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We have some sales data that I feel (but may be wrong) follows a curve. I came up with a formula to closely approximate (via trial and error).

My formula: \begin{equation} y^* = \left(\frac{x}{7.2}\right)^{0.36} - 0.907 \end{equation}

The most important piece of data is the $x=1000 y=5.0000$.

Actual data and result of formula:

$\begin{array}{rrr} x & y & y^*\\ 10000& 12.5000& 12.62494741\\ 5000& 10.9905& 9.636614115\\ 4000& 9.7405& 8.822754854\\ 3000& 8.3279& 7.865511637\\ 2000& 6.7967& 6.674080351\\ 1000& 5.0000& 4.999909285\\ 500& 4.2937& 3.695454490\\ 400& 3.7937& 3.340192038\\ 300& 3.1491& 2.922340218\\ 200& 2.4116& 2.402261599\\ 100& 1.5000& 1.671459423\\ 50& 0.9750& 1.102044252\\ 40& 0.8250& 0.946966567\\ 30& 0.6525& 0.764567632\\ 20& 0.4575& 0.537545081\\ 10& 0.2250& 0.218538361 \end{array}$

Can you get closer?

My concern are the values for x values: 4000, 5000 are quite a bit off.

  • 0
    you should be using a linear regression model with a suitable transformation of variables – 2017-02-23

1 Answers 1

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This is not an answer, just an illustration of past ones for future ones.

The figure below plots your data (blue line) and three additional lines. The magenta line (b data) is your equation. The yellow line (c data) is produced by taking log of your $x$ and $y$ variables and running regression of $\log(y)$ on a constant and $\log(x)$. The green line (d data) is what @David suggests above (he just deleted the post I believe).

enter image description here

a = {{10000, 12.5}, {5000, 10.9905}, {4000, 9.7405}, {3000, 
    8.3279}, {2000, 6.7967}, {1000, 5}, {500, 4.2937}, {400, 
    3.7937}, {300, 3.1491}, {200, 2.4116}, {100, 1.5}, {50, 
    0.975}, {40, 0.825}, {30, 0.6525}, {20, 0.4575}, {10, 0.225}};
b = Table[(x/7.2)^0.36 - 0.907, {x, 10, 10000}];
c = Table[x^(0.562)*Exp[-2.3], {x, 10, 10000}];
d = Table[(-2*10^(-7)) x^2 + 0.0029*x + 1.3752, {x, 10, 10000}];
ListPlot[{a, b, c, d}, Joined -> True]