CAS Exam MAS-II Spring 2019, Question 41
Study guide: Exam MAS-II
You are reviewing a dataset with 100 observations in four variables: X_1, X_2, X_3, and X_4. You analyze this data using two principal components:
\begin{align*}
Z_1 &= \varphi_{11}X_1 + \varphi_{21}X_2 + \varphi_{31}X_3 + \varphi_{41}X_4 \\
Z_2 &= \varphi_{12}X_1 + \varphi_{22}X_2 + \varphi_{32}X_3 + \varphi_{42}X_4
\end{align*}You are given the following statements:
I. \sum_{i=1}^{100}\left(\sum_{j=1}^{4}\varphi_{j1}x_{ij}\right)^2 = \sum_{i=1}^{100}\left(\sum_{j=1}^{4}\varphi_{j2}x_{ij}\right)^2
II. \sum_{j=1}^{4}\varphi_{j1}\varphi_{j2} = 0
III. \sum_{j=1}^{4}\varphi_{j1}^2 + \sum_{j=1}^{4}\varphi_{j2}^2 = 1
Determine which of the preceding statements are always true.
- A) I only
- B) II only
- C) III only
- D) I, II and III
- E) The answer is not given by (A), (B), (C), or (D)
Answer this question and see the worked solution