1

0

1

0

1

0

1

0

1

0

1

0

1

1

1

1

1

1

1

1

1

1

1

1

d on this design matrix D, a linear model was formulated as below,

was a vector of gene expressions for one gene, ߚ was a vector of

rs and ߝ was an error vector.

ݔൌܦߚ൅ߝ

(6.7)

ormula can be re-written as below, where ݔ௜

஺ and ݔ௝

஻ represented

ressions of two experimental conditions.

ۉ

ۈ

ۈ

ۈ

ۈ

ۈ

ۇ

ݔଵ

஻

ݔଶ

஻

⋮

ݔ௡^஻

ݔଵ

஺

ݔଶ

஺

⋮

ݔ௠

஺ی

ۋ

ۋ

ۋ

ۋ

ۋ

ۊ

ൌ

ۉ

ۈ

ۈ

ۈ

ۇ

1

0

1

0

⋮

1

1

1

⋮

1

⋮

0

1

1

⋮

1^ی

ۋ

ۋ

ۋ

ۊ

ሺߚଵ

ߚଶሻ^௧൅ ߳

(6.8)

that the above equations are for one gene. In limma, ߚଵ and ߚଶ

ated based on the expressions of all genes in a data set. Therefore,

mation of ߚଵ and ߚଶ using the limma package will be more

uppose ߚ^መଵ and ߚ^መଶ are the estimations using a regression analysis

based on all genes. In addition, ߤ̂஺ and ߤ̂஻ are assumed to stand

population means of a gene. The estimated ߚ^መଶ can be re-

ed and is shown below, which is what the fold change is,