pricing grid base calculation

Question

I am useless at maths and have been trying to figure this out for ages. I am creating an website for a client which prices fabric based on square inch of material. Their supplier gave them the attached table but I cannot work out the base price per square inch to use as a multiplier. Is there a formula that can work this out?

I have been calculating the base square in price by dividing the price by square in but it changes as the size goes up? When finished the customer should be able to enter width and height and get a price?

Sorry if this seem pretty obvious but its wrecking my head

Thanks in advance

Joe

Answer 1

As said in comments, a table lookup is probably the best since you will recover the exact price (this will not be the case using regression since the model could be not perfect).

Anyway, what I would suggest is to plot the values in each row and column and try to see if the prices are linear or quadratric. Suppose that the price is quadratic in both directions. This means that the model could be $$P=(a_0+a_1 W+a_2 W^2) +(b_0+b_1 W+b_2 W^2)S +(c_0+c_1 W+c_2 W^2)S^2$$ that is to say that you face a simple multilinear regression with $8$ predictors which are $$W,S,WS,WS^2,W^2,W^2S,W^2S^2,S^2$$ This would be simple to do using matrices. For sure, afterwords, you will need to check the standard deviations to possibly exclude some factors.

Answer 2

All the values left of 60 width and up from 42 drop fit roughly $18.77+0.94({\text{width+drop}\over6}-8)$ and beyond that I'm not much help. But as everyone says, All they need to do is change it and you're no longer able to find it easily without lookup.