Algorithm 2. Variable selection pseudocode.

input: List of all explanatory variables $\mathit{X}$, distance function $dist\left(C_i,C_j\right)$, correlation matrix ($\mathit{M}$), target variable ($\mathit{y}$)

output: List of the best explanatory variables ($\mathit{B}$)

1:     create empty cluster list $\mathit{C}$

2:     for each $j$ = 1 to $p$ do

3:       create a cluster for each variable $C_j=\left\{X_j\right\}$

4:     end

5:     calculate distance matrix $\mathit{D}$ as $1-\left|\mathit{M}\right|$

6:     repeat

7:       $d_{i,j}^{min}$ = find smallest element $d_{i,j}$ in $\mathit{D}$ for all $C_i,C_j\in \mathit{C}$

8:       if $d_{i,j}^{min}>0.9$ then

9:         break repeat

10:     end

11:     merge cluster $C_j$ and cluster $C_i$

12:     update distance matrix $\mathit{D}$

13:   end

14:   create empty $MSE\_list$

15:   for each $j$ = 1 to $p$ do

16:     $MSE$ = estimate mean square error of $j$-th variable for prediction of $\mathit{y}$

17:     update $MSE\_list$ based on $MSE$

18:   end

19:   for each $C_i\in \mathit{C}$ do

20:     select variable based on the $\mathrm{MSE}\_\mathrm{list}$ and add to $\mathit{B}$

21:   end

22:   return $\mathit{B}$