Coefficient of regression (Finlay and Wilkinson, 1963) is calculatd based on regression function.
Variety with low coefficient of regression is considered as stable.
Under the linear model
$$Y =\mu + b_{i}e_{j} + g_{i} + d_{ij}$$
where Y is the predicted phenotypic values, \(g_{i}\), \(e_{j}\) and \(\mu\) denoting
genotypic, environmental and overall population mean,respectively.
The effect of GE-interaction may be expressed as:
$$(ge)_{ij} = b_{i}e_{j} + d_{ij}$$
where \(b_{i}\) is the coefficient of regression and \(d_{ij}\) a deviation.
Coefficient of regression may be expressed as:
$$ b_{i}=1 + \frac{\sum_{j} (X_{ij} -\bar{X_{i.}}-\bar{X_{.j}}+\bar{X_{..}})\cdot
(\bar{X_{.j}}- \bar{X_{..}})}{\sum_{j}(\bar{X_{.j}}-\bar{X_{..}})^{2}}$$
where \(X_{ij}\) is the observed phenotypic mean value of genotype i(i=1,..., G)
in environment j(j=1,...,E), with \(\bar{X_{i.}}\) and \(\bar{X_{.j}}\)
denoting marginal means of genotype i and environment j,respectively.
\(\bar{X_{..}}\) denote the overall mean of X.