Exercise 2

Suppose that a dataset has mean $\threevec{13}{5}{7}$ and that its associated covariance matrix is $C=\begin{bmatrix} 275 & -206 & 251 \\ -206 & 320 & -206 \\ 251 & -206 & 275 \end{bmatrix}$.

1. What fraction of the variance is represented by the first two principal components?

2. If $\threevec{30}{-3}{26}$ is one of the data points, find the coordinates when the demeaned point is projected into the plane defined by the first two principal components.

3. If a projected data point has coordinates $\twovec{12}{-25}$, find an estimate for the original data point.