CAS Exam MAS-II Fall 2019, Question 41
Study guide: Exam MAS-II
You are given:
- A data set contains 500 observations for five predictor variables
(X_1, X_2, X_3, X_4, X_5). - Each predictor has been standardized to have mean 0 and standard deviation 1.
- Each of the 500 observations takes the form
(x_{1i}, x_{2i}, x_{3i}, x_{4i}, x_{5i})foriranging from 1 to 500. - For each observation, a new predictor
Zis calculated by projecting onto the first principal component. - The projection for the
i^{th}observation is denoted byz_i.
The total variance present in the data set is equal to 4 and \sum_{i=1}^{500} z_i^2 = 750.
Calculate the proportion of variance explained for the first principal component.
- A) Less than or equal to 0.20
- B) Greater than 0.20 but less than or equal to 0.30
- C) Greater than 0.30 but less than or equal to 0.40
- D) Greater than 0.40 but less than or equal to 0.50
- E) Greater than 0.50
Answer this question and see the worked solution