Suppose that the data set contains three variables, and the normalized versions

Order Details:
Suppose that the data set contains three variables, and the
normalized versions are labeled as 1, 2,
and 3. Also, assume that the
PCA assumption is p = 1v1
+ _2v2, where v1 = (11,
21, 31)T
and v2 = (12, 22,
32)T are
the first two columns in the matrix V.
(a) Show that the PCA assumption can be written as 3
= 1 +2,
where  = (3122
_ 32
»
Suppose that the data set contains three variables, and the
normalized versions are labeled as 1, 2,
and 3. Also, assume that the
PCA assumption is p = 1v1
+ _2v2, where v1 = (11,
21, 31)T
and v2 = (12, 22,
32)T are
the first two columns in the matrix V.
(a) Show that the PCA assumption can be written as 3
= 1 +2,
where  = (3122
_ 3212)/ =
(3211
_ 3121)/,
and  = 1122
_ 1221.
This assumes, of course, that 0.
(b) Using the result from part (a), show that the PCA
assumption, when expressed in terms of the original, unnormalized, data
variables, can be written as
               
where 1, 2
and 3 are the means of 1,
2 and 3,
respectively. Also,  = 3/1
and  = 3/2,
where 1, 2,
and 3 are the scale factors
used for the respective variables.
»

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