This question considers the role of sensitivity analysis approaches for supervised learning models.

(a) Explain the role of sensitivity analysis in terms of understanding the properties of a model. In particular, address the issue of how variation in model inputs can be assessed, and why this is important.

(b) Explain how sensitivity analysis can be performed for a linear regression model and highlight the assumptions used to hold certain variables constant during the analysis. Give one example where these assumptions may be invalid.

(c) In relation to the SOM-MLR model described in lectures, describe how the prototype vectors created for the SOM can be used to support sensitivity analysis for the local linear models associated with each prototype. In addition, explain why this approach overcomes some of the issues you have highlighted in part (b).