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62 CHAPTER 5 Auto LOS Model 5.1 Model Development redundant explanatory variables (e.g., average travel speed and number of stops) and by retaining those explanatory Identification of Key Variables variables that were highly correlated with the mean clip rat- A correlation analysis was performed to determine what ing. The explanatory variables included in the stepwise relationships may exist between the dependent variable regression exercise were as follows: (i.e., individual participant ratings of LOS) and a dataset of 78 independent variables represented in the video clips or Space mean speed, transformations of said variables (i.e., log of mean travel Number of stops, speed). The correlation analysis revealed that no less than Stops per mile, 69 variables had a statistically significant relationship with Presence of median, individual participant ratings of LOS. Presence of exclusive left-turn lane, Exhibit 65 summarizes the correlation analysis, including Presence of trees rating, and Kendall's tau rank correlation coefficients. Some variables Pavement quality rating. have not been included in order to reduce the size of the table. For example, transformations of variables have not been in- Forward stepwise regression techniques were used to allow cluded because they tend to have the same or similar tau rank for the inclusion of variables into the model only if they could correlation coefficient patterns and significance values. Care increase the ability of the model to predict the dependent was taken in selecting explanatory variables included in the variable shown through the increase in R-square value. The modeling effort so as to avoid including variables that were results of the stepwise multiple linear regression are shown in highly correlated with each other. Exhibit 67. The adjusted R-square value for the overall model Exhibit 66 illustrates the correlation analysis done of the is 0.673. explanatory variables to understand the relationships be- The model is tween these variables. In this table, the tau rank correlation Mean Auto LOS = 3.8 - 0.530(Stops) - 0.155(Median) coefficients are shown for correlations between space mean + 0.355(Left-Turn Lane) + 0.098(Trees) speed and the previously listed explanatory variables. In this + 0.205(Pavement Quality) (Eq. 9) table, all significance values are <0.10, meaning the relation- ships are statistically significant at the 90% level. Where Mean Auto LOS = 6.0 for LOS A and 1.0 for LOS F Stops = number of times in video clip that auto Linear Regression Tests speed drops below 5 mph. Linear regression techniques were first explored to deter- Median = 3 if raised median (curbs between mine if a multiple linear relationship might exist that could opposing traffic streams), 2 if two-way estimate the mean rating obtained for each video clip shown left-turn lane, 1 if no opposing traffic in Phase I and/or II of the study. stream (one-way street), 0 if no separa- Independent variables to be used to estimate the depend- tion between opposing traffic streams. ent variable (mean clip rating) were selected from the larger Left-Turn Lane = one if present, zero otherwise. Exclusive set of explanatory variables. This was done by controlling for left-turn lane can be of any length or

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63 Exhibit 65. Correlation Between Explanatory Variables and LOS Ratings. Variable tau Rank Correlation Significance Coefficient p-value Space Mean Speed 0.317 0.000 Total Travel Time -0.315 0.000 Lane Width 0.307 0.000 Number of Stops per Mile -0.307 0.000 Sign Quality 0.268 0.000 Tree Presence 0.248 0.000 Sidewalk Width -0.244 0.000 Has Ex Left-Turn Lane 0.223 0.000 Pedestrian Presence -0.218 0.000 Number of Signals per Mile -0.217 0.000 Control Delay per Mile -0.210 0.000 Speed Limit 0.198 0.000 Median Presence 0.175 0.000 Stops per Signal -0.159 0.000 Lane Marking Quality 0.110 0.000 Median Width 0.107 0.000 Variation in Speed -0.084 0.000 Number of Through Lanes -0.065 0.003 Separation Between Sidewalk and Travelway 0.055 0.010 width. Two-way left-turn lanes do not presence of an exclusive left-turn lane, those variables which count as exclusive left-turn lanes. were significant in Model 1. This new model's details are pro- Trees = 3 if many, 2 if some, 1 if few or none vided in Exhibit 68. Pavement Quality = 4 if new, 3 if typical, 2 if cracked, 1 if poor. In this model each of the two variables, number of stops, and presence of an exclusive left-turn lane were significant at The R-square statistic for this model equals 0.673, mean- the 0.05 level resulting in the following: ing 67 percent of the variation in mean participant ratings can be estimated by the model; however, several variables Mean Auto LOS = 4.327 - 0.622 (Stops) included in the model do not contribute significantly to + 0.293 (Left Turn Lane) (Eq. 10) the overall model predictive power, as indicated by their high p-values. Where To address the inclusion of variables that are not statistical Mean Auto LOS = 6.0 for LOS A and 1.0 for LOS F contributors to the model, another regression model was Stops = Number of times in video clip that auto developed that included only the number of stops and the speed drops below 5 mph. Exhibit 66. Correlation Between Space Mean Speed and Other Explanatory Variables. Variable tau Rank Correlation Coefficient Space Mean Speed 1.00 Total Travel Time 0.617 Lane Width -0.694 Number of Stops per Mile 0.270 Sign Quality 0.442 Tree Presence 0.474 Sidewalk Width -0.423 Has Ex Left-Turn Lane 0.264 Pedestrian Presence -0.445 Number of Signals per Mile -0.270 Control Delay per Mile -0.721 Speed Limit 0.381 Median Presence 0.147 Stops per Signal -0.462 Lane Marking Quality 0.111 Median Width 0.117 Variation in Speed -0.287 Number of Through Lanes -0.222 Separation Between Sidewalk and Travelway 0.104