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\subsection{Disaggregated Speed Regression}  To better manage results due to the number of variables, kmeans clustering is employed. Several clusters were performed using between 3 and 6 centroids to find a suitable model that i) produces the most meaningful and interpretable clusters, ii) produces a random effects regression model with explanatory power, and iii) where p-values still remain relatively significant. However, because we know the different indicators are statistically independant, we may find that different clusters offer different explanatory power. TABLE Table~\ref{tab:cluster_speed_profile}  lists the distribution of observations (at the site level and at the disaggregated level) for the clusters used to model speed and offers a short profile for each. Variable statstics are presented in TABLE. \begin{table}  \caption{K-means cluster profile for speed regression}  \label{tab:cluster_speed_profile}  \begin{tabular}{llll}  Cluster & Description & Groups & Observations \\ \hline  c1\_s & Arterial with wide lanes, far distance to upstream intersections, and very low flow ratios, mixed land-usage & 6 & 5,232 \\  c2\_s & Regional, single lane highways in industrial complex with mixed flow ratios & 6 & 13,267 \\  c3\_s & A mix of highway ramps and arterials with extremely polarized flow ratios & 13 & 17,130 \\  c4\_s & Residential collectors with reasonably well mixed flow ratios and short upstream distance to nearest intersection & 6 & 325 \\  c5\_s & Traffic circle converted to roundabout (2 lanes, extremely large diameters, tangential approach angle) & 4 & 10,295 \\  c6\_s & 2 lane arterials near commercial or institutional land use and very high flow ratios. & 6 & 14,840 \\  ~ & ~ & ~ & ~ \\  ~ & ~ & ~ & ~ \\  \end{tabular}  \end{table}  \begin{verbatim}  cluster64 |  54580 | Freq.  ----------+-----------  1 | 6 | Arterial with wide lanes, far distance to upstream intersections, and very low flow ratios; mixed LU  2 | 6 | Regional, single lane highways in industrial complex with mixed flow ratios  3 | 13 | A mix of highway ramps and arterials with extremely polarised flow ratios  4 | 6 | Residential collectors with reasonably well mixed flow ratios and short upstream distance to nearest intersection  5 | 4 | Traffic circle converted to roundabout (2 lanes, extremely large diameters, tangential approach angle)  6 | 6 | 2 lane arterials near commercial or institutional land use and very high flow ratios.  cluster6454580 |  | Freq. Percent Cum.  ------------+-----------------------------------  1 | 5,232 8.56 8.56  2 | 13,267 21.72 30.28  3 | 17,130 28.04 58.32  4 | 325 0.53 58.86  5 | 10,295 16.85 75.71  6 | 14,840 24.29 100.00  ------------+-----------------------------------  Total | 61,089 100.00    \end{verbatim}  \begin{verbatim}  cluster6454580 | n_star~s n_app_~s n_exit~s n_slip~e a_quad~e r_out_~t r_in_s~t d_app_~r app_sp~t flowra~o