What are the steps to fitting equations to data?

Answer 1

• The first step is to determine the nature of the relationship: whether it is linear, quadratic, a higher polynomial, a power function, an inverse, trigonometric, whatever. A scatter plot is a simple way to do this.
• The next step is to determine whether that relationship applies across the whole of the domain or if it changes across it. The extension of a spring is linearly related to the mass hanging from it - until a point where the spring is over-stretched and the relationship (as well as the spring) breaks down. Some systems, particularly those with feedback mechanisms, can become chaotic.
• If necessary, divide up the domain into sub-domains within each of which the relationship is maintained.
• You may wish to consider transformation of the data.
• Then use regression methods to fit a least squares equations. This is an equation that minimises the squares of the differences between the observed values and those given by the equation (the fitted values).
• With a large number of variables you will need to consider removing variables that are correlated with one another. as well as those that contribute little to the regression.