Simple Estimates vs Model for calculating mean and variance of population I have a univariate data set that's approximately normally distributed. I am happy to assume that the population is normally distributed, and I'd like to estimate the mean and variance of the population.
My textbook suggests (as I understand it) that since my sample size is large (1000's of data points), it is reasonable to take the sample mean and sample variance as my estimates for the population sample/variance.
However, I'm also vaguely aware that regression can be used to fit a model to data. So in the case of my problem, which is a more reasonable approach (and why?):


*

*Just use the sample mean/variance values as estimates for the population mean/variance

*Fit the data to a normal model and use the calculated mean/variance.

 A: If I understand your question, and you mean using a least squares model of the form $Y=\beta + \epsilon$ where $\epsilon\sim N(0,\sigma^2)$ these two approaches are equivalent. 
A simple R example will demonstrate this:
#generate pseudo-data
set.seed(0)
n <- 1000
x <- rnorm(n)

# approach 1: calculation    
sum(x)/n #mean
mse <- sum((x-mean(x))^2)/n #mse
se <- sqrt(mse/n) #std error

# approach 2: model
model <- lm(x~1)
model$coefficients[1] #mean
sqrt(sum(model$residuals^2)/n)/sqrt(n) #standard error

A: I was about to make the same point as David, except illustrating using Stata rather than R:


. summarize length

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
      length |        74    187.9324    22.26634        142        233

. regress length

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  0,    73) =    0.00
       Model |           0     0           .           Prob > F      =       .
    Residual |  36192.6622    73  495.789893           R-squared     =  0.0000
-------------+------------------------------           Adj R-squared =  0.0000
       Total |  36192.6622    73  495.789893           Root MSE      =  22.266

------------------------------------------------------------------------------
      length |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   187.9324   2.588409    72.61   0.000     182.7737    193.0911
------------------------------------------------------------------------------

I've added the bolding to highlight that the mean and standard deviation are the same as the estimate of the constant and root mean square error from a linear regression with no covariates.
