Computing the Standard Error of the Estimate from the ANOVA table My question is quite straightforward, but I did not find a clear answer anywhere.
I'm computing the Standard Error of the Estimate (SEE) by doing the square root of the Residuals Mean Square output of the anova table:
anovatable<-anova(lm(carb~hp,data=mtcars))

anovatable

Analysis of Variance Table

Response: carb

          Df Sum Sq Mean Sq F value    Pr(>F)    
hp         1 45.469  45.469  38.527 7.828e-07 ***
Residuals 30 35.406   1.180                      

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

SEE<-sqrt(anovatable$`Mean Sq`[2])
SEE
[1] 1.086363    

Is it the correct way of doing it?
Is there any already implemented way in R to obtain the SEE? If so, It will be better than accessing the Mean Sq term for Residuals, since its position depends upon the number of predictors.
 A: The standard error of the estimate (SEE) is the following where $SSE$ is the sum of squares of the ordinary residuals (this sum of squares is also called the deviance) and $n$ is the number of observations and $k$ is the number of coefficients in the model.  (The intercept counts as a coefficient so $k=2$ in the case of the example shown in the question.)
$ \sqrt{SSE / (n - k)} $
In R, it can also be calculated from a model object using the sigma function so any of these work (assuming no NA's):
fm <- lm(carb ~ hp, data = mtcars)

sigma(fm)
## [1] 1.086363

sqrt(sum(resid(fm)^2) / (nrow(mtcars) - 2))
## [1] 1.086363

sqrt(deviance(fm) / (nobs(fm) - length(coef(fm))))
## [1] 1.086363

summary(fm)$sigma
## [1] 1.086363

sqrt(anova(fm)["Residuals", "Mean Sq"])
## [1] 1.086363

If what you meant was the standard errors of the coefficient estimates then there would be one for each coefficient and those standard errors would be any of the following where the last one makes use of an estimate of $var(\hat{\beta})$ being $\hat{\sigma}^2 (X'X)^{-1}$
sqrt(diag(vcov(fm)))
## (Intercept)          hp 
## 0.459500176 0.002845806 

coef(summary(fm))[, "Std. Error"]
## (Intercept)          hp 
## 0.459500176 0.002845806 

sigma(fm) * sqrt(diag(solve(crossprod(model.matrix(fm)))))
## (Intercept)          hp 
## 0.459500176 0.002845806 

A: The residual error ist something very different that the standard error of the estimate of a predictor.
The residual standard deviation tells you how precisely you can estimate y if you know all the predictors. 
On the other hand, the standard error of the estimate for an predictor tells you how precisely your estimate for the coefficient is. 
An important distinction is that given enough data you can make the standard errors of estimates arbitarily small, but you will never be able to decrease the residual standard error below a specific amount. 
For example, if you have enough data for your country you will be able to estimate the influence of Gender on Body Height (standard error of gender coefficient almost zero) very exactly, but you will always a residual error of about 7-8 cm. 
In R you get the standard error of the estimator coefficients by using summary(model). 
A: What you've computed is the standard deviation of the residuals, which is not what you want. Also note that in your model, hp is a continuous covariate, so this is not really ideal for an ANOVA model but more of a regression model (what you've computed is the F test for the regression).  To calculate the standard error of the estimate, compute as follows
$$ se = \sqrt{
        \frac{MS_{error}}{N-2}
         } $$
However, I think it would be more meaningful to run this model as a regression model. As such, you would get a standard error for both the intercept and the slope.
