Consider the linear regression model, $$ y_i=f_i(boldsymbol{x}|boldsymbol{beta})+varepsilon_i, $$ where $y_i$ is the response or the dependent variable at the $i$th case, $i=1,cdots, N$ and the predictor or the independent variable is the $boldsymbol{x}$ term defined in the mean function $f_i(boldsymbol{x}|boldsymbol{beta})$. For simplicity, consider the following simple linear regression (SLR) model, $$ y_i=beta_0+beta_1x_i+varepsilon_i. $$ To obtain the (best) estimate...