The method which is the most appropriate method to fit a unique curve from a given data is sum of square

The method you're referring to is known as the "Least Squares Method" or "Method of Least Squares". This is a standard approach in regression analysis to approximate the solution of overdetermined systems by minimizing the sum of the squares of the residuals made in the results of every single equation.

Here's a step-by-step guide on how it works:

1. Define the equation of the curve: The first step is to define the equation of the curve you want to fit to your data. This could be a straight line (y = ax + b), a quadratic equation (y = ax^2 + bx + c), or any other function that best represents your data.

2. Calculate the residuals: The residual is the difference between the observed value and the value predicted by your curve. For each data point, you calculate the residual by subtracting the predicted value from the observed value.

3. Square the residuals: To ensure that all residuals are positive and to give more weight to larger differences, you square each of the residuals.

4. Sum the squared residuals: You then add up all the squared residuals. This gives you a single number that represents the total error of your curve fit.

5. Minimize the sum of the squared residuals: The goal is to find the curve that gives the smallest possible sum of squared residuals. This is done by adjusting the parameters of your curve (the coefficients a, b, c, etc.) until you find the values that give the smallest sum.

This method is widely used because it's relatively simple and it often gives good results. However, it's not always the best method for every situation. It assumes that all errors are equally important, which might not be the case in some datasets.