# Innovation in Company Labor Productivity Management: Data Science Methods Application
## 3 Experimental Results
### Exploratory Data Analysis and Visualization
Therefore, the analysis of these factors' interrelationships in order to identify their significant influence on the modeled indicator--labor productivity--is to carried out using different metrics. So, to measure the relationship between labor productivity, age and the number of children, we use the Pearson correlation coefficient, to assess the effect of education level on labor productivity we calculate Spearman's rank correlation coefficient, and to assess the influence of categorical variables on labor productivity we apply multivariate analysis of variance. Using multivariate analysis of variance (ANOVA) we test the hypothesis about the equality of the mean values for the corresponding levels of factors pairs (labor productivity and the presence of chronic diseases, labor productivity and gender, etc. for all seven dichotomous variables). We tested hypothesis of equality of mean values and this hypothesis is rejected for three factors--\"gender\", the presence of chronic diseases (\"chron_dis\") \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Value** & **Index** & **Value** \\ \hline Mean & 262.7 & Minimum value & 123 \\ Mode & 208 & Maximum value & 416 \\ Median & 231.5 & Standard deviation & 84.2 \\  & & Variation & 0.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive statistics for the LP variable. Figure 3: 3D surface plots (**a**) and contour plots (**b**) for the variable “labor_perf” depending on variables “age” and “child”. and the presence of bad habits (\"bad_hab\"). For the other five factors, this hypothesis is accepted, since the calculated values of the [PERSON]'s \(F\)-test are less than the tabular value at a significance level of 0.05. Thus, the factors \"gender\", \"chron_dis\" and \"bad_hab\" are significantly associated with labor productivity \"labor_pert\", while the other four factors do not have a statistically significant effect on it. Estimation of the Pearson coefficient for pairs of age--labor productivity and children--labor productivity has shown that age has a statistically significant inverse effect of its average strength on labor productivity ([PERSON]'s correlation coefficient is about 0.32), and the children does not have any significant impact on labor productivity (the calculated value of Student's \(t\)-test is less than the tabular value at a significance level of 0.05). Calculation of [PERSON]'s correlation coefficient to assess the influence of education on labor productivity showed that these factors are not correlated, which contradicts the generally accepted thesis that the quality of an employee's education contribute to the growth of his labor efficiency. To exclude false correlations, we construct a matrix of partial correlations, Table 3.  
The table shows that variables as \"age\", \"gender\", \"chron_dis\" and \"bad_hab\" affect labor productivity (significant correlations are marked in red). In addition, close partial correlations are observed between factors \"chron_dis\" and \"bad_hab\", \"bad_hab\" and \"health_self-ass\", \"bad_hab\" and \"bad_health\", \"nutt\" and \"health_self-ass\" also between a pair of factors \"chron_dis\" and \"age\". This explains an existence of poor nutrition, bad habits cause chronic diseases and poor health. At the next stage we test several different specifications regression models. The modeling takes into account different predictors scales as well as their multiple correlations. Modeling results for the best model are given in Table 4. The regression model includes a set of predictors, in that number multiplicatively related predictors that have linear correlations with the modeled variable--labor productivity. The model gives an idea of the quantitative influence of the selected predictors on labor productivity. The combined effects of factors especially increase their negative influence. Thus, such factors combination as the frequency of feeling unwell and the presence of bad habits reduces labor productivity as much as possible (on average by 477 rub/h).