Polynomial regression analysis.

Y = {Y₁...Y_m} — gene expression sample
X = {X₁...X_m} — corresponding time poins
so value Y_i is measured at the time moment X_i.
We shall construct linear (multiple) regression:

So, whole system will be:

where e is distributed like N(0,σ²)
Let us consider:

Will find β_i ∀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: {b_i=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: