-The estimated dimenionality is 4 as each arm of the robot has two degrees of freedom i.e. 2 angles(to exactly define the configuration).
-The sharp drop in residual variance is upto 4 dimensions as expected. The K(neighbourhood function) affects the graphs to a very high extent. After 4th dimension the residual variance starts changing again as we can depict the picture in just 4 dimensions.
-We have taken the value of K to be 6 in this part. We have used tangent distance as the metric as we can see that euclidean distance won't be able to capture the distance along the manifold.

-The euclidean distance is not appropriate because we are not able to judge the dimensionality from this graph as given in the results.
-We also have taken the graph for the value of K to be 2 in which we saw the irregularity as rise in residual variance as we increase the dimenssion from 1 only. We get the minima on dimension 1 only.