Your company is developing a medical device that will define a new market. You have been tasked with generating a Bass diffusion model that could be used to give your company some insight into the possible growth patterns of this market. You get started by finding an analogous device $($that also defined a new market$)$ and capture yearly sales data for this device, as shown in the table below:

$\backslash$table$[[$Year$,$Sales per year$],[1,2711],[2,3556],[3,3893],[4,4400],[5,6600],[6,6925],[7,5680],[8,6792],[9,6693],[10,4495],[11,6613],[12,7069],[13,7906]]$

a$)$ Using the sales per year data provided, and regression techniques, estimate the initial probability of adoption, diffusion rate, and market size. Hint: The general form of the model that you will want to use is shown below, where $Y[t-1]$ reflects the cumulative sales to the given time period.

$s(t)=p(0)**m+(q-p(0))Y[t-1]-(\frac{q}{m})(Y[t-1]{)}^2$

b$)$ Create plots for the sales per year as a function of years, and the cumulative sales