In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns. An overdetermined system is almost always inconsistent when constructed with random coefficients. However, an overdetermined system will have solutions in some cases, for example if some equation occurs several times in the system, or if some equations are linear combinations of the others.
#1 A system of three linearly independent equations, three lines, no solutions
#2 A system of three linearly independent equations, three lines (two parallel), no solutions
#3 A system of three linearly independent equations, three lines (all parallel), no solutions
#4 A system of three equations (one equation linearly dependent on the others), three lines (two coinciding), one solution
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable in the input dataset and the output of the (linear) function of the independent variable.
Residuals to a quadratic fit for correctly and incorrectly converted data.
