where $$x$$ is a vector holding our model parameters, of which there are $$n_\text{var}$$. We have $$n_\text{res}$$ data points, and $$r_i(x)= y_i - \varphi(t_i;x), \quad i = 1,...,n_\text{res}$$ is the $$i^{th}$$ residual, equal to the difference between the observed and predicted values of the independent variable at time $$t_i$$, denoted $$y_i$$ and $$\varphi(t_i;x)$$ respectively. The loss function $\chi$ has desirable properties such as being bounded from below, and increasing with $$\abs{r_i\left(x\right)}$$. Summing over all data points then, the objective function will be small when the model fits the whole dataset well, which is what we want.