Why does the linear regression algorithm assume the input residuals (errors) to be normal distributed? I am trying to know the assumptions of linear regression (LR). I understand linear regression needs the relationship between the independent and dependent variables to be linear, but LR also assumes the input residuals to be normally distributed. Please help me understand this.
 A: Well, first thing first - Linear regression does not assume the residuals are normally distributed. Linear regression is an approach to find the best fitted linear model to the observed data. 
Now, we, the observers, look at the residuals and we can assume that these are distributed normally. Why? well, for once, if it does, it gives us a lot of power - from finding confidence intervals and doing hypothesis testing to even more application and tools that can only be performed under the assumption that the residuals are distributed from some distribution. The use of normal distribution is cause this probability distribution is very well understood, it's properties are usually easily computed, and it's geometric interpretation comes up and describe many things in the measurable world. 
A: Take a standard normal random variable.
$$z  \sim \mathcal{N}(0,1)$$
It has the property that if I add $\mu$ to $z$ then 
$$(\mu+ z) \sim\mathcal{N}(\mu,1)$$
So now, consider linear regression.  Linear regression states that the mean of the outcome conditioned on the covariates is a linear combination of the covariates.  Let $\mu(x) = \beta_0 + \sum_i x_i \beta_i$.  Then,
$$ y\vert x \sim \mathcal{N}\left(\mu(x), \sigma^2 \right) $$
Going backwards now, that means that
$$ (y\vert x - \mu(x) ) \sim \mathcal{N}(0,\sigma^2)  $$
So as you can see, as a consequence of assuming that the likelihood of our model is normal, the residuals (that is, the data minus the predicted conditional mean) is normally distributed with mean 0 and some constant variance.
