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\subsubsection{Yielding Post-Encroachment Time}  A stepwise linear regression is performed on median yPET following $\zeta_{PET} < 5$~seconds at each site, to test all explainable differences between sites, shown in Table~\ref{tab:analysis_zones}. yPET observations are seperated separated  into lead yPET---when the roundabout road user enters the merging zone first---and lag yPET---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. Meanwhile, while Outside Radius and Flow are found to be associated with lag yPET, having a moderately powerful relationship, region is not found to be significantly correlated with median lag yPET either. 
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A stepwise linear regression of motion pattern-based serious $TTC_{15^{th}cmp}$ events (measured in events per hour) is performed, using the previously mentioned weighted SEC methodology with a literature-standard threshold of $\zeta < 1.5$~seconds. No statistically significant model is found to explain $TTC_{15^{th}cmp_{\zeta < 1.5}}$ events, however.  Finally, Next,  a SCC regression is attempted. As this SCC TTC  data is hierarchical, a hierarchical---tens of thousands of TTC observations at each site---a  random effects regression model is used, using the log of the dependent variable $TTC_{15^{th}cmp}$: \begin{equation}  ln(TTC_{15_{ij}}) = \alpha + {\sum}_{k} \beta_k X_{kij} + u_{ij} + \epsilon_{ij} 
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for $j=1,...,m$ pairs of road users and for sites $i=1,...,n$ (merging zones), where $\alpha$ is the model intercept, $\beta_k$ is the coefficient of factor $X_{kij}$ for $k=1,...,m$ factors, $u_{ij}$ is interaction-specific random error (also referred to as the \textit{between} error), and $\epsilon_{ij}$ is the ``ordinary'' regression error (also refereed to as the \textit{within} error). The random effects model adjusts the fixed-effects model with the between-effects model. It models the mean response from means calculated from the interction for each group. In this way, the random effects model is a weighted average of the fixed-effects and between-effects models.   Results of the regression  are shown in Table~\ref{tab:se_regression_ttc_continuum}. This The regression  yields a moderately predictive model with a between $R^2 = 0.425$ (accounting (which accounts  for differences between merging zones). This is The difference in safety between sites seems to be in large part  accounted for by the Swedish Site variable, as it is associated with increasing TTC by 0.293~s on average, an increase in expected $TTC_{15^{th}cmp}$ of 0.293~s,  thus leading to hypothetical reductions suggesting that sites located in Sweden benefit from a non-trivial reduction  in collision probability. Construction year (or elapsed time since roundabout construction) is not found to be correlated significantly suggesting that, at this time scale at least, acclimatisation to roundabouts is not a significant effect.  A very  minor within-effect is also noted, with fifteen-second traffic exposure being  associated with an increasing TTC. As $TTC_{15^{th}cmp}$ at a rate of 0.017s per road user present within 15 seconds. This appears to be somewhat counterintuitive, but it might suggest that increasing driving complexity really does have a positive effect on increasing driver alertness. Furthermore, as  evidenced with the angle of incidence parameter, interactions with a small angle of incidence, i.e. rear end conflicts, are seem to be  associated with lower TTC $TTC_{15^{th}cmp}$  values than with a larger angle of incidence, i.e. side swipe conflicts.Finally, construction year (or elapsed time since roundabout construction) is not found to be correlated significantly.  %The sign and magnitude of the coefficient associated with this parameter is consistent with the coefficient for angle of incidence observed in Chapter~\ref{ch:C3}. Finally, it is worth noting that the approach dominance and absolute flow ratio parameters are not significantly correlated with TTC as is the case with the Québec roundabout merging zone exclusively.   \begin{table}[ht] 
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\hline  & Coefficient & P>|t| \\  \hline   _cons & 0.583 & 0.000 \\ Swedish Site & 0.293 & 0.029 \\ \hline Fifteen Second Exposure & 0.01690 & 0.000 \\ Interaction Angle & 0.003279 & 0.000 \\ \hline   \textbf{Within $R^2$} & \multicolumn{2}{p{1.25in}}{0.0540} \\  \textbf{Between $R^2$} & \multicolumn{2}{p{1.25in}}{0.4244} \\ 
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%  %Results of this model are presented in Table~\ref{tab:se_regression} Sweden (between groups effect) is associated with a significant increase in TTC (and thus more available reaction time in the event of a collision-course). TTC also increased as a result of a larger micro-exposure and as the interaction angle increased, suggesting that increased traffic and head-on (or at least side-swipe) collision courses were beneficial in increasing available reaction time.  %  %