R help - Sep 2024 - Calculation of VCV matrix of estimated coefficient

Hi,

I am trying to replicate the R's result for VCV matrix of estimated
coefficients from linear model as below

data(mtcars)
model <- lm(mpg~disp+hp, data=mtcars)
model_summ <-summary(model)
MSE = mean(model_summ$residuals^2)
vcov(model)

Now I want to calculate the same thing manually,

library(dplyr)
X = as.matrix(mtcars[, c('disp', 'hp')] %>% mutate(Intercept
= 1));
solve(t(X) %*% X) * MSE

Unfortunately they do not match.

Could you please help where I made mistake, if any.

Thanks

The number you need for MSE is

sum(residuals(model)^2)/df.residual(model)

On Wed, Sep 4, 2024 at 3:34?PM Daniel Lobo <danielobo9976 at gmail.com>
wrote:
>
> Hi,
>
> I am trying to replicate the R's result for VCV matrix of estimated
> coefficients from linear model as below
>
> data(mtcars)
> model <- lm(mpg~disp+hp, data=mtcars)
> model_summ <-summary(model)
> MSE = mean(model_summ$residuals^2)
> vcov(model)
>
> Now I want to calculate the same thing manually,
>
> library(dplyr)
> X = as.matrix(mtcars[, c('disp', 'hp')] %>%
mutate(Intercept = 1));
> solve(t(X) %*% X) * MSE
>
> Unfortunately they do not match.
>
> Could you please help where I made mistake, if any.
>
> Thanks
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
https://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

sigma(model)^2 will give the correct MSE.  Also note that your model
matrix has intercept at
the end whereas vcov will have it at the beginning so you will need to
permute the rows
and columns to get them to be the same/

On Wed, Sep 4, 2024 at 3:34?PM Daniel Lobo <danielobo9976 at gmail.com>
wrote:
>
> Hi,
>
> I am trying to replicate the R's result for VCV matrix of estimated
> coefficients from linear model as below
>
> data(mtcars)
> model <- lm(mpg~disp+hp, data=mtcars)
> model_summ <-summary(model)
> MSE = mean(model_summ$residuals^2)
> vcov(model)
>
> Now I want to calculate the same thing manually,
>
> library(dplyr)
> X = as.matrix(mtcars[, c('disp', 'hp')] %>%
mutate(Intercept = 1));
> solve(t(X) %*% X) * MSE
>
> Unfortunately they do not match.
>
> Could you please help where I made mistake, if any.
>
> Thanks
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
https://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.


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