# Aggression Detection in Social Media from Textual Data Using Deep Learning Models
## 4 Results
### Hypothesis Testing and Significance of the Emotional Features
Table 8 presents a statistical summary of a binomial logistic regression model that has been fit to predict the outcome based on the values of the emotional features in the tweet data records. The entries of Table 8 include an estimate, z-score, standard error, p-value, and significance of each of the coefficients returned by the regression model. The significance level is represented by asterisks and a high significance of a coefficient is represented by more asterisks. As illustrated in Table 8, most coefficients have a high significance level. The first five probabilities yielded by the logistic regression model are 0.46, 0.37, 0.53, 0.39, and 0.37, which can be considered close to 50%. To verify the adequacy of the logistic regression model, a hypothesis testing was utilized, considering a \(null\) hypothesis in \(H(0)\): \(\beta_{1}=0,\beta_{2}=0,...\beta_{n}=0\), which indicates a null relationship between the response variable and the emotional features as input features. The learning model can be considered efficient if there is any \(\beta\
eq 0\)\(null\) hypothesis. The hypothesis testing was conducted using the ANOVA test, which yielded two performance measures, including the \(null\) and residual deviance. The \(null\) deviance indicates how effectively a model with only an intercept term can predict the response variable. However, the residual deviance shows how the input predictors, emotional features, can help in a good prediction of the response variable. A lower value of the residual deviance than the \(null\) deviance indicates a better performance of the learning model using the emotional features. The retrieved residual and null deviance values are 20,888 and 21,407, respectively. So, the \(null\) hypothesis can be rejected and the association between the emotional features in the classification of the collected tweets, if it is aggressive or non-aggressive, is ensured. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Emotional Feature** & **N** & **Mean** & **SD** & **Min** & **Q1** & **Q3** & **Max** \\ \hline Anger & 20,001 & 3.014 & 5.964 & 0 & 0 & 4.348 & 75 \\ Anticipation & 20,001 & 1.472 & 3.708 & 0 & 0 & 0 & 50 \\ Anxiety & 20,001 & 2.162 & 4.874 & 0 & 0 & 3.333 & 100 \\ Disgust & 20,001 & 3.109 & 6.235 & 0 & 0 & 4.348 & 100 \\ Joy & 20,001 & 1.532 & 4.097 & 0 & 0 & 0 & 100 \\ Sadness & 20,001 & 2.292 & 5.038 & 0 & 0 & 3.571 & 100 \\ Surprise & 20,001 & 0.748 & 2.753 & 0 & 0 & 0 & 100 \\ Trust & 20,001 & 1.485 & 3.864 & 0 & 0 & 0 & 100 \\ \hline \end{tabular}
\end{table} 
Table 7: Emotional features, statistical summary. Figure 4: Histograms of the emotional features. Figure 5: Boxplots of the emotional features. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Estimate** & **Standard Error** & **z Value** & **Pr(\textgreater{}1\textgreater{}1)** & **Significance** \\ \hline
**Intercept** & \(-0.5531\) & \(0.0205\) & \(-26.9310\) & \(\textless{}2\times 10^{-16}\) & *** \\
**Anger** & \(0.0003\) & \(0.0057\) & \(0.0520\) & \(0.9588\) & \\
**Anticipation** & \(0.0023\) & \(0.0059\) & \(0.3970\) & \(0.6914\) & \\
**Anxiety** & \(-0.0088\) & \(0.0066\) & \(-1.3270\) & \(0.1846\) & \\
**Disgust** & \(0.0474\) & \(0.0054\) & \(8.7020\) & \(\textless{}2\times 10^{-16}\) & *** \\
**Joy** & \(-0.0380\) & \(0.0067\) & \(-5.7090\) & \(1.13\times 10^{-8}\) & *** \\
**Sadness** & \(0.0228\) & \(0.0064\) & \(3.5660\) & \(0.0004\) & *** \\
**Surprise** & \(-0.0061\) & \(0.0079\) & \(-0.7690\) & \(0.4420\) & \\
**Trust** & \(-0.0140\) & \(0.0063\) & \(-2.2390\) & \(0.0252\) & \\ \hline \end{tabular}
\end{table} 
Table 8: Statistical summary of a binomial logistic regression using emotional features.