- #1

- 152

- 0

Code:

```
x v1 v2 v3
1 112 14.4 52
2 120 15 53
3 128 15.5 54
4 136 16.2 55
5 144 16.9 56
6 152 17.6 57
7 160 18.5 58
8 168 19.4 59
9 176 20.4 60
10 184 21.5 61
```

Here is what I know about the data:

It is rounded down / floored to the nearest significant digit (i.e. 1 for v1 and v3, 0.1 for v2).

Columns v1 and v3 look linear (e.g. first order polynomial).

Column v2 looks higher order(probably second, but not sure).

I think (but am not sure) that the input parameters are always 1 order of magnitude less than the results.

Now, for v1 and v3, this makes things fairly straightforward.

Our function is

y = ax + b

a = (v

_{max}- v

_{min}) / 9

b = v

_{min}- a

Because the values are floor, a could potentially vary. The biggest possible difference will be within 1 of our values, so we have

a = (v

_{max}- v

_{min}) / 9 ±(1/9)

2 things give me trouble:

1. Column v2

2. A good way for making the function fit the data exactly without having to brute force it, i.e. mess around until I find a value for

**a**and

**b**which fit exactly.

Notes:

- This isn't a homework question.
- I don't have a strong mathematical background (I know the basics of calculus, but not enough for practical use). That said, not averse to trying to tackle complex subjects.