**4. Empirical research**

To assess the factors of influence of cluster elements and management organizations on innovative development and the level of competitiveness of national innovation systems in Russia and world countries, an experimental decision was made to implement statistical analysis using multiple linear regression models [15].

The empirical objectives of the study favored the determination of the following hypotheses, which reflect the meaning of the updated research questions:


For the implementation of statistical analysis, 29 linear regression models were created with the participation of 119 variables, which were constructed from 9 databases containing 6656 values. Data on Russian innovation clusters were obtained from the Internet portals of the Russian Cluster Observatory [6], the values of innovation subindices and the Global Innovation Index (GII) were found on the World Intellectual Property Organization (WIPO) page, and the competitiveness ratings of states were found in the data from IMD World Competitiveness Center [12]. All data came out in 2021 and represented the most recent information provided by the publishers. This decision was made due to the need for alternative options found in the free Internet access.

To avoid the adverse effects of autocorrelation, multicollinearity, heteroscedasticity, and the size of outliers on the objectivity of the obtained statistical results, tests are carried out on the assumptions of the quality of the used models [16]. The Durbin-Watson test was used, the coefficients were studied by the test on variance inflation factor, and the graphical analysis was produced. For this reason, 23 models were assessed and established, which leveled out the conflicting interactions of variables in the implementation of regression analysis [17]. The workflow of the operations performed in the context of regression analysis can be seen in **Figure 3**.

The threat of unreliability of the obtained results is potentially present due to the limited number of observations, which eliminates the possibility of removing every cause of the statistical outliers when improving the quality of regression models. Another source of doubt about the validity of the obtained results is the indices from the Russian Cluster Observatory, WIPO, and IMD, on which databases the analysis was executed [13]. Also, the adequacy of using the WIPO's data regarding the countries' innovation achievements to represent the success of the countries' clusters can come under scrutiny. However, after conducting the qualitative analysis, the author believes this approach can be justified since the innovation clusters significantly impact the countries' innovation development.

In the first section of the regression analysis, 20 regions were selected to uncover the impact of variables on the innovation index of clusters in Russia. These regions were initiated according to pilot projects of the country's innovative cluster development [3].

To confirm or reject the first hypothesis, the relationship among the leading macroeconomic indicators, the educational potential of the population, the financing of research and development, the effectiveness of research and development, the export of goods and services, the regulatory and legal framework for innovation policy, the organizational support for innovation policy, budget expenditures on science, and innovations on the dependent variable—innovation index of cluster regions of Russia —is explored. This procedure is presented in **Table 8**.

### **Figure 3.**

*Methodical thinking behind the regression analysis. Source: The figure and research were designed and carried out by the authors.*


### **Table 8.**

*First variables' influence on the innovation index of clusters in Russia.*

According to the analysis of all variables, the effectiveness of research and development has a high statistical significance (0.00388) with the regional innovation index. On average, each change in research and development performance is accompanied by an increase in the innovation index by 0.364625, while other variables remain the same.

The export of goods and services (0.07029) and budget expenditures on science and innovations (0.08543) have the minimum significance. The first variable provides a positive effect of 0.217058, and the second is 0.155944 on the performance indicator of the statistical model.

For these variables, p-values allow us to move away from the first null hypothesis (H0-1) to accept that the variables are related to the innovation index.

Based on the adjusted R-square value (0.7058), the fitted model explains 70.58% of the statistical relationships of the linear regression variables. Also, the model's p-value (0.002566 < 0.05) demonstrates the rejection of the null hypothesis about the absence of effects of variables on the result, which confirms the statistical reliability of this regression analysis.

Like the last time, a new group of variables was compiled to accept or refute the first hypothesis. It aims to explore the relationship between the leading macroeconomic indicators, the potential of digitalization, scientific personnel, the innovative activity of organizations, small innovative businesses, the cost of technological innovation, the effectiveness of the innovative activity, export of knowledge, and

participation in federal scientific, technical, and innovation policy with the same dependent variable. This procedure is presented in **Table 9**.

According to the analysis of all predictors, the moderate statistical significance (0.0477) with the innovation index of the region is observed when looking at the cost of technological innovation. On average, each change in the cost of technological innovation is accompanied by an increase in the innovation index by 0.08538 when other variables remain unchanged. Also, the p-value allows us to move away from the first null hypothesis (H0–1) to accept that the predictor has a relationship with the output indicator.

Based on the adjusted R-square value (0.8744), the fitted model explains 87.44% of the statistical relationships of the linear regression variables. Also, the model's pvalue (0.0000884 < 0.05) demonstrates the rejection of the null hypothesis about the absence of effects of variables on the result, which confirms the statistical reliability of this regression analysis.

A review of the subindices of the new group of variables is carried out to accept or reject the first hypothesis. It is done to see if there is any impact on the dependent variable from the share of organizations implementing technological innovations, the share of organizations implementing nontechnological innovations, the share of organizations developing technological innovations on their own, the share of


### **Table 9.**

*Second group's variables' influence on Russia's innovation index.*

### *Policies for Improving the Efficiency of Innovative Clustering in an Emerging Market DOI: http://dx.doi.org/10.5772/intechopen.112150*

organizations participating in scientific cooperation, the share of small enterprises implementing technological innovations, the intensity of costs for technological innovations, the share of innovative products, the share of new innovative products, and the share of organizations that have reduced material and energy costs as a result of innovation. This procedure is presented in **Table 10**.

Looking at the analysis results of all variables, the moderate statistical significance (0.042635) and (0.023314) can be observed in the share of organizations participating in scientific cooperation and the intensity of costs for technological innovation. These variables increase the innovation index of the region by 0.119038 and 0.126316 when other variables remain unchanged. For these variables, the p-value allows us to move away from the first null hypothesis (H0-1) to accept that the variables are related to the output variable.

The minimum significance (0.098626) with an impact (0.092058) on the innovation index also has the share of small enterprises that carried out technological innovations.

Based on the adjusted R-square value (0.8306), the fitted model explains 83.06% of the statistical relationships of the linear regression variables. Also, the model's pvalue (0.0003683 < 0.05) demonstrates the rejection of the null hypothesis about the


### **Table 10.**

*Third group's variables' influence on Russia's innovation index.*

absence of effects of variables on the result, which confirms the statistical reliability of this regression analysis.

Going forward, the detailed group of variables is reviewed to see if they influence the innovation index of Russian cluster regions. The group includes the export of goods, nonresource exports of goods, exports of services, the share of exports in the volume of innovative products, patent activity abroad, the export of technologies, and the share of foreign students of higher education programs. This procedure is visualized in **Table 11**.

There is visible a moderate statistical significance (0.04952) of the export of services. This variable increases the dependent variable by 0.12507 when other variables remain unchanged. Also, patent activity abroad has a minimum significance (0.08445) and influence (0.10925) on the output variable.

For these variables, the p-value allows us to accept that the variables are related to the innovation index.

The fitted model explains 50.46% of the statistical relationships of the linear regression variables. Also, the model's p-value (0.02154 < 0.05) demonstrates the rejection of the null hypothesis about the absence of predictor effects on the final result, confirming the moderate statistical reliability of this regression analysis.

Further, the review of the variables from the new group of subindices is carried out. The model tests if there is an impact on the innovation index of clusters in Russia


### **Table 11.**

*Fourth group's variables' influence on Russia's innovation index.*
