**Due date**: Oct. 17, 2017

- Suppose that
*A*is a matrix with singular values .- a.
- Show that if with , then .
- b.
- Let
*u,v*be any pair of orthonormal vectors in . Show that*u,v*are right singular vectors of*A*.

- Let be a full rank matrix with , let denote the skinny
SVD of , and let denote its skinny QRD. Show that

- Let

Find Householder matrices such that

satisfies and . - The file

http://www.utdallas.edu/~ammann/stat6341scripts/Sleep.data

contains measurements of body weight, brain weight, sleep time, and life span for a set of mammals.**[a]**Construct a regression model to predict`LifeSpan`based on the other variables.**Note**:`BodyWgt, BrainWgt, LifeSpan`are heavily skewed, so a*log*transformation of those variables would be appropriate. Construct appropriate diagnostic plots to show whether or not the model assumptions are reasonable.**[b]**Use backward selection with BIC to select the best model. Use this model to predict`LifeSpan`for*homo sapiens*. How does this predicted value compare to the actual life span for*homo sapiens*?**[c]**Since the two brown bats and the Echidna are very different from other mammals, remove those observations from the data and repeat a,b.

2017-11-01