How to estimate formula by a table

Question

Given some table, where $y=f(x)$, and I believe $f(x)=a*x^3+b*x^2+c*x+d$

But the trick is that

• values in table are rounded (I dont know is it floor, ceiling or just round to nearest)
• not every value is present

What is best way to go, to estimate that formula (I guess its to minimize error between table value and formula results) and determine rounding scheme?

Table Link on google sheets and its preview:

Answer 1

You can do a linear least squares fit. Excel will do it for you and give you the coefficients. You can choose the degree of the polynomial. It will give you $a,b,c,d$. Any numerical analysis text will provide a writeup. The rounding is just like measurement noise.