multiple regression using bootstrap

Dear Faiz,

Bootstrapping R^2 using Boot() is straightforward: Simply write a function that
returns R^2, possibly in a vector with the regression coefficients, and use it
as the f argument to Boot(). That will get you, e.g., bootstrapped confidence
intervals for R^2. (Why you want that is another question.) See the example in
?Boot that shows how to bootstrap the estimated error variance (without the
regression coefficients).

On the other hand, bootstrap hypothesis tests aren't entirely
straightforward (and you might ask yourself why you need them when you have
bootstrap confidence intervals). If memory serves, there's a discussion in
the Davison  and Hinkley reference in ?Boot (I don't have a copy of the book
at my current location, so I can't check). There's also a brief
discussion in Sec. 21.4 of my Applied Regression Analysis and Generalized Linear
Models, 3rd ed.

I hope this helps,
 John

-----------------------------
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
Web: socialsciences.mcmaster.ca/jfox/

> -----Original Message-----
> From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of faiz
rasool
> Sent: Monday, February 26, 2018 6:30 AM
> To: R-help at r-project.org
> Subject: [R] questions about performing Robust multiple regression using
> bootstrap
> 
> Dear list,
> 
> I am slightly confused about how I  can do the following in R.
> 
> I want to  perform   robust multiple regression. I?ve used the Boot
> function in CAR package to find confidence intervals and standard errors.
> Inadition to these, I want to find the  robust estimates  for the F test
and  r-
> square. Finally, I  would like to know the significance levels of bootstrap
results.
> 
> Below I  explain my question  using commented R code.
> 
> [1] reg=lm(a~b+c+d+e) # perform multiple regression.
> [2] library(car) #load the car package.
> [3] bootstrap=Boot(reg) #perform bootstrap using the Boot function in car
> package.
> [4] summary(bootstrap) #show the results of bootstrap.
> [5]now  I would like to type a code that can give me robust estimates  of
R-
> square, F tests, and  significance  levels for coefficients and f.
> 
> 
> Thanks for any help.
> 
> Regards,
> Faiz.
> 
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