## Polynomial regression analysis.

Y = {Y1...Ym} — gene expression sample
X = {X1...Xm} — corresponding time poins
so value Yi is measured at the time moment Xi.
We shall construct linear (multiple) regression:
So, whole system will be:
where e is distributed like N(0,σ2)
Let us consider:
Will find βi ∀i out of condition S → min, i.e. we should solve system:
Also we need estimation of coefficients dispersion, we can derive it
from:
Approximation for σ2 is:
To test hypothesis H0: {bi=0} we shall use statistic:
In case H0 is true this statistic is distributed like Student random
value with n-p-1 degrees of freedom.
So we estimate P-value:
where: