I have a set of objects of different sizes (measured in square metres). I know the price of some of them. I want to use the known prices to find the missing prices.
Here is the data I have:
\begin{array}{c c} 0.13 m^2 & 7500\\ 0.13 m^2 & 7500\\ 0.15 m^2 & ?\\ 0.20 m^2 & ?\\ 0.20 m^2 & ?\\ 0.40 m^2 & ?\\ 0.65 m^2 & ?\\ 1.03 m^2 & ?\\ 1.18 m^2 & 15000 \end{array}
I have tried this function:
$a=$size $b=$min price $c=$min size $d=$max size
$x= a-c$; $y = (a*100/d)*x$; $w = b*y/100$; $z= b+w$
If I understand you correctly, you have two objects with a "dimension" of $0.13$ mt (metres?) that have a price of $7500$, you have one object with a dimension of $1.18$ mt that has a price of $15000$ and you have other objects with known dimension but no known price.
You would like to find a formula for price based on dimension.
Let the dimension be $x$.
You want to find a function for the price: $p(x)$
You will need to decide on the type of function you want to to have.
Possible candidate functions include:
Linear: $p(x)=ax+b$
Exponential: $p(x)=ka^x$
Power: $p(x)=kx^a$
These have two parameters which can be estimated from the two data points you have.
Other candidates might be more complicated and would therefore need either more data or more information about the function.
For example, quadratic: $p(x)=ax^2+bx+c$
If you want a linear function, then the gradient $a = \frac {15000 - 7500}{1.18 - 0.13}=\frac {7500}{1.05} =\frac {50000}{7}$.
Substituting the known value $p(0.13)=7500$ gives:
$\frac {50000}{7} \times 0.13 + b = 7500$
$6500+7b = 52500$
$7b = 46000$
$b = \frac {46000} 7$
$p(x)=\frac {50000}{7}x + \frac {46000} 7$
$p(x)=\frac {50000x + 46000} 7$