I'm an artist.
I'm trying to find a way to calculate the price of paintings of varying sizes.
I have tried to come up with some kind of equation to vary the price based on square cm.
The thing is, you cannot have a fixed price per cm2 for paintings, as a very small one would be too cheap, or a large one be too expensive.
For example, a painting that is 20x20 cm (400cm2) costs $15000.
That's a price of $37,5 per cm2.
If I apply that to a painting that is 175x200 cm, it would cost $1312500. wow.
In reality, a painting that size has an approx price of $125000.
So, I need some kind of equation, based on data from real world examples. I have tried to figure out how to do it, but I'm getting nowhere. My best guess is to try curve fitting a quadratic equation, but I can't figure out how to derive it.
Can you help? A smooth fit to the data is sufficient, as all data points are choosen inexactly up to this point. (i.e my gallerist and I have only made up approximate prices based on what is "reasonable" for a specific size of work).
I would like an equation where I only have to enter the dimensions of the painting (cm2) and I get the appropriate price/cm2.
Here's a few data points:
$\begin{array}{rRr} \text{Area (cm}^2\text{)} & \text{Price per area} & \text{Price} \\ \hline 400 & 37.500 & 15000 \\ 1849 & 16.225 & 30000 \\ 2107 & 14.238 & 30000 \\ 2907 & 12.040 & 35000 \\ 5600 & 8.036 & 45000 \\ 9801 & 5.101 & 50000 \\ 12000 & 4.660 & 55920 \\ 24000 & 3.958 & 95000 \\ 35000 & 3.571 & 125000 \\ 50000 & 3.000 & 150000 \\ \end{array}$