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
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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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plz solve question (c) with explanation within 30-40 mins and get upvotes
Transcribed Image Text:crash
329
201
263
170
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
107300
107500
97100
125600
71900
53000
46000
43600
479
160
257
87
65
132
58
32
53
70
64
y = -13.1 + 0.002 * x
45700
45700
59900
68400
66600
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 R
using the following equations:
103
52
63100
47
47
65700
63400
65700
83
54
66100
69700
R² =1- SSE
SST
68
71
68100
69600
96
64
20
50
85
79
66500
55700
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
27000
26700
crash frequency for segment i; ỹ= average observed crash frequency for all segments; and n
= number of segments (= 48).
26400
24000
22400
11
(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)
E:(xi – x)²
53
73
where x = observed AADT for segment i; x = 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 (tenit,0.025 = 2.01 for
sample size = 48); and 3) the confidence interval in the sketch.
21900
31
24
17
20900
24000
22400
22200
20200
17300
12100
6450
44
25
18
7
(c) Based on the sign of the coefficient b, discuss the effect of AADT on crash frequency. Is the
effect realistic? Explain.
1
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