Data Fitting

By Muhammad Al-Salamah

Suppose you want to find the least-squares regression of the form

to n observations. Here, β's are constants and the regression coefficients which need to be calculated. The regression function can be determined by solving the unconstrained problem:

where the pairs (x_i, y_i) are the observations and β₀, β₁, β₂, and β₃ are the variables.

Data fitting of this type is commonly called nonlinear regression; and as in all types of regression, the least squares method is used as it gives a consistent solution.