*3.1. Checking Xn for Collinearity*

Collinearity checks were performed in 128 multitudes of *X*1–16 variables in eight territories included in the study. Regression models were computed with all independent variables to find *VIF*s. Application of *VIF* > 5 criteria resulted in the elimination of high-collinear *Xn* variables from the models in respective territories (Table 5)—some of the water-use and environmental variables in the western and central territories of the Russian Arctic and economic variables in the Far East.


**Table 5.** Coefficient of multiple determination (*R*2) and variance inflationary factor (*VIF*) values of *X*1–16 variables to be selected for the model.

Note: \* collinearity detected. Source: authors' development

### *3.2. Selection of the Best Subsets*

Best-subsets stepwise regression with the remaining *Xn* allowed to identify several more variables with high collinearity: *X*<sup>13</sup> in territories 1 and 2, *X*<sup>5</sup> in territory 2, *X*<sup>3</sup> in territory 3, *X*<sup>4</sup> in territory 5, and *X*<sup>4</sup> in territory 6. Based on the parameters of adjusted *R*<sup>2</sup> and Mallows' *Cp* statistic, the best subsets of variables (one per territory) were chosen out of competing multitudes (Table 6).

**Table 6.** Subsets of *Xn* variables selected for the inclusion in the model per territories.


Source: authors' development.

#### *3.3. Multiple regression*

Multiple regression analysis was performed in 112 multitudes (fourteen *Yn* regressands and eight territories) with respective adjusted arrays of independent variables. High *R*<sup>2</sup> in individual multitudes and average *R*<sup>2</sup> demonstrated that all variations were well explained (Table 7).


**Table 7.** *R*<sup>2</sup> coefficients across the territories and regressands.

Source: authors' development.

Generalization of *Xn* values for eight territories allowed to reveal the health-related effects of independent variables in the entire Arctic Zone of Russia (Table 8). *X6*, the percentage of households with available sources of running water, posed the most diverse effects on selected health parameters, from the highest positive to the most negative. Air and water pollution massively had a net detrimental effect on the incidence rates of the diseases under study (excluding *X*<sup>4</sup> eliminated from the subsets in most of the western territories of the Arctic Zone and *X*<sup>2</sup> not considered in territories 3, 5, and 6). Economic parameters (excluding high-collinear *X*<sup>15</sup> and *X*<sup>16</sup> in the eastern areas of the Arctic Zone) made a positive impact on the reduction of the incidence rates. The effects of nutritional variables varied across *Yn*, the most positive being consumption of fish and marine mammals in case of the diseases of the circulatory and nervous systems.

**Table 8.** The effects of independent variables on *Yn*: generalization for the Russian Arctic \*.


Note: \* for particular *Xn*, the generalizations cover only those territories in which the respective *Xn* is included in the per-territorial models; HP—the highest positive impact of *Xn* on the reduction of *Yn*; P—positive impact of *Xn* on the reduction of *Yn*; N—negative impact of *Xn* on the reduction of *Yn*; EN—extremely negative impact of *Xn* on the reduction of *Yn*. Source: authors' development.
