Problem # $5[20$ points$].$ Consider the method of sensors reporting data by aggregating the samples

and constructing a regression polynomial representation of the phenomenon being monitored. The

network is arranged in a tree$-$structure, with each node being a clusterhead $(CH).$ The $CH$ receives

information in the form of $,$ sensed value$)$ from sensors in a fixed region around it$,$

computes the polynomial and then sends the coefficients of the polynomial to the parent node. The

parent $CH$ then adds its own points, constructs a new polynomial and repeats the forwarding step.

This process continues till the data reaches the root node, resulting in significant savings in energy, as

only a fixed number of bits are transmitted from each $CH$ to its parent. Identify and explain two major

shortcomings of this method.