# On a Certain Research Gap in Big Data Mining for Customer Insights
## 5 Verification of Research Findings
### Trends Analysis  
Considering the time series regarding the number of scientific documents in given years, for all three phrases: \"big data analytics\", \"big data mining\", and \"temporal big data\", a clear upward trend is noticeable, which proves that researchers are becoming increasingly interested in these topics over time. Performing a trend analysis in the case of the phrase \"temporal big data mining\" is not possible, due to the presence of only 2 articles in the Scopus database corresponding to this phrase (for the abstract, keywords and title). With the help of only two references (i.e., a time series consisting of two observations), it is pointless and impossible to create a trendline and thus analyze it.  
It was decided that the trend analysis methodologies (predictions) will be used to analyze these time series, with prior examination of the fit of the data in the model using the coefficient of determination \(R^{2}\). This coefficient takes the values 0;1 the larger its value, the higher the match of the dataset. It is expressed by the following formula, as presented in [178]:  
\[R^{2}=\frac{\sum_{t=1}^{n}(\hat{y}_{t}-\overline{y})^{2}}{\sum_{t=1}^{n}(y_{t}- \overline{y})  
The exponential trend formula is as follows:  
\[Y_{t}=\alpha_{0}*\alpha_{1}{}^{t}*e^{t} \tag{3}\]  
The power trend formula is as follows:  
\[Y_{t}=\alpha_{0}*t^{\alpha 1}*e^{t}. \tag{4}\]  
The logarithmic trend formula is as follows:  
\[Y_{t}=\alpha_{0}+\alpha_{1}\ln(t)+\varepsilon_{t}. \tag{5}\]  
For further and deepened discussion for linear/polynomial trends, see [179; 180], and for logarithmic, exponential, and power trends, see [181; 182]. The study compares the models estimated using the ordinary least squares (OLS) methodology [183; 184], which is broadly used in scientific research [185; 186; 187; 188].  
For each dataset, individual regressions (characterized by exponential, linear, logarithmic, second-order polynomial, and power trendlines) were compared with respect to the matching (fitting) degree of the dataset, using the \(R^{2}\) coefficient. The trendlines with the highest \(R^{2}\) coefficient were selected for further processing.  
The trendlines in various regression models were expressed by trend function equations, in tabular comparison with the values of the determination coefficients. To calculate the values of \(R^{2}\) coefficients, as well as the function of the particular trendlines, and to visualize the results in the form of charts, Microsoft Excel 2019 software was used.  
Using regression and trend analysis to predict future values for a given phenomenon can bring enormous value, among others for determining the directions and forms of development of accompanying phenomena. It may turn out to be useful in the scientific or business spheres, depending on the subject of research. Thanks to researching trends, it is simpler to gather knowledge about threats and challenges but also about opportunities faced, for example, by a company, industry, country, region, etc.  
The usefulness of the trend analysis is confirmed in scientific research from various fields. For example, there is a study that used trend analysis to analyze the phenomena of road accidents and to eliminate them [189]. Prediction of future values with the use of trend analyzes also turns out to be useful in temperature and climatological studies [190; 191; 192]. Furthermore, trend analysis approach is widely used to investigate and prevent the COVID-19 spread [193; 194; 195].