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From page 167... ... 167 Overview This appendix presents the validation analysis of the L03 data-poor models. Appendix H of the L03 Report contains a set of models that predict the following travel time index (TTI) Read the entire page →
From page 168... ... 168 the validation, the mean TTI was plugged into the model equations to calculate the reliability statistics, which were then compared to the measured values. Table D.1 shows that far fewer section-year data points were generated for the peak period than for the midday period. Read the entire page →
From page 169... ... 169 value for comparison, set here to be zero. To draw a conclusion, if the calculated t-value is larger than some threshold ta (e.g., a = 5%) Read the entire page →
From page 170... ... 170 and suggesting that some data transformation may be needed to get a better fit to the data. The histogram in Figure D.3 and the normality plot in Figure D.4 show that the distribution of residuals close to the mean varies less than that for a normal distribution. Read the entire page →
From page 171... ... 171 regions. The t-test results reject the null hypothesis that the average of the residuals is zero. Read the entire page →
From page 172... ... 172 show a nonconstant variance, but none of the residuals are large. The residuals do not follow a normal distribution. Read the entire page →
From page 173... ... 173 normality plot in Figure D.12 indicate that the residual distribution has less variance compared with a normal distribution. The 95% confidence interval of estimated residual mean does not include zero, and the t-test yields a p-value of 0.0233 (Table D.6) Read the entire page →
From page 174... ... 174 confirms that most of the residuals are above the zero reference line, with a positive skew in the residual distribution. The estimated residual mean is 0.0358 with an estimated confidence interval of 0.0194 to 0.0522. Read the entire page →
From page 175... ... 175 the California, Salt Lake City, and Spokane data sets and underestimate it in the Minnesota data. Residual analysis indicates violation of the basic normality, zero error mean, and constant error variance assumptions (summarized in Table D.7 with all "not satisfactory" assessments) Read the entire page →
From page 176... ... 176 Region Specific califoRnia The scatter plot of California data samples shows an initial tendency to fall below the predicted curve until the mean TTI exceeds 1.7, at which point the data samples tend to be above the predicted curve (Figure D.21) Read the entire page →
From page 177... ... 177 overestimation tends to increase as the mean TTI increases, meaning that the residuals are positively correlated with the predicted values. The residuals are not normally distributed. Read the entire page →
From page 178... ... 178 The measured standard deviation increases faster than the predicted standard deviation. The histogram (Figure D.27) Read the entire page →
From page 179... ... 179 (Figure D.31) Read the entire page →
From page 180... ... 180 Summary Overall, nonconstant variance is a problem for all data sets, and the nonzero residual mean is a problem for all data sets except for Salt Lake City. The California data set presents relatively good residual distributions that closely follow a normal distribution. Read the entire page →
From page 181... ... 181 Figure D.34. Residual plot -- PctTripsOnTime50mph -- AllData. Read the entire page →
From page 182... ... 182 (Figure D.37) Read the entire page →
From page 183... ... 183 The t-test results show sufficient evidence to reject the zero residual mean hypothesis. Summary The PctTripsOnTime50mph data-poor model can largely predict the data trend of the measured validation data sets but tends to underestimate PctTripsOnTime50mph, especially when the mean TTI is small. Read the entire page →
From page 184... ... 184 distribution closely follows a normal distribution when the residual is less than zero but is skewed when the residual is larger than zero. The Student's t-test yields a p-value less than 0.0001, indicating that the null hypothesis can be rejected at a 95% level of confidence, as shown in Table D.18. Read the entire page →
From page 185... ... 185 the measured PctTripsOnTime45mph decreases much more slowly than the predicted curve. The residuals are positively correlated with the predicted value, which implies lack of fit. Read the entire page →
From page 186... ... 186 concave-like shape. A nonconstant variance problem is also indicated by the cone shape in the residual plot. Read the entire page →
From page 187... ... 187 Table D.21. Statistical Residual Analysis Results -- PctTripsOnTime30mph -- AllData Table D.21.a. Read the entire page →
From page 188... ... 188 the Spokane data satisfy the zero residual mean assumption. The normal-distributed residual assumption and the constant residual variance assumption are not satisfied in any regional data set. Read the entire page →
From page 189... ... 189 Appendix D Attachment 95th-Percentile TTi Model California Figure D.57. Residual plot -- 95th-percentile TTI -- California. Read the entire page →
From page 190... ... Minnesota Table D.23. Residual Analysis -- 95th-Percentile TTI -- California (continued) Read the entire page →
From page 191... ... 191 Salt Lake City Figure D.63. Residual plot -- 95th-percentile TTI -- Salt Lake City. Read the entire page →
From page 192... ... 192 Spokane Figure D.66. Residual plot -- 95th-percentile TTI -- Spokane. Read the entire page →
From page 193... ... 193 90th-Percentile TTi Model California Table D.27. Residual Analysis -- 90th-Percentile TTI -- California Table D.27.a. Read the entire page →
From page 194... ... 194 Minnesota Figure D.72. Residual plot -- 90th-percentile TTI -- Minnesota. Read the entire page →
From page 195... ... 195 Salt Lake City Figure D.75. Residual plot -- 90th-percentile TTI -- Salt Lake City. Read the entire page →
From page 196... ... 196 Spokane Figure D.78. Residual plot -- 90th-percentile TTI -- Spokane. Read the entire page →
From page 197... ... 197 80th-Percentile TTi Model California Figure D.81. Residual plot -- 80th-percentile TTI -- California. Read the entire page →
From page 198... ... 198 Minnesota Figure D.84. Residual plot -- 80th-percentile TTI -- Minnesota. Read the entire page →
From page 199... ... 199 Salt Lake City Figure D.87. Residual plot -- 80th-percentile TTI -- Salt Lake City. Read the entire page →
From page 200... ... 200 Spokane Figure D.90. Residual plot -- 80th-percentile TTI -- Spokane. Read the entire page →
From page 201... ... 201 Standard deviation of TTi Model California Figure D.93. Residual plot -- standard deviation of TTI -- California. Read the entire page →
From page 202... ... 202 Minnesota Figure D.96. Residual plot -- standard deviation of TTI -- Minnesota. Read the entire page →
From page 203... ... 203 Salt Lake City Figure D.99. Residual plot -- standard deviation of TTI -- Salt Lake City. Read the entire page →
From page 204... ... 204 Spokane Figure D.102. Residual plot -- standard deviation of TTI -- Spokane. Read the entire page →
From page 205... ... 205 Percentage of On-Time Trips with Over 50 mph Mean Speed California Figure D.105. Residual plot -- percentage of on-time trips over 50 mph -- California. Read the entire page →
From page 206... ... 206 Minnesota Figure D.108. Residual plot -- percentage of on-time trips over 50 mph -- Minnesota. Read the entire page →
From page 207... ... 207 Salt Lake City Figure D.111. Residual plot -- percentage of on-time trips over 50 mph -- Salt Lake City. Read the entire page →
From page 208... ... 208 Spokane Figure D.114. Residual plot -- percentage of on-time trips over 50 mph -- Spokane. Read the entire page →
From page 209... ... 209 Percentage of On-Time Trips with Over 45 mph Mean Speed California Figure D.117. Residual plot -- percentage of on-time trips over 45 mph -- California. Read the entire page →
From page 210... ... 210 Minnesota Figure D.120. Residual plot -- percentage of on-time trips over 45 mph -- Minnesota. Read the entire page →
From page 211... ... 211 Salt Lake City Figure D.123. Residual plot -- percentage of on-time trips over 45 mph -- Salt Lake City. Read the entire page →
From page 212... ... 212 Spokane Figure D.126. Residual plot -- percentage of on-time trips over 45 mph -- Spokane. Read the entire page →
From page 213... ... 213 Percentage of On-Time Trips with Over 30 mph Mean Speed California Figure D.129. Residual plot -- percentage of on-time trips over 30 mph -- California. Read the entire page →
From page 214... ... 214 Minnesota Figure D.132. Residual plot -- percentage of on-time trips over 30 mph -- Minnesota. Read the entire page →
From page 215... ... 215 Salt Lake City Figure D.135. Residual plot -- percentage of on-time trips over 30 mph -- Salt Lake City. Read the entire page →
From page 216... ... 216 Spokane Figure D.138. Residual plot -- percentage of on-time trips over 30 mph -- Spokane. Read the entire page →

From page 167...

... 167 Overview This appendix presents the validation analysis of the L03 data-poor models. Appendix H of the L03 Report contains a set of models that predict the following travel time index (TTI)