# Engineering Supply Chain Transportation Indexes through Big Data Analytics and Deep Learning
## 3 Results  
### Statistical Analysis  
This section of the study focuses on the extraction of important statistical metrics and coefficients for the imminent deployment of simulation models based on FNN deep learning procedures. The authors opted to perform descriptive statistics, correlation, and linear regression analyses to gather the required coefficients. For the descriptive statistics analysis, the metrics of mean, minimum, maximum, and std. deviation were used to provide important information regarding the variables' distributions (both dependent and independent ones), which can be seen in Table 2. To aid in the selection of independent variables for the linear regressions and the simulation models, the authors performed a correlation analysis based on Pearson's coefficient (Table 3). The most significant correlations are presented with * and ** to indicate statistical significance at the 95% and 99% levels, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Mean** & **Min** & **Max** & **Std. Deviation** \\ \hline Freight Index & 1.20 & 1.12 & 1.28 & 0.04 \\ Shipments & & & & \\ Freight Index & 4.44 & 4.10 & 4.67 & 0.17 \\ Expenditures & 3.70 & 3.47 & 3.88 & 0.11 \\ Truckload Line & 158.93 & 149.23 & 168.60 & 6.64 \\ Haul Index & & & & \\ Net Trailer & 28,630.75 & 16,400.00 & 56,949.00 & 12,846.14 \\ Orders & 72.40 & 72.20 & 72.80 & 0.20 \\ Authority Score & 55.78 & 50.20 & 61.40 & 3.87 \\ Branded Traffic & 14,647,035,33 & 11,882,021.00 & 17,824,613.00 & 1,888,192.67 \\ Organic Taffic & 24,437,840.08 & 17,760,939.00 & 30,389,621.00 & 4,516,413.74 \\ Paid Traffic & 394,464.33 & 163,806.00 & 574,521.00 & 122,727.12 \\ Paid Costs & 1,363,788.41 & 717,103.00 & 2,676,244.00 & 500,493.54 \\ Bounce Rate & 0.61 & 0.57 & 1.00 & 0.03 \\ Pages per Visit & 2.50 & 2.00 & 3.00 & 0.20 \\ Time on Site & 696.74 & 555.00 & 1006.00 & 168.60 \\ Website & 15,888,074.43 & 13,230,273.00 & 18,363,549.00 & 1,812,070.90 \\ Website Visits & 39,887,735.57 & 34,754,017.00 & 44,989,600.00 & 4,231,610.37 \\ \hline \hline \end{tabular} N = 180 observation days for the five selected Supply Chain Firms.  
\end{table} 
Table 2: Descriptive Statistics of the five Supply Chain Firms during the past six months. In Tables 4 and 5, the Freight Shipments Index and Freight Expenditure Index were used as dependent variables, with the rest of the big data analytic metrics used as independent ones. The model with the best score in terms of R\({}^{2}\), \(p\)-value, and Akaike criterion was selected. The Freight Shipments Index's linear regression is verified overall with R\({}^{2}\) = 1.00 and a \(p\)-value = 0.000 \(<\) a = 0.01 level of significance. All of the independent variables had \(p\)-values below the a = 0.01 level of significance. For every 1% increase in the authority score, paid costs, bounce rate, time on site, and website visits, the Freight Shipments Index increases by 1.7%, decreases by 105.1%, increases by 32.2%, decreases by 7.5%, and increases by 64% accordingly. Therefore, the first research hypothesis (H1) is verified, and the Freight Shipments Index of supply chain firms can be affected by the big data analytics of their websites. The linear regression of supply chain firms' Freight Expenditure Index is also overall verified with R\({}^{2}\) = 1.00 and a \(p\)-value = 0.000 \(<\) a = 0.01 level of significance. The independent variables of website big data analytics with the most significant impact on the dependent variable were the same as the Freight Expenditure Index's regression model. When authority score, paid costs, bounce rate, time on site, and website visits increase by 1%, the Freight Expenditure Index varies by \(-\)22.5%, \(-\)120.7%, 55.5%, 24.8%, and \(-\)74.7%, respectively. Hence, the paper's second research hypothesis (H2) is also verified, meaning that the Freight Expenditure Index of supply chain firms can be reduced by the adjustment of their website big data analytics.