INTRODUCTION
Sweet potato (Ipomoea batatas) is believed to have its center
of origin in tropical America. The sweet potato was brought to Europe
by Columbus and subsequently introduced to Africa and Asia by Portuguese
and Spanish traders. The status of the sweet potato in most parts of the
tropics is that of a minor secondary crop. However, cultivation is increasing
as it gives high yields and requires minimum attention during cultivation.
According to (FAO, 2004) statistics world production is 127,000,000 tons.
The majority comes from China with a production of 105,000,000 tons from
49,000 km^{2} (FAO, 2004). Other Asian producing countries include:
Indonesia, Japan, Korea and Taiwan. Brazil is the most important commercial
grower, but sweet potatoes are mainly consumed domestically and do not
enter international trade either in the fresh state or in a processed
form.
In Africa, sweet potato is an important part of the staple diet of the
populations in tropical regions where it is grown up to an elevation of
2,000 m. Nutritionally, sweet potatoes usually have a rather higher protein
content than other tubers such as cassava and yams. Protein content varies
from 1 to 2.5%. Carotenes, precursors of vitamin A production are often
present in yellow varieties. Sweet potatoes are usually consumed without
special processing. The fresh tuber is boiled, baked, roasted or fried
as chips, which may be sold as snacks or may be salted and eaten like
potato crisps. Sweet potato flour and starch may also be prepared. The
leaves of sweet potato rich in carotenes, provitamin A and calcium are
also a valuable addition to the diet. Sweet potato varieties with dark
orange flesh and richer in vitamin A than light fleshed varieties and
their increased cultivation is being encouraged in Africa where vitamin
A deficiency is a serious health problem.
Sweet potatoes are often considered a small farmer`s crop. However, in
African countries such as Burundi, Rwanda and Uganda, sweet potato is
a staple food. According to (FAO, 2004), Percapita production in Burundi
was 130 kg.
In Africa, sweet potato is grown in abundance around upland lakes in
the East African Rift valley (Uganda, Rwanda, Burundi, Tanzania, Kenya).
It is also found in most African regions with large variations in relief
(Cameroon, Guinea, Madagascar) or where the dry season is too marked for
cassava growing like in the SudanSahelian fringe or in North Africa.
In Nigeria, sweet potato is grown in Sokoto, Zamfara, Kebbi, Kaduna, Kano,
Katsina, Gombe, Bauchi and parts of Plateau and Nassarawa states. Nigeria
is producing an average of 2,520 tons although sweet potato is not a major
crop in Nigeria (Anonymous, 2001).
The purpose of the study is to apply a linear transformation to the p
observed variables x_{1}, x_{2}, ..., x_{p} of
the growth and yield characters of sweet potato, to produce a new set
of uncorrelated and standardized variates Z_{1}, Z_{2},
...,Z_{p}. The use of principal component in data reduction had
been studied by many authors among which are Aitken (1937), Hotelling
(1933) and Essa and Nieuwoudt (2003).
The statistical packages used for the analysis is Genstat (1913).
MATERIALS AND METHODS
The data used for this research work are the growth and yield characters
obtained in a trial conducted at the Institute for Agricultural Research
Farm SamaruZaria (11°11` N, 07° 38`E and 688 m altitude) during
the 2004 and 2005 rainy season.
The treatments of the trial consisted of two varieties of sweet potato,
three rates of inorganic fertilizer and three rates of organic fertilizer.
All possible combinations of the treatments were made and assigned in
plots. The experimental design was randomized complete block design with
three replications. The plots were regularly observed to record data relating
to the experiment.
Population Principal Components
Principal components are particular linear combinations of the p random
variables X_{1}, X_{2},..., X_{p}. Geometrically,
these linear combinations represent the selection of a new coordinates
system obtained by rotating the original system with X_{1},X_{2},...,
X_{p }as the coordinates axes. Principal components depend solely
on the covariance matrix Σ (or the correlation matrix ρ) of
X_{1}, X_{2},..., X_{p}. Let the random vector
X^{1} = [X_{1},X_{2},..., X_{p}] have
the covariance matrix Σ with eigen values λ _{1} ≥λ
_{2} ≥... ≥λ _{p} = 0.
Considering the linear combination,
Y_{1}=e^{1}_{1 }X=e_{11
}X_{1}, + e_{21 }X_{2}, +... + e_{p1 }X
_{p}
Y_{2}=e^{1}_{2 }X=e_{12 }X_{1},
+ e_{22 }X_{2}, +... + e_{p2 }X _{p}
Y p=e^{1}_{p }X=e_{1p }X_{1}, + e_{2p
}X_{2}, +... + e _{pp }X _{p} 
Then, Var (Y_{i})=e^{1}_{i}
Σ e _{i
}cov (Y_{i}, Y_{k})=e^{1}_{i} Σ
e _{k} 

Then the principal components are those uncorrelated linear combination
Y_{1}, Y_{2},..., Y_{p }whose variances are as
large as possible (Richard and Wichern, 1974).
Basic Assumptions
In principal component analysis the basic equations are
α_{i} = Q _{i r} Z_{r}
(i, r, = 1,2,..., P) 
Table 1: 
Latent root and vectors for growth characters 

tr (Σ _{growth}) = 2450 
Table 2: 
Latent root and vectors for yield characters 

tr (Σ _{yield}) = 166966 
Where: 
Z_{r} 
= 
The rth component, 
Q_{ir } 
= 
The weight of the rth component in the ith variates in matrix notation, 
X 
= 
QZ, 
X 
= 
{α_{1}, α_{2}....α_{p} }, 
Z 
= 
{Z_{1},,Z_{2},... Z_{p}} and Q = {Q _{ir}}. 
We first transform to new variates Y_{1}, Y_{2},..., Y_{p}
Satisfying,
Where, Y = (Y_{1}, Y_{2},...,Y _{p}) and U is
an orthogonal matrix. Let Ur denotes the rth column of U.
Then, U_{1} is chosen first in such a way that the variance of
Y_{1} is maximized. When this is done, U_{2} is chosen
so that the variance of Y_{2} is maximized, subject to the conditions
that Y_{2} is uncorrelated with Y_{1}.
Procedure for Obtaining Latent Root and Vector
• 
Obtain the variancecovariance Σ matrix for the
pvariates. 
• 
Obtain an identity matrix I, in the order of Σ. 
• 
Multiply a scalar λ with the I matrix. 
• 
Equates the det I Σλ I = 0. 
The value of λ are the latent root. For any latent root there exist
a corresponding latent vectors, obtained by (v) Σ x = λx.
RESULTS AND DISCUSSION
Using Pearson correlation coefficient, the bivariate relationship showed
that the number of branch of sweet potato at harvest is positive and highly
correlated with vine length of sweet potato. Vine length of sweet potato
is positive and highly correlated with number of leaves of sweet potato
at harvest. Number of tuber/hill of sweet potato is negative and highly
correlated with number of branches of sweet potato. Tuber fresh weight
is positive and highly correlated with total dry matter of sweet potato
at harvest. Tuber dry weight of sweet potato is positive and highly correlated
with tuber fresh weight.
The first two principal component that explain the total variation in
the original pvariates for the growth characters are:
The first principal component explain 60.9% of the total variation in
the pvariates. The second principal component explain 31.58% of the total
variation in the pvariates. The first and second principal component
explain 92.48% of the total variation in the pvariates. Which reduces
the dimensionality of the original data as shown in Table
1.
The first Principal component that explain the total variation in the
original pvariates for the yield characters is:
The first principal component explain 93.65% of the total variation in
the pvariates as in Table 2.
The above component as shown that the total dry matter and vine length
of sweet potato are the most important variable in growth character. Also,
the tuber fresh weight is the most important variable in the yield characters
of sweet potatoes. This is in conformity with the findings of Muhammed
(2001).
CONCLUSION
In explaining the growth parameters for sweet potatoes (Ipomodea batatas
L.), from the components in Eq. 1, total dry matter
is having the highest coefficient and the vine length the highest in Eq.
2. Therefore, in explaining the growth parameters for Ipomodea batatas
L., both the total dry matter and vine length explain most of the variation
in growth parameters. Likewise in Eq. 3 the tuber fresh
weight is shown to have the highest coefficient, which indicates that it
is the parameter with the most variance in explaining the yield of sweet
potatoes.