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Let $x_{1}, x_{2}$ denote the variables for the two-dimensional data in Exercise $1 .$ Find a new variable $y_{1}$ of the form $y_{1}=c_{1} x_{1}+c_{2} x_{2},$ with $c_{1}^{2}+c_{2}^{2}=1,$ such that $y_{1}$ has maximum possible variance over the given data. How much of the variance in the data is explained by $y_{1} ?$

$y _ { 1 } = 0.95 x _ { 1 } - 0.32 x _ { 2 }$variance percentage: 93.33$\%$

Algebra

Chapter 7

Symmetric Matrices and Quadratic Forms

Section 5

Applications to Image Processing and Statistics

Introduction to Matrices

McMaster University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

02:26

Use the definition of vari…

02:53

Given multivariate data $\…

06:24

Derive the shortcut formul…

08:12

Variation 2 Find the stand…

07:11

(a) Use the properties of …

05:36

$[\mathbf{M}]$ The covaria…

08:35

(a) Compute the covariance…

12:38

Random variables Given ind…

01:46

Suppose the $x$ -coordinat…

11:41

Let $Z_{X}$ be the standar…

according to a previous exercise, this new variable. Why one We will be 0.9 for 65 x y minus 0.3 to a to a steppin x two, Um, and this variable subject to the constant that's on the coefficient in front, off X one next to our normalized. And, uh, why one has next to impossible variants over the given data. Um, so the various imitate eyes explained by why one, um, so the president do job flow? A very is explained by where, when we will be lambda one over lambda one plus lamb that you both this Agon values are, um, in the previous x ice. So the president you will be about 93.33%. So why one explains about 93.33% off Berries.

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13:53

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