Confidence interval for sigma in a purely fixed effect model - r

Question

Is there a standard way to estimate confidence interval for the variance parameter of a linear model with fixed-effect. E.g. given:
reg=lm(formula = 100/mpg ~ disp + hp + wt + am, data = mtcars)
how can I get the confidence interval for the variance parameter. confint only details fixed effect and lmer from lme4 does not accept model without level-2 random-effect, which is my case here.

Answer 1

Unfortunately, you have to implement it yourself.
Like so :
reg <- lm(formula = 100/mpg ~ disp + hp + wt + am, data = mtcars)
alpha <- 0.05
n <- length(resid(reg))
sigma <- summary(reg)$sigma
sigma*n/qchisq(1-alpha/2, df = n-2) ; sigma*n/qchisq(alpha/2, df = n-2)
> sigma*n/qchisq(1-alpha/2, df = n-2) ; sigma*n/qchisq(alpha/2, df = n-2)
[1] 0.4600539
[1] 1.287194
It comes from the relation :

Answer 2

I assume you are looking for the summary() function.
The code shows the following:
data(mtcars)
reg<-lm(formula = 100/mpg ~ disp + hp + wt + am, data = mtcars)
summary(reg)
# Call:
# lm(formula = 100/mpg ~ disp + hp + wt + am, data = mtcars)
#
# Residuals:
# Min 1Q Median 3Q Max
# -1.6923 -0.3901 0.0579 0.3649 1.2608
#
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 0.740648 0.738594 1.003 0.32487
# disp 0.002703 0.002715 0.996 0.32832
# hp 0.005275 0.003253 1.621 0.11657
# wt 1.001303 0.302761 3.307 0.00267 **
# am 0.155815 0.375515 0.415 0.68147
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# Residual standard error: 0.6754 on 27 degrees of freedom
# Multiple R-squared: 0.8527, Adjusted R-squared: 0.8309
# F-statistic: 39.08 on 4 and 27 DF, p-value: 7.369e-11
To select it, you can store the summary as a variable and select the coefficients.
summa<-summary(reg)
summa$coefficients
With that, one can select the sd covariate that you want and do the confidence interval with the % of interest. To learn the confidence interval, one can read how it is done here
R does it automatically using confint(object, parms, level)
In your case, confint(reg, level = 0.95)