Figure 1: Data sample for PCA. 6. PCA. (15 points) You are given data sample X as depicted in Fig. 1. Answer the following questions. (a) (5 points) Assume you want a one dimensional representation of the data samples, what is the principle component (PC)? Draw the PC on Fig. 1 as a line. (b) (5 points) If we project four samples onto this PC, what is the value of each projection (assuming the origin's projection is zero)? (c) (5 points) What is the variance of the projected samples? What is the approximation error of using this PC