mecautionsmustbe notedat this point.

First, you cannot determinethe

useof the relationshipfromthe correlationcoefficient.

Two variablesmay be

hly correlatedfor oneof threereasons: (1)

X causesY,

(2)

Y causesX, or

both X and Yare causedby somethird variable.Awell known storythat

stratesthe danger of inferring causationfroma correlationcoefficient betwee

numberof storksand the numberof births in Europeancities(that is, the

re storks,the morebirths).

Insteadof issuinga dramatic announcement

pporting the mythical powersof storks,further investigationwas carried out.

s found that storksnestin chimneys,which in turn led to the conclusionthat a

rd variable was responsiblefor the relationshipbetweenstorksand births -

e of city.

Large citieshad morepeople,and hencemorebirths; and more

uses,and hencemorechimneys,and hencemorestorks. Thus, attribution

usality is a logical or scientific problem,not a statisticalone.

=f

x1,x2, . . . ., xn

Y

2

=

∂Y

∂X1

. Sx
1

?
? ?

?
? ?

2

+

∂Y

∂X2

. Sx
2

?
? ?

?
? ?

2

+ . . . .

+

∂Y

∂Xn

. Sx
n

?
? ?

?
? ?

2

∂Y

∂X1

. Sx
1

?
? ?

?
? ?

2

SY

2

X100%

sume deterministic model:

en the variance of Y is:

(making some assumptions)

e % of variance of Y due to

X1is:

regression, we assume

Y =

bx1+

a

+

error

R2

=

b Sx
1

SY

?
? ?

?
? ?

2

⇒The proportion of the variance Y

due to X1,assuming Y is a linear function of X1.