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 of $\beta_0$ and $\beta_1$, we solve for the least residual sum of squares (RSS) given by, $$ S=\sum_{i=1}^{n}\varepsilon_i^2=\sum_{i=1}^{n}(y_i-\beta_0-\beta_1x_i)^2. $$ Now suppose we want to fit the model to the following data,**Average Heights and Weights for American Women**, where*weight*is the response and*height*is the predictor. The data is available in R by default.