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IMAGE imgs/section_3_pgmkr_601.gif
IMAGE imgs/section_3_pgmkr_602.gif IMAGE imgs/section_3_pgmkr_605.gif IMAGE imgs/section_3_pgmkr_606.gif

R

2"

"THEMEANING

OF

Assume deterministic model:

f (x1,

. . . ., x

n)

Y

=

x

2,

Then the variance of Y is:

(making some assumptions)

[!]
IMAGE imgs/section_3_pgmkr_6300.gif [!] [!] [!]Y
[!]X1

[!] 2 . Sx[!]
1[!]

[!]
[!] [!]Y IMAGE imgs/section_3_pgmkr_6302.gif [!] [!]X2

2 . S[!]
x[!] [!]
2

[!]
IMAGE imgs/section_3_pgmkr_6304.gif [!] [!] [!]Y
[!]Xn

[!] 2 . Sx[!]
n[!]

SY2

=

+

+

. . . .

+

IMAGE imgs/section_3_pgmkr_6301.gif

The % of variance of Y due to

X1is:

IMAGE imgs/section_3_pgmkr_6306.gif

X100%

S2
Y

In regression, we assume

Y =

bx
1+

a

+

error

[!] [!] [!]

IMAGE imgs/section_3_pgmkr_6307.gif

2

R2

[!]

=

The proportion of the variance Y

IMAGE imgs/section_3_pgmkr_604.gif

due to X1,

assuming Y is a linear function of X1.

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