Importance of estimating $\sigma^2$ in linear Statistical model Statistical model for Complete Randomized design
$y_{ij} = \mu + \tau_i + \epsilon_{ij}$
where, $i$ denotes treatment and $j$ denotes observation.
$i=1,2,...,k\quad and \quad j=1,2,..., n_i$
$y_{ij}$ be a random variable that represents the response obtained on the $jth$
observation of the  $ith$ treatment.
$\mu$ is the overall mean of the response $y_{ij}$
$\tau_i$ is the effect on the response of $ith$ treatment.
$\mu_i = \mu + \tau_i$
here $\mu_i$ denotes the true response  of the $ith$ treatment.
and $\epsilon_{ij}$ is the random error term represent the sources of nuisance variation that is, variation due to factors other than treatments.
the assumption is $\epsilon_{ij}\sim^{iid} N(0,\sigma^2)$
By Least Square Estimation Procedure we estimate $\mu\quad and\quad\tau_i$.


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*Why is it also important to estimate $\sigma^2$?
 If we do not estimate it , what will be the effect? 


Any help including reference will be appreciated.

Without estimating the error variance you cannot estimate the variability in your parameters and hence cannot conduct hypothesis tests.
