# Analyzing Data Reduction Techniques: An Experimental Perspective
## 8 Experimental Evaluation
### Lossy Data Reduction Algorithms
#### 8.1.3 Linear Regression  
The goal of using Linear Regression was to gain insights into data patterns and build a new model based on these insights. Linear Regression implementation from the scikit-learn library in Python [44] unfolds in three key steps. The first divides the dataset into training and testing. Then, the model was fitted to the training data, capturing relationships within the dataset. Finally, the trained model was used to reconstruct the dataset using its learned patterns. It is important to note that Linear Regression is effective when working with pre-processed data, underscoring the importance of a well-organized and digested dataset for optimal results. Table 8 shows promising results for the Linear Regression algorithm. However, it is crucial to clarify that these results are based on data generated from a predictive model, highlighting the context-specific nature of this approach. It is critical to recognize that Linear Regression may not be appropriate for all solutions, particularly in scenarios without predictive modeling. Observations indicate that the model achieves impressive results but also exhibits remarkable efficiency in data reduction, further underscoring its potential applicability in some contexts. However, the algorithm loses information in string-based data, which may impact execution time. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Data Type** & **Name** & \begin{tabular}{c} **Original** \\ **Size** \\ **(MB)** \\ \end{tabular} & \begin{tabular}{c} **Final** \\ **Size** \\ **(MB)** \\ \end{tabular} & \begin{tabular}{c} **Percentage** \\ **Variance** \\ **(MB)** \\ \end{tabular} & \begin{tabular}{c} **Execution** \\ **Time** \\ **(ms)** \\ \end{tabular} & \begin{tabular}{c} **Processing** \\ **Time per** \\ **MB** \\ **(ms/MB)**2 \\ \end{tabular} \\ \hline \begin{tabular}{c} Temporal, \\ Numeric \\ \end{tabular} & \begin{tabular}{c} Electric \\ Production \\ \end{tabular} & 0.0730 & 0.0600 & \(\mathbf{-17.81\%}\)1 & 0.0006 & **0.0082** \\ \hline \begin{tabular}{c} Numeric \\ \end{tabular} & \begin{tabular}{c} Accelerometer \\ **Smoke Detection** \\ \end{tabular} & \
\begin{tabular}{c} 3.7000 \\ 5.8000 \\ \end{tabular} & 3.2100 & \(\mathbf{-13.24\%}\) & 0.2240 & 0.0605 \\ \hline
\begin{tabular}{c} 1 \\ \end{tabular} The best result for percentage variance. 2 The best result is in bold. \\ \end{tabular}
\end{table} 
Table 7: Quantization algorithm results. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Data Type** & **Name** & \begin{tabular}{c} **Original** \\ **Size** \\ **(MB)** \\ \end{tabular} & \begin{tabular}{c} **Final** \\ **Size** \\ **(MB)** \\ \end{tabular} & \begin{tabular}{c} **Percentage** \\ **Variance** \\ **(MB)** \\ \end{tabular} & \begin{tabular}{c} **Execution** \\ **Time** \\ **(ms)** \\ \end{tabular} & \begin{tabular}{c} **Processing** \\ **Time per** \\ **MB** \\ **(ms/MB)**2 \\ \end{tabular} \\ \hline \begin{tabular}{c} Temporal, \\ Numeric \\ \end{tabular} & \begin{tabular}{c} Daily Minimum \\ Temperatures in \\ Melbourne \\ \end{tabular} & 0.0558 & 0.0118 & \(\mathbf{-78.78\%}\) & 0.003 & 0.0538 \\ \begin{tabular}{c} Temporal, \\ Numeric \\ \end{tabular} & 0.0730 & 0.0144 & \(\mathbf{-80.27\%}\) & 0.006 & 0.0822 \\ \begin{tabular}{c} Monthly Beer \\ Production in \\ Austria \\ \end{tabular} & 0.0690 & 0.0170 & \(\mathbf{-75.36\%}\) & 0.004 & 0.0580 \\ \hline \begin{tabular}{c} Numeric \\ \end{tabular} & \begin{tabular}{c} Accelerometer \\ Smoke Detection \\ \end{tabular} & 3.7000 & 0.7670 & \(\mathbf{-79.27\%}\) & 0.040 & 0.0108 \\ \begin{tabular}{c} Temporal, \\ Text \\ \end{tabular} & \begin{tabular}{c} IoT \\ Temperatures \\ \end{tabular} & 5.8000 & 1.3140 & \(\mathbf{-77.34\%}\) & 0.050 & 0.0086 \\ \hline \
\begin{tabular}{c} Temporal, \\ Text \\ \end{tabular} &
\begin{tabular}{c} IoT \\ Temperatures \\ \end{tabular} & 6.7000 & 1.2977 & \(\mathbf{-80.63\%}\)1 & 0.008 & **0.0012** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Linear Regression results.