## 4 Results and Discussions
### Methods for Post Analysis  
After computing SE, data were analyzed using inferential statistical methods including Poisson Regression (PR) and Negative Binomial Regression (NBR). Regression modelling techniques were used to analyze the association between multiple variables with count outcome data. Linear regression is not suitable for counting data. PR applies to the count or rate data. The count data are quantified with a count variable that is taken from discrete non-negative number values in a fixed interval. As a Cobb-Douglass production \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Year** & **Classifier/Method** & **Affective States** & **Accuracy** &
\begin{tabular}{c} **Offline Classroom** \\ **Environment** \\ \end{tabular} \\ \hline
2014 [35] & \
\begin{tabular}{c} Linear regression, \\ multinomial logistic \\ regression \\ \end{tabular} &
\begin{tabular}{c} not engaged, nominally engaged, \\ engaged, very engaged \\ \end{tabular} & Not Reported & \(\times\) \\ \hline
2015 [44] & SVM & low, medium, and high attention \\
2017 [45] & SVM, logistic regression & engaged and distracted & 90\% & \(\times\) \\ \hline
2019 [12] & CNN &
\begin{tabular}{c} not engaged, normally engaged, \\ and highly engaged \\ \end{tabular} & 89\% & \(\times\) \\ \hline
2020 [23] & Inception v3 & engaged, non-engaged, neutral & 86\% & \(\times\) \\ \hline
2021 [21] & \
\begin{tabular}{c} LSTM and TCN, fully \\ connected neural network, \\ SVM, and RF \\ \end{tabular} &
\begin{tabular}{c} low-level, high-level \\ engagement \\ \end{tabular} & 63\% & \(\times\) \\ \hline
2021 [22] & Neural Turing Machine & \
\begin{tabular}{c} completely disengaged, barely \\ engaged, engaged, and highly \\ engaged \\ \end{tabular} & 61\% & \(\times\) \\ \hline Proposed method &
\begin{tabular}{c} VGG16 \\ (Extended layers) \\ \end{tabular} & engaged, non-engaged & 90\% & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of accuracy with existing methods. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Training Platform** & **Training Time (h)** & **Testing Accuracy (\%)** & **Testing Time** \\ \hline Google-Colab-Pro & & Accuracy 0.90 & \\ (16 GB GPU, 25 GB & & Precision 0.93 & \\ memory, 147 GB & & Recall 0.93 & 6 s/frame \\ storage) & & F-measure 0.93 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time and accuracy obtained for the proposed method. function [55], the output is a function of inputs. In our case, we consider engagement and non-engagement as a function of session and gender by this production function. \[\text{Eng}=\text{f}(\text{Session},\text{Gender}) \tag{1}\]  
In the generalized linear models, the response variable is a binary variable such as in the form of yes or no, 0 or 1, or A or B. Hence, the relationship between the dependent and independent variables may not be linear. \[y_{i}=\alpha+\beta_{i}X+\text{e}_{i}i=1,2,\ldots n \tag{2}\]  
In Equation (2), \(y\) is the dependent variable, \(\alpha\) is the constant other than factors that affect the dependent variable, \(\beta\) is the coefficient, and \(X\) is the independent variable. For the analysis of our problem, we formulated the following four equations: Equations (3)-(6). More precisely, Equations (3) and (4) are modelled for an engaged variable concerning the independent variables of session and gender, respectively. Equations (5) and (6) are formulated for the non-engaged variable concerning the independent variable session and gender, respectively. \[\text{Eng}=\text{Const.}+\beta_{1}\text{Session}+\varepsilon_{t} \tag{3}\]  
\[\text{Eng}=\text{Const.}+\beta_{1}\text{Gender}+\varepsilon_{t} \tag{4}\]  
\[\text{Non\_Eng}=\text{Const.}+\beta_{2}\text{Session}+\varepsilon_{t} \tag{5}\]  
\[\text{Non\_Eng}=\text{Const.}+\beta_{2}\text{Gender}+\varepsilon_{t} \tag{6}\]  
Although PR modelling is widely used for the analysis of count data, it does not handle over-dispersed data. PR assumes that the outcome variable follows Poisson distribution, which means that the mean and variance are equal.