Creating a function of three variables from experimental data

Question

I have been working in a project in which I have to collect the following data over a timespan:

1. Temperature of a room
2. Humidity inside the room
3. Amount of CO2 present in the room
4. Number of persons in the room

I have already conducted the experiment and have built a datasheet having data of CO2 ($C$) , Temperature ($T$), Humidity ($H$), and number of persons ($S$). Now, from the datasheet we have to create a function $f$ such that $C=f(S,T,H)$. And I am not getting how to do it. Can I get a solution to my problem?

Answer 1

You can use linear regression for your problem. Simply you need to form a function that

$$y = a_0 + a_1 \cdot x_1 + a_2 \cdot x_2 + a_3 \cdot x_3 $$

where $a_0$, $a_1$, $a_2$ and $a_3$ are what you need to find, while $y$, $x_1$, $x_2$, $x_3$ are $C$, $S$, $T$, $H$ respectively.

You can use Matlab, R, Python to find the best values of $a_0$, $a_1$, $a_2$, and $a_3$.

Answer 2

If the model is supposed to be linear wtih respect to each of the variables $S,T,H$, it will write $$C=a_0+a_1\,S+a_2\,T+a_3\, H+a_4\,ST+a_5\,SH+a_6\,TH+a_7\,STH$$ and you just face a simple multilinear regression problem.