R help - Apr 2023 - Bias and variance tradeoff

Dear R-experts,

Here below a toy example to calculate the MSE (mean squared error).?

Starting from this equation : MSE = bias^2 + variance + irreducible error

I am trying to get the bias and the variance in addition to the MSE. How to get
them both?

Many thanks for your help.


#########################################################
#Data
y=c(23,34,54,34,23,34,43,45,56,65,45,42,32,35,37,41,54,56,53,45)
x1=c(2,4,3,5,4,6,4,3,2,1,2,3,4,3,5,6,7,6,4,3)
x2=c(11,12,13,21,14,13,15,17,18,16,21,21,23,19,11,10,19,17,16,11)
x3=c(45,46,34,24,47,48,50,40,41,39,37,34,50,56,53,51,37,48,49,53)

#Fit the model
model=lm(y~x1+x2+x3)
?
#Calculate MSE
model_summ=summary(model)
mean(model_summ$residuals^2)
###########################################################

Off topic I think. This is a statistical question, not an R programming
question.

There are certainly many internet tutorials on this  -- e.g. "bias and
variance in linear models" as a search term. You might also consider search
terms like "shrinkage estimators", "penalized regression".
"regularization", "ridge regression,"and the like if you
care to go deeper.

Cheers,
Bert

On Wed, Apr 26, 2023 at 1:32?PM varin sacha via R-help <r-help at
r-project.org>
wrote:
> Dear R-experts,
>
> Here below a toy example to calculate the MSE (mean squared error).
>
> Starting from this equation : MSE = bias^2 + variance + irreducible error
>
> I am trying to get the bias and the variance in addition to the MSE. How
> to get them both?
>
> Many thanks for your help.
>
>
> #########################################################
> #Data
> y=c(23,34,54,34,23,34,43,45,56,65,45,42,32,35,37,41,54,56,53,45)
> x1=c(2,4,3,5,4,6,4,3,2,1,2,3,4,3,5,6,7,6,4,3)
> x2=c(11,12,13,21,14,13,15,17,18,16,21,21,23,19,11,10,19,17,16,11)
> x3=c(45,46,34,24,47,48,50,40,41,39,37,34,50,56,53,51,37,48,49,53)
>
> #Fit the model
> model=lm(y~x1+x2+x3)
>
> #Calculate MSE
> model_summ=summary(model)
> mean(model_summ$residuals^2)
> ###########################################################
>
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