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An observational study is a type of epidemiological study when the researcher observes the situation but is not able to change the conditions of the experiment. The statistical analysis of the observational study of the population of Lermontov city (North Caucasus) was conducted. In the initial group, there were 121 people with lung cancer diagnosis and 196 people of the control group. Statistical analysis was performed only for men (95 cases and 76 controls). The use of logistic regression with correction on age gives the value of odds ratio 1.95 (0.87÷4.37; 90% CI) per 100 working levels per month of combined (occupational and domestic) radon exposure. It was demonstrated that chronic lung diseases are an additional risk factor for uranium miners but it is not a significant risk factor for general population. Thus, the possibility of obtaining statistically reliable results in the observational studies when using the correct methods of analysis is demonstrated.

We consider the problem of finding the dependence of the coefficients of a multiple regression model and the coefficients of the simple correlation models that describe the predictor variables. We show that the dependence is described by a matrix equality.Studying the dependence of response to multifactor influence is a current and difficult problem in mathematical statistics. As a rule, to obtain the exact dependence of the response on the factor variables (also called predictors) turns out an exceedingly complicated and practically useless problem even in the case of a functional dependence. Moreover, the absence of functional dependence of the variables is typical if these variables are stochastic. In this case the description of the expected dependence is approximate and can be expressed by some functional equation for means.An exact statement of the corresponding problem is considered in regression analysis. The simplest and most elaborated model of regression analysis assumes a linear statistical dependence of a stochastic response variable Y and predictor variables X 1 , X 2 , . . . , X n . Then we can model the dependence of Y on X 1 , X 2 , . . . , X n by a linear regression equation, i.e., the multiple linear regression equationThe constants b 0 , b 1 , . . . , b n are solutions to the variational problem of minimizing the mean square deviation (where E is the expectation):(2) Therefore, the problem of finding multiple regression equations for the response to a given tuple of predictors changes as soon as so does the tuple of predictors or the response itself. In regression analysis the dependence of the coefficients of the regression models constructed by different systems of predictors is usually not considered since we can hardly expect any dependence in these models in general.However, accounting for the statistical dependence both among the predictors as well as the response and part of the predictors makes seeking relation of the coefficients of linear regression models more meaningful.Consider the following problem. Take a tuple of n + 1 random variables X 1 , X 2 , . . . , X n , Y , with, generally speaking, arbitrary distribution (we assume however that among X 1 , X 2 , . . . , X n there are no constants). In the linear regression models below the variables X 1 , X 2 , . . . , X n are predictors and Y is the response. To estimate the dependence of Y on X 1 , X 2 , . . . , X n consider the linear regression equation, i.e., the multiple linear regression equation (1).Assume that for every two predictors X i and X j we have found the linear regression equation x i = c 0ij + c ij x j , i,j = 1, 2, . . . , n,where the coefficients c 0ij and c ij are solutions to the variational problem min c 0ij ,c ij E(X i − c 0ij − c ij X j ) 2 , i,j = 1, 2, . . . , n.Ekaterinburg.

The aim of this study was to determine the effect of smoking on BMI in male adolescents and explore the relationship between smoking status and diet. Methods: A cross-sectional epidemiological study into the health and diet of adolescents was carried out based on a representative sample of 375 vocational school male students aged 16–17 in the city of Chelyabinsk (Russian Federation). The students and their parents filled out verified questionnaires on their socioeconomic status, diet, and smoking status. Students’ height and body weight were measured. A comparative analysis of diets was performed between groups of smokers and non-smokers (149 and 226 individuals, respectively), and the relationship between smoking, body mass index, and actual diet was estimated. The methods used included descriptive statistics, Student’s t-test, Mann–Whitney U test, comparison of proportions, and moving average. Results: Non-smoking adolescent boys tended to have excess body mass compared with smokers (19.0% and 12.1%, respectively). Smokers (adolescent boys) consumed less meat, cereals, beans, and cheeses and more sweet beverages, added sugar, coffee, and alcohol. The bulk of the smokers’ diet was composed of carbohydrates (p = 0.026) and, to a lesser extent, proteins (p = 0.006). Conclusions: Significant differences were discovered in the diet between smokers and non-smokers (among adolescent boys), and smoking was associated with several indicators of unhealthy diet patterns. This is an important conclusion for developing a future program that could additionally protect at-risk groups of adolescents.

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