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64 Exhibit 67. Multiple Linear Regression Model #1. Statistical Significance Variable Standard Coefficient t-Statistic (p-value) Constant 3.8 9.832 0.00* Number of Stops -0.530 -4.154 0.00* Median Presence -0.155 -0.898 0.377 Presence of Ex. Left-Turn Lane 0.355 1.903 0.067* Tree Rating 0.098 0.816 0.421 Pavement Quality 0.205 1.556 0.130 *Statistically Significant at the 0.10 confidence interval Left-Turn Lane = Presence of exclusive left-turn lane at all otherwise. Exclusive left-turn lane can be intersections. Equals one if present, zero of any length or width. otherwise. Exclusive left-turn lane can be This model has an adjusted R-square value of 0.545, infe- of any length or width. rior to Models 1 and 2. The lowest value that this model can This second model has an adjusted R-square value of produce is 2.673, the value of the constant. Thus the LOS 0.647, slightly inferior to Model 1. could never be below LOS E. Similar model formats were attempted using average space mean speed as the primary predictor of mean participant rat- Limitations of Linear ing; however, the adjusted R-Square values were lower at Regression Modeling 0.545, meaning only 54.5% of the variation in mean partici- pant ratings could be explained by the model. For this model, Linear regression techniques are not particularly the best explanatory variables space mean speed, presence of an ex- model specification choice when modeling ordered response clusive left-turn lane, and tree rating were included in the variables in that linear regression models attempt to deter- stepwise regression analysis. In this case, tree rating did not mine the best-fitting linear equation according to the least- contribute significantly to the prediction power of the model square criterion, such that the sum of the squared deviations and so was removed. Exhibit 69 contains statistical informa- of the predicted scores from the observed scores is minimized tion for Model 3. to give the most accurate prediction. This assumes that, for a The end result is a model of the following form measured change in the explanatory variables, there is a measured linear change in the dependent variable, namely Mean Auto LOS = 2.673 + 0.479 (Speed) the mean participant rating. Linear regression models also + 0.403 (Left-Turn Lane) (Eq. 11) predict a continuous variable, which is different than what Where was asked of participants in the study. For example, linear re- Mean Auto LOS = 6.0 for LOS A and 1.0 for LOS F gression models will also predict values such as 3.42 LOS, Speed = average space mean speed in mph. lying between LOS C and D. Left-Turn Lane = Presence of exclusive left-turn lane at all These limitations led the research team to investigate the intersections. Equals one if present, zero use of cumulative logistic regression, which can predict the Exhibit 68. Multiple Linear Regression Model #2. Statistical Significance Variable Standard Coefficient t-Statistic (p-value) Constant 4.327 16.428 0.00* Number of Stops -0.622 -5.152 0.00* Presence of Ex. Left-Turn Lane 0.293 2.427 0.021 *Statistically Significant at the 0.05 confidence interval Exhibit 69. Multiple Linear Regression Model #3. Statistical Significance Variable Standard Coefficient t-Statistic (p-value) Constant 2.673 10.483 0.00* Space Mean Speed 0.479 3.657 0.01* Presence of Ex. Left-Turn Lane 0.403 3.075 0.004* *Statistically Significant at the 0.05 confidence interval