We have discussed the basis of linear regression as fitting a straight line through a plot of data. However, there may be circumstances where the relationship between the variables is non-linear (i.e.

That is the the basic form of linear regression by hand. Note that there ARE other ways to do this - more complicated ways (assuming different types of distributions for the data).

Sebastian Calonico, Matias D. Cattaneo, Rocío Titiunik, Optimal Data-Driven Regression Discontinuity Plots, Journal of the American Statistical Association, Vol. 110, No. 512 (December 2015), pp. 1753 ...