Question: Exercise 14.5.4. Let v1 = (2,1,1,0), v2 = (0,1,1,0), v3 = (0,0,0,2), and = 3 i=1 viv i . (a) Find the principal components

Exercise 14.5.4. Let v1 = (2,1,1,0), v2 = (0,1,−1,0), v3 = (0,0,0,2), and

Σ =

3Σ

i=1 viv

i .

(a) Find the principal components of Σ .

(b) What is the predictive variance of each principal component? What percentage of the maximum prediction error is accounted for by the first two principal components?

(c) Interpret the principal components.

(d) What are the correlations between the principal components and the original variables?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Linear State Space Systems Questions!

This is all the info In response to a growing awareness of gluten allergies, Crane Bakery tried using gluten-free flour in its three most popular cookies. After several attempts and a lot of inedible...

Determine whether... 1. Determine whether the given vectors are linearly independent; if linearly depen- dent, find a linear combination that vanishes. (e) v1 = (2, 1, 0, 0), v2 = (3, 0, 1, 0), v3 =...

Problem #3: Which of the following sets of polynomials form a basis for P2? (i) p1 = 1 + x, p2 = 7x+ x . p3 = 1+9x+x2 (ii) p1 = 1 + 4x + 6x-; p2 = 5+x (iii) p1 = 1, p2 = 1 - 3x, p3 = x, PA = x- (A)...

A linear tranformation T : R3 R3 maps (1, 0, 0) to (2, 1, 5), (0, 1, 0) to (1, 2, 7) and (0, 0, 1) to (3, 1, 6). Find a vector u in R3 for which T(u) = (5, 4, 17). Is u unique?

please help me with this question Let V1 = [0, 0, 6, 0], V2 = [3, 4, 0, 0] and V3 = [ - 2, 0, 1, 1). Use the Gram-Schmidt procedure to construct an ordered orthonormal basis (W1, W2, W3) for span(V1,...

unit II q12. Summarized on the right is the sale (in thousands) of the top five products in 2002. Use this information to calculate what percent of the sales of these five products was due to product...

Let T = -2 1 1 0 2 -3 0 3 Let w = " and denote I3 = (c) Express an arbitrary vector v = nation of eigenvectors of T. " (a) i). Calculate det (T-xI3) for any x to find the characteristic polynomial of...

Uing python answer these questions as per attached bellow data. NBC problem The file Bank.csv contains data on 5000 customers of Universal Bank. The data include customer demographic information...

Using Python to answer these questions for NBC problem. And attached bellow the same data as the pervious answered questions NBC problem The file Bank.csv contains data on 5000 customers of Universal...

Describe what the following products of matrices do: 0 [1 0 0 0 1 0 - 2 0 0 1 -3 0 0 0 1 1 0 V3 0 2 0 0 -V30] 0 0 1 0 0 2 1 0 0 0 1 ] 0 1 0 0 2 0 0 1 1 3 0 0 0 1

please answer 3 and 4 in details. Thank you! 3. (25 points) Suppose we randomly select 5 students from STAT3025. Let X1, ..., Xs denote their grades on the first quiz, and Y1, ..., Y's denote the...

Q2/ A punch for making holes in steel plates is shown in fig.2a . Assume that a punch having diameter d = 20 mm is used to punch a hole in an 8 mm plate, as shown fig.2b, if a force P= 110 kN is...

A conventional assumption in production theory is free disposal, namely y Y y Y for every y x where x > x means that xi >...

which of the following if true? 1 . a cost center is a responsibility center. 2 . the basic objective of responsibility accounting is to charge each manager with those costs and / or revenues over...

The lack of innovation and entrepreneurial focus at American Express (AmEx) may be because of hubris, inertia, and a lack of capability. The firms performance in 2014 was not, by any means, what...

Exercise 2.10.1 Consider a regression model Y = X +e, e N(0, 2I) and suppose that we want to predict the value of a future observation, say y0, that will be independent of Y and be distributed N(x 0...

Exercise 2.6 Prove relation (4). (YAY)V1 (YAY)+( )(Z V1 Z)( ) = (Y Z)(Y Z )+(Y Z)D1( w)(Y Z) + ( )(ZZ+ Z D1( w)Z )( ) .

Exercise 2.5 Show that A is the perpendicular projection operator onto C(X) when the inner product between two vectors x and y is defined as xV1y.

View Policies Show Attempt History Current Attempt in Progress Indigo Steel Company, as lessee, signed a lease agreement for equipment for 5 years, beginning December 31, 2020. Annual rental payments...

eBook Show Me How Print Item Changes in Current Operating Assets and Liabilities-Indirect Method Blue Circle Corporation's comparative balance sheet for current assets and liabilities was as follows:...

View Policies Current Attempt in Progress TLC Corp. is considering purchasing one of two new diagnostic machines. Either machine would make it possible for the company to bid on jobs that it...