## 2 Materials and Methods
We excluded those patients from the analysis who had less than 14 valid logged days after all the above steps have been executed. We defined the 90-day weight change percentage (WCP) as  
\[WCP=\frac{(final\ body\ weight-initial\ body\ weight)*90}{initial\ body\ weight*duration\ of\ observation\ in\ days}*100\ [\%]\]  
In line with accepted dietary guidelines [8; 15; 22; 23; 24] and similar studies [13; 14; 25], we considered a person a successful weight loser (SWL) if their weight loss percentage exceeded 3%, and unsuccessful (UWL) otherwise. Belonging to the success group was treated as the main dependent variable in the statistical analysis. Aside from the SWL, we computed the weight ratios of all dietary sets for each patient for the whole observation period. The initial independent variables included the patients' age and gender. In order to characterize the patients' compliance, an additional adherence ratio was computed as the ratio of the number of fully logged days with respect to all days. Finally, we also used the average daily weight ratios of the various dietary sets as independent variables in the analysis. The data analysis posed two questions: first, is there a significant change or trend (either positive or negative) in the body weight of the patients during the trial; second, can we relate any independent variables to an observed significant change or trend. To answer these questions, we first performed a paired-samples T-test and Wilcoxon signed rank test using the initial and 90-day body weights of all patients to check whether there was a significant change at the group level. We also performed a Mann-Kendall trend test for each patient to check if there is a significant temporal trend in the change of their body weight during the observation. This test can handle missing days, does not assume a particular distribution, and delivers an estimated slope of the trend-line by the Theil-Sen method that is quite robust for outliers [26]. If the trend was significant for a patient, the weight-loss slope (WL-slope) was also treated as a dependent variable. We note that a higher negative slope denotes more rapid weight loss. In order to track the changes in patients' preferences, we also computed the trends of the average weight ratios for the most important sets separately for the SWL and UWL sub-groups in the first 90 days of the observation. In order to find a connection between therapeutic success and nutrition, we computed the Pearson correlation between the WL-slope and the important dietary set weight ratios in the cohort of those patients with a significant WL trend, either positive or negative. As a last step in the analysis of the main hypothesis, we built Ordinary Least Squares linear regression models to find any significant predictors of the two dependent variables; i.e., WCP and WL-slope, using the age, gender, logging adherence, the averaged ratio of the raw fruit/vegetable set, and the daily average dietary fiber consumption as independent variables. We used the forward likelihood model selection method. The linear regression method approximates the dependent variable as the linear combination of the independent variables plus a constant. The coefficient computed for each independent variable carries information on the role and importance of the variable [27]. The secondary hypothesis about the effect of more telemedical support was checked using two-sample \(t\)-tests. For each statistical test, the relevant assumptions, such as missing values, normality of distributions, univariate/multivariate outliers, multicollinearity, homoscedasticity, etc., were checked, and the appropriate corrections were performed. Throughout the analysis, \(p\)-values \(p<0.05\) were regarded as statistically significant. The data analysis was performed with the Python Statsmodels ver. 0.14, Python Scipy ver. 1.13 and IBM SPSS Statistics ver. 29.0.0 software packages. For the cleaning, transforming and storing of the anonymized trial data, Microsoft SQL Server ver. 2019 database technology was used.