deletions | additions       diff --git a/subsection_Regression_Results_subsubsection_Speed__.tex b/subsection_Regression_Results_subsubsection_Speed__.tex  index 247f5bf..13cf097 100644  --- a/subsection_Regression_Results_subsubsection_Speed__.tex  +++ b/subsection_Regression_Results_subsubsection_Speed__.tex 
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\subsection{Regression Results}  \subsubsection{Speed}  A stepwise linear regression is performed on mean road user merging zone speed measured (in km/h) at each merging zone individually, testing all explainable differences between sites, shown in Table~\ref{tab:analysis_zones}. Table~\ref{tab:analysis_zones}, with the exception of accident statistics, given that this dataset isn't as reliable.  The coefficients of regression, adjusted $R^2$, Wald test score, and number of observations are provided in Table~\ref{tab:se_regression_mean_speed}. Note that roundabout outside radius, flow ratio, land use, urban density, and construction year were not significant in predicting mean speed. Instead, a relatively  good model (with an adjusted $R^2 = 0.658$) with only two factors remains: \begin{itemize}  \item A significant reduction in mean speed of 4.5~km/h is observed at the Swedish sites.  \item Increases in hourly traffic volume are correlated with reductions in mean speed as well. This is not surprising, given standard traffic flow theory (e.g.\ Greenshield's Model).  \end{itemize}  These The  conclusions are similar to those drawn from of the regression analysis support what was suggested in  the exploratory analysis, suggesting concluding  that regional effects such as education, enforcement (recall that all sites in this study have identical posted speed limits), or culture might be in play instead. %stepwise, pr(.1001) pe(.1): regress mean_speed sweden hourlyflowvehhln outsideRadius_m yearsSinceBuilt flowRatio lu2 d2 d3  %stepwise, pr(.1001) pe(.1): regress start_gap_lt5s_median sweden hourlyflowvehhln outsideRadius_m yearsSinceBuilt flowRatio lu2 d2 d3 
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& \multicolumn{2}{p{1.25in}}{\textbf{Mean Speed}} & \multicolumn{2}{|p{1.25in}}{\textbf{Median Lag yPET}}\\  & \textbf{Coefficient} & \textbf{$P>|t|$}& \textbf{Coefficient} & \textbf{$P>|t|$}\\  \hline   \_cons constant  & 35.898 & 0.000 & 1.303 & 0.018 \\ Swedish Site & -4.460 & 0.007 & - & - \\  Outside Radius (m) & - & - & .0798 & 0.010 \\  Flow (per hour per lane) & -0.0240 & 0.003 & -.00336 & 0.001 \\ 
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\subsubsection{Yielding Post-Encroachment Time}  A stepwise linear regression is performed on median $yPET_{\zeta < 5}$ at each site, to test all explainable differences between sites, as shown in Table~\ref{tab:analysis_zones}. $yPET_{\zeta < 5}$ observations are separated into lead $yPET_{\zeta < 5}$: when 5}$---when  the roundabout road user enters the merging zone first; and first---and  lag $yPET_{\zeta < 5}$: when 5}$---when  the approach road user enters the merging zone first. The coefficients of regression, adjusted $R^2$, Wald test score, and number of observations are provided in Table~\ref{tab:se_regression_mean_speed}. No suitable regression model is found for lead $yPET_{\zeta < 5}$. Meanwhile, while Outside Radius and Flow are found to be associated with lag $yPET_{\zeta < 5}$, having a moderately powerful relationship, region is not found to be significantly correlated with median lag $yPET_{\zeta < 5}$ either. 
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\label{tab:se_regression_ttc_continuum}  \begin{tabular}{p{2.0in}|p{0.75in}p{0.5in}}  \hline  & \textbf{Coefficient} & \textbf{$P>|t|$}\\ \hline   _cons constant  & 0.583 & 0.000 \\ Swedish Site & 0.293 & 0.029 \\  \hline   Fifteen Second Exposure & 0.01690 & 0.000 \\ 
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\textbf{Within $R^2$} & \multicolumn{2}{p{1.25in}}{0.0540} \\  \textbf{Between $R^2$} & \multicolumn{2}{p{1.25in}}{0.4244} \\  \textbf{Overall $R^2$} & \multicolumn{2}{p{1.25in}}{0.0204} \\  \textbf{Wald prob prob.  $> F$} & \multicolumn{2}{p{1.25in}}{0.0000} \\ \textbf{Observations} & \multicolumn{2}{p{1.25in}}{23565} \\  \textbf{Groups} & \multicolumn{2}{p{1.25in}}{19} \\  \hline 
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%  %is performed for mean speed and median lag yPET, controlling for the factors listed in Table~\ref{tab:analysis_zones}. Results of these regression models are presented in Table~\ref{tab:se_regression}.   %  %Most of the factors in Table~\ref{tab:analysis_zones} are not found to be significantly associated with speed, except for hourly flow per lane, which had, unsuprisingly, unsurprisingly,  a negative effect on speed (i.e. congestion). Overall speeds were significantly reduced with a coeficient coefficient  of 4.5~km/h at Swedish roundabouts compared to Québec roundabouts. The model yields good predictive power, with an adjusted $R^2$ of 0.658. %  %Roundabout radius and hourly traffic had a positive and negative effects on median lag yPET, respectively, suggesting that smaller roundabouts and higher flows result in generate more aggressive yielding (unsurprising given that space is more constrained and fewer gaps are present). There was no difference between Swedish and Québec roundabouts in this regard. Median lead yPET was not significantly associated with any factors at all.  %