crash 329 201 AADT Question 3 (" The records of crash frequency and annual average daily traffic volume (AADT) in 2009-2012 were collected from 48 roadway segments of Highway 401 between Windsor and London in Ontario. The data are stored in data-2009-2012.txt posted on Blackboard. A crash frequency model was developed to predict the number of crashes based on AADT using a linear regression model as follows: 103600 107300 263 170 479 160 257 87 107300 107500 97100 125600 71900 53000 65 132 58 32 53 70 64 46000 43600 45700 45700 59900 68400 66600 y = -13.1 + 0.002 * x where y = crash frequency (“crash" in the file) and x = AADT. (a) Plot the graphs of the observed crash frequencies (x-axis) and the predicted crash frequencies using the above linear regression model (y-axis) in a scatter chart. Calculate the value of R² using the following equations: 103 52 47 63100 65700 63400 65700 47 83 54 SSE R =1- SST 66100 69700 68100 69600 66500 55700 27000 68 71 Συ- 96 64 20 50 85 79 11 where SSE = the sum of squares of errors (or the unexplained variance by the model), SST = the total variance in the data, y,= observed crash frequency for segment i; ŷ,= the predicted crash frequency for segment i; ỹ= average observed crash frequency for all segments; and n = number of segments (= 48). 26700 26400 24000 22400 (b) Calculate the t-statistics of the coefficient of AADT (b = 0.002) using the following equation: 38 49 23100 21300 42 17 21300 21800 23400 21500 SSE/(n – 2) V£:(xt – x)² 53 73 where x, = observed AADT for segment i; & = average observed AADT for all segments. 70 85 36 66 18100 19300 21000 Assess statistical significance of the coefficient b at a 95% confidence interval using hypothetical testing. Assume null hypothesis (Ho): b is not statistically different from zero and alternative hypothesis (H1): b is statistically different from zero. Sketch a t-distribution curve and show 1) the calculated t-statistics; 2) the critical values of t-statistics (tent,0.025 = 2.01 for sample size = 48); and 3) the confidence interval in the sketch. 21900 20900 31 24 17 24000 22400 44 25 22200 20200 17300 (c) Based on the sign of the coefficient b, discuss the effect of AADT on crash frequency. Is the effect realistic? Explain. 18 7 12100 6450