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First International Conference on Construction In Developing Countries (ICCIDC–I) “Advancing and Integrating Construction Education, Research & Practice” August 4-5, 2008, Karachi,, Pakistan

Blackspot Study and Accident Prediction Model Using Multiple Liner Regression

Fajaruddin Mustakim

Lecturer, Department of Building and Construction Engineering, Universiti Tun Hussein Onn Malaysia fajardin@uthm.edu.my

Ismail Yusof

Head of Department, Department of Geotechnical and Transportation Engineering, Universiti Tun Hussein Onn Malaysia

Ismail Rahman

Deputy Dean, Faculty of Civil and Enviromental Engineering, Universiti Tun Hussein Onn Malaysia

Abdul Aziz Abdul Samad Dean, Faculty of Civil and Enviromental Engineering, Universiti Tun Hussein Onn Malaysia

Nor Esnizah Binti Mohd Salleh

Undergraduated, Faculty of Civil and Enviromental Engineering, Universiti Tun Hussein Onn Malaysia Abstract Factor that affect the risk of increased injury in the event of an automotive accident include reckless driving, environmental factor and roadway condition. The purpose of this study is to develop an accident prediction model for Federal Route 50 by using multiple linear regression analysis. The road accident trend and blackspot ranking were established at Federal Route (FT50) Batu Pahat – Ayer Hitam. It revealed that the percent accident reduction by changing the measures of each variables are, one access point per kilometer reduction can reduce accidents by 9.32 %, 5 kilometer per hour speed reduction can reduce accidents by 27.2%, 100 vehicle per hour volume reduction can reduce accidents by 4.33 % meanwhile an increment of one second in gap will reduce accident by 1.20%. Keywords Blackspot ranking, accident prediction model 1. Introduction Road accidents are one of the major contributors of human deaths in Malaysia. In the year 2006, 341,252 accidents were recorded, resulting in an average 18 deaths from road accidents every single day. Federal Route 50 from Batu Pahat to Ayer Hitam experienced 5,917 road accidents between the years 2000 and 2006, killing 188 people and injuring 1,330 people. The primary objective of the study is to identify factors that contribute to the cause of accident and the development of an accident prediction model for Federal Route 50.

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Growth in urbanization and in the number of vehicle in many developing countries has led to the increase in traffic accidents on road networks which were never designed for the volumes and types of traffic which they are now required to carry. In addition, unplanned urban growth has led to incompatible land uses, with high levels of pedestrians/vehicle conflicts. The drift from rural areas to urban centre often result in large numbers of new urban resident unused to such high traffic levels. Many developing countries continue to repeat the mistakes of the industrialized countries , many still permit linear development with direct access from frontage properties along major roads even though this is know to lead to safety problems. It is possible to identify hazardous sections of the road network so that appropriate remedial measures can be undertaken to reduce the likelihood and severity of accidents at those locations. This has proven to be one of the most cost-effective ways of improving road safety in industrialized countries. Accident prediction models have been developed through statistical analysis for this purpose. An accident model is generally an algorithm pitting a dependent variable against several independent variables, each of which is assigned a constant. The dependent variable in an accident prediction model is the number of accidents, while the independent variables may be quantitative variables such as road cross-section dimensions, horizontal curvature and traffic volume, speed and of qualitative variable such as type of terrain, road shoulder and median. There is an extensive literature devoted to analysis of traffic accidents and crash modeling. The majority of this literature references the studies that deal primarily with analysis of crash involvement and prediction of crash. Since this research deal with analysis of injury severity and its accident factors, this review attempts only to present the most relevant work in his area. Logistic regression (a type of regression where the dependent is a categorical as opposed to a numerical variable) has been the most popular technique in developing injury severity prediction models. Lui and McGee (1998) used logistic regression to analyze the probability of fatal outcomes of accidents given that the crash has occurred. In yet another study a logistic regression approach was used to examine a contribution of individual variable to the injury severity (Al-Ghamdi, 2002). The study was limited to 560accident obtained from the police records in Riyadh, Saudi Arabia. According to the logistic regression results, out of nine independent variables used in this study, only two were found to be statistically significant with respect to the injury severity: location and cause of accident. For example, the odds of being in a fatal accident at a non-intersection location are 2.64 higher than those at an intersection, and the odds of severe injury increases on accidents caused by over-speeding and entering the wrong way traffic. Use of artificial neural network as the modeling approach in analysis of crash-related injury severity has been relatively scarce. The only related study that was found in the literature employed artificial neural networks to model the relationship between driver injury severity and crash factors related to driver, vehicle, roadway, and environment characteristics (Abdelwahab and Abdel-Aty 2001). Road traffic accident is a rare, random, multi factor event always preceded by a situation in which one or more road user have failed to cope with their environment, resulting in a collision on the public highway be recorded by police (Radin, 2005). Transportation is an essential part of modern existence, linking the various activities in which people participate especially at home, work, school and go to shopping or recreation. From Royal Malaysian Police (PDRM) data, every year accident in Malaysia constant increase year by year and Johor is among highest after Wilayah Perseketuan (Figure 1).

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Figure 1 : Number of Accident By State,(1997-2006)

Malaysian Police statistic of road accident in Johor, federal road FT 050 among those highest occurred accident in the accident records. From Figure 2, 994 case of road accidents recorded in the year 2005, 999 case of road accidents recorded in the year 2006 and in year 2007 with 731 case.

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Figure 2 : Number of accident along FT 050 (2000-2007) Source : PDRM (2007)

2.0 Methodology The accident analysis process involves the identification of accident blackspot locations, establishment of general patterns of accident, analysis of the factor involved, site studies, and development of an accident prediction model using Multiple Linear Regression.

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2.1 Data Collection Accident data were collected from Batu Pahat Traffic Police Station, Batu Pahat Public Work Department, Bukit Aman Royal Malaysia Police, Road Transport Department, Parit Raja Health Clinic Center, Universiti Tun Hussein Onn Malaysia (UTHM) and Road Safety Research Center UPM Serdang. The accident database was obtained from the POL27 and the crash records were collected from the year 2000 to 2007. 2.2 Analysis Of Accident Data The purpose of preliminary analysis of the traffic accident data is to determine the broad of the accident problem. At this stage the general patterns and trend of accident are established. Types of accident trend and statistics for the FT 50 were:

a) Total number of accident at FT 050 for year 2000 to 2007. b) Accident by hours of the day for year 2003 to 2007. c) Accident by type of fault for year 2003 to 2007. d) Total number of fatal by fault categories for year 2003 to 2007.

2.3 Identify Blackspot Location Identification and prioritisation of accident blackspot location were carried out by using the following methods: (i) Ranking accident point weightage (ii) Ranking of the top ten accident sections accident 2.4 Site Investigation The site investigation is a very important element of any accident investigation. The site investigation purpose to support the data from analysis, this is can give the best result in the study. For example the number of junction might give impact to the traffic. The function of site investigation include : a) To confirm accident causal factors as suspected from the analysis. b) To correlate analysis findings and additional information with the site, route or area to gain a better

appreciation of the problems. c) To identify any accident causal factor that were not apparent through the analysis of the data. d) To observe traffic and road user behaviour. 2.5 Accident Prediction Model The model consists of several independent or explanatory variables, encompassing elements from road geometry to traffic condition. For this study, the variables which have considerable effect are 85th

percentile speed, volume study, gap (in second) and number of access points per kilometer. The data were collected in-field. The study section used for collecting data was about 5 kilometers long, it involves KM 19, KM 20, KM 21, KM 22 and KM 23 of Federal Route 50. By traversing the entire length of the road to observe the number of access points, the number of major access point per kilometer for every section is obtained. Traffic volume and spot speed were obtained over 2-hour time periods of field survey at each section, namely the morning (0700 - 0900 hrs), midday (1200 - 1400 hrs) and evening (1700 - 1900 hrs). Speed measurements, gap study, and volume study were taken at every section using a Trax Mite which is

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a traffic counter and classifier. The 85th percentile speeds were determined from spot speed measurement using SPSS program. 3.0 Result And Data Analysis 3.1 Total Road Accident Percentage of accidents at federal road FT 050 (km 1 to km 40) from year 2000 to 2007 show in Figure 3. The highest percentage of accidents is year 2004 and 2007 with 15 %. The second highest is year 2003, 2005 and 2006 with 14 % and followed by year 2002 with 13 %. The lowest percentage of accident is year 2000 with 4 %. This means the impact of upgrading the route from two-lane road to a four-lane road can be increase the accident number especially during its construction stage from year 2002 to 2004. The road was an upgrading of the existing road with cross of two lane two way to four lanes undivided carriageway on February 15, 2002 and was completed on August 14, 2004.

20004%

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Figure 3: Analysis percentage number of accidents at FT 050 (2000-2007)

3.2 Accident Data By Hour Of The Day Figure 4 shows the worst accident by hour of the day from year 2003 to 2007 along FT 050. The highest number of accident occurred at 1601 to 1800 namely 4.01 pm to 6.00 pm, recorded at 754 accident case. Second highest was at 1401 to 1600 namely 2.01 pm to 4.00 pm involving 665 accident case and the third highest at 1201 to 1400 or 12.00 pm to 2.00 pm with 641 case. For the lowest recorded at 0401 to 0600 or 4.01 am to 6.00 am with 69 accident case.

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Figure 4: Analysis accidents data by hour in the day at FT 050 (2003-2007) 3.3 Accident Data By Type Of Fault According Batu Pahat Distric Police data accident, many factor contributing to road accident along federal road FT 050. Table 5 shows the faults data which cause occurred fatal along FT 050 from year 2003 to 2007. From Figure 5 shows the accident by type of faults along FT 050 from year 2003 to 2007. The highest rank is driving to close with 2749 accident case and followed by accident at junction with 1784 accident case. While, the lowest rank is tired or wear and racing, where both of faults value is 15 case.

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Figure 5: Accident data by type of fault (2003-2007)

3.4 Ranking Accident Point Weightage By using this formula the accident will be classified into four main categories. For fatal it will be multiply with 6.0, while serious injury multiply with 3.0, slight injury must multiply with 0.8 and damage only multiply with 0.2. The Accident Point Weightage (APW) and accident ranking at federal road FT 050 can be shown in Appendix A.

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3.5 Ranking Of The Top Ten Accident Section (Km) Table 1 show the top ten accident ranking by weightage and study location among the top ten accident ranking by weightage, kilometre 20 with 89.20 weighting point and kilometre 21 with 67.80 weighting point. The analysis was based on data compile over three year starting from January 2004 to 2007.

Table 1: Analysis for Top ten accident ranking by weightage

1=Fatal, 2=Serious, 3=Slight, 4=Damage, APW=Accident Point Weightage 3.6 Analysis Accident Data At Study Location The accident history data were collected from Traffic Police Station, Batu Pahat. The analysis accident data by year 2000 to 2007, where federal road stretch km 1 to km 38.Km 19, km 20, km 21, km 22 and km 23 were selected as the study location based on the blacksport site on Accident Blackspot Map from Public Works Department of Batu Pahat (JKR). 3.7 Number of Accident at Study Location by Section (km) From Figure 6, the highest number of damage only accident is at km 21 with 142 and the lowest number of damage only accident is at km 19 and km 20 with equal value with 102 accidents. While for the serious injury categories, the highest is at km 21 with 3 accidents. For serious injury at 19 km, 20 km and 23 km not occurred. The highest number of fatal is km 20 and the lowest is km 22 and km 23 with 1 accident. Slight injury always occurred for every study location, from Figure 4.6 show at km 20 is the highest occurred accident with 26 and km 22 is the lowest number of accident with 22. The highest accident total from the Figure 4.4 at km 21 with 170 and the lowest at km 19 with 121 case.

Km Type of Road

Accident Jumlah APW ln(APW) Rank 1 2 3 4

5 9 4 50 119 182 129.80 4.87 1 10 8 5 37 105 155 113.60 4.73 2 2 4 2 30 210 246 96.00 4.56 3 9 5 3 43 100 151 93.40 4.54 4 20 8 0 26 102 136 89.20 4.49 5 24 6 3 28 85 122 84.40 4.44 6 8 6 1 32 96 135 83.80 4.43 7 4 2 2 26 172 202 73.20 4.29 8 6 3 2 33 104 142 71.20 4.27 9 21 2 3 23 142 170 67.80 4.22 10

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Number of Accident at Study Location by Section, km

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Serious Injury Fatal Slight Injury Damage Only Total Figure 6 : Number of accident at study location from year 2004 to 2007

3.8 Independent Variable of the Accident Prediction Model Independent Variable of the Accident Prediction Model used in the study is Access Point, Speed, Hourly Traffic Volume and Gap obtained from traffic study. 3.8.1 Speed Speed is very important for this analysis. It is because from speed, value of 85th Percentile speed can be obtained. The speed data obtained from the previous study. Table 4.3 shown an average of 85th Percentile speed from speed data analysis.

Table 2: Average of 85th Percentile

Km 19 20 21 22 23

85th Percentile 66.54 78.47 76.51 72.77 73

3.8.2 Traffic Volume Per Hour and Number of Access Point For data traffic volume per hour (HTV), can be obtained from number of vehicle in speed data analysis. While Access Point (per km) shown in (Appendix B). 3.8.3 Gap A gap is normally defined as the amount of time, in second, between the end of one vehicle and the beginning of the next. From the data, value of gap obtained as Table 3. The maximum average of gap for vehicle is 3.92 this mean it is lack of adequate gap for the vehicles to make a turning at the site because the gap needed for the right turning is 4 to 5 seconds.

Table 3: Average of gap

Km 19 20 21 22 23 Gap 2.81 3.37 3.17 3.67 3.92

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3.9 The Accident Prediction Model 3.9.1 Multiple Linear Regression Method From the data shown in Appendix B , a regression analysis is performed using Microsoft Excel and the result of analysis are obtained as shown in Appendix C and Appendix D. Based on the results of the analysis, the accident prediction model for Federal Route 50 takes the following equation: In (APW)0.5 = 0.0212( AP ) + 0.0007 (HTV 0.75 + GAP 1.25) + 0.0210 ( 85th PS)

Where,

APW = accident point weightage AP = number of access points per kilometer HTV = hourly traffic volume Gap = amount of time, between the end of one vehicle and the beginning of the next in second. 85th PS = 85th percentile speed

The model has an R-square of 0.9987, which means that 99.87 % of the variation in the number of accident has been explained the regression line. The T- test also indicates that the model is significant and can be used for the prediction of the number of accidents (refer to Appendix D). Decrement of vehicle speed, access point, traffic volume and increment of gap are likely to have an influence effect of reduction on the road traffic accidents. 4.0 Conclusion The research determine that number of accidents for study location (km 19, km 20, km 21, km 22, and km 23) at FT 050 always increase according accident data from year 2001 to 2007 have shown the total is 1074 accident with 30 fatalities, 36 serious injury, 204 slight injury and 804 damage only. Based on the Accident Point Weightage (APW), at kilometre 5 is the highest with 129.8 weighting point. This was followed by kilometre 10, kilometre 2, kilometre 9, kilometre 20, kilometre 24, kilometre 8, kilometre 4, kilometre 6 and kilometre 2, which km 20 and km km 21 is the study location . The highest number of damage only accident is at km 21 with 142 and the lowest number of damage only accident is at km 19 and km 20 with equal value with 102 accident. While for the serious injury categories, the highest is at km 21 with 3 accident. For serious injury at 19 km, 20 km and 23 km not occurred. The highest number of fatal is km 20 and the lowest is km 22 and km 23 with 1 accident. Slight injury always occurred for every study location, which at km 20 is the highest occurred accident with 26 and km 22 is the lowest number of accident with 22. The highest accident total is at km 21 with 170 and the lowest at km 19 with 121 case. 4.1 Accident Prediction Model Further study of the research was to develop predictive models relating traffic accidents with the road environment and traffic flows. Multiple regression techniques were used to estimate the model parameters. The regression equation that can be used to predict accident rates as developed from this study takes the following form: In (APW)0.5 = 0.0212( AP ) + 0.000704 (HTV 0.75 + GAP 1.25) + 0.0210 ( 85th PS) Where the range of values applicable to this model are as follows:

Table 4: Range of values applicable to this model

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Independent Variable Range of Va lues

Number of access points per kilometer (AP) 6-12 Hourly traffic volume (HTV) 1597-3952 vph Gap (second) 2.75-3.97 85th percentile speed (85th PS) 63.30-82.20 kph

The result of the analyses provide sufficient evidence to support the hypothesis that the existence of a larger major junction density, an increase in traffic volume and vehicle speed in Federal Route 50 are the contributors to traffic accidents. Reduction of vehicle speed, access point, traffic volume and gap are likely to have an influential effect on the road traffic accidents. The percent accident reduction by changing the measures of each parameters are, one access point per kilometer reduction can reduce accident by 9.32%, 5 kilometer per hour reduction can reduce accident by 27.2%, and 100 vehicle per hour reduction can reduce accident by 4.33% meanwhile an increment of one second in gap will reduce accident by 1.20%. More importantly, the significant accident predictive model developed in this study is applicable in road safety improvement and could serve as a basis for further research work of Federal Route in Malaysia especially and developing countries generally. 5.0 Reference Abdul Kareem (July 2003);“Review Of Global Menace of Road Accidents with Special Reference to Malaysia”- A Social Perspective, Malaysia Journal of Medical Science.Vol10. No.2, (31-39). Al-Masaeid, Hashem R, Suleiman, Ghassan (2004); Relationships between urban planning variables and traffic crashes in Damascus. Road & Transort Research. Berhanu, G.(2004); Model relating traffic safety with road environment and traffic flow on arterial roads in Addis Ababa. Adis Ababa University, pp 697-704. Cheol Oh, Jun-Seok Oh, Stephen G.Ritchie and Myungsoon Chang (2000); Real-Time Estimation of freeway Accident likelihood. Institute of Transportation Studies University of California, Irvine, USA pp 12-15. Hadayeghi, Shalaby and Persaud (2003); Macro- Level Accident Prediction Models for Evaluating The Safety of Urban Transportation Systems. Annual Meeting of the Transportaion Research Board, TRB, Washington D.C Hadi, Mohammed A., Jacob Aruldhas, Lee-Fang Chow, and Joseph A. Wattleworth (1995); Estimating Safety of Cross-Section Design for Various Highway Types Using Negative Binomial Regression, Transportation Research Record, 1500: 169-177. K.M.Lum, Hendry S.L. Fan, S.H.Lam and P.Olszewski (1998); “Speed-Flow Modelling of Arterial Roads in Singapore”, Journal of Transportation Engineering./May/Jun 213-222. New Strait Times Malaysia (February 6,2006), Monday; page 10 Radin Umar Radin Sohadi and C.J Baguely, The Identification, Prioritising and Analysis Of Accident Blackspots In Malaysia, REAAA Journal/January 1994. Radin Umar Radin Sohadi, Chai W.L., Hussain H, Law T.H (2001); “Modelling of Traffic Accidents Along Major Trunk Roads in Malysia”, Journal IEM.vol. 62 No. 3 2001. Transportation Research Laboratory, TRL 421 Report (March 2000); The Effects of Drivers’ Speed on the Frequency of Road Accidents. World Disaster Report (1998); International Faderation of Red Cross and Red Crescent Societies

Transport and Research Laboratory, UK.

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Appendix A Ranking Accident Point Weighting Along a Route F050 (KM 1-40) Over a 4 Years Period

(2004-2007)

Km Type of Road Accident

Total APW In(APW) Rank Fatal

Serious Injury

Slight Injury

Damage Only

1 3 0 24 142 169 65.60 4.18 16 2 4 2 30 210 246 96.00 4.56 3 3 1 0 27 201 229 67.80 4.22 11 4 2 2 26 172 202 73.20 4.29 8 5 9 4 50 119 182 129.80 4.87 1 6 3 2 33 104 142 71.20 4.27 9 7 3 2 28 103 136 67.00 4.20 13 8 6 1 32 96 135 83.80 4.43 7 9 5 3 43 100 151 93.40 4.54 4

10 8 5 37 105 155 113.60 4.73 2 11 2 3 14 23 42 36.80 3.61 27 12 3 3 9 56 71 45.40 3.82 22 13 1 2 20 53 76 38.60 3.65 25 14 5 1 14 48 68 53.80 3.99 20 15 4 1 3 24 32 34.20 3.53 29 16 4 3 14 32 53 50.60 3.92 21 17 4 1 5 37 47 38.40 3.65 26 18 5 4 15 66 90 67.20 4.21 12 19 5 0 14 102 121 61.60 4.12 17 20 8 0 26 102 136 89.20 4.49 5 21 2 3 23 142 170 67.80 4.22 10

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Appendix B

22 1 1 10 110 122 39.00 3.66 24 23 1 0 16 125 142 43.80 3.78 23 24 6 3 28 85 122 84.40 4.44 6 25 1 0 14 36 51 24.40 3.19 32 26 2 1 7 28 38 26.20 3.27 31 27 1 0 5 18 24 13.60 2.61 37 28 4 0 4 46 54 36.40 3.59 28 29 7 4 6 40 57 66.80 4.20 14 30 7 2 7 62 78 66.00 4.19 15 31 4 4 11 83 102 61.40 4.12 18 32 2 3 17 110 132 56.60 4.04 19 33 2 1 7 64 74 33.40 3.51 30 34 1 0 1 52 54 17.20 2.84 35 35 2 0 4 23 29 19.80 2.99 33 36 2 0 2 21 25 17.80 2.88 34 37 1 0 1 13 15 9.40 2.24 38 38 0 0 0 27 27 5.40 1.69 40 39 2 0 1 7 10 14.20 2.65 36 40 0 0 4 21 25 7.40 2.00 39

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Appendix C

Time No Section

ln (APW)0.5 AP

HTV 0.75 + GAP 1.25 85 PS

(km) (per km) (kph) 7.00 – 8.00 1 19 2.0291 9 256.3 67.95 8.00 – 9.00 2 19 2.0291 9 400.28 68.28

12.00 – 1.00 3 19 2.0291 9 448.07 67.44 1.00 – 2.00 4 19 2.0291 9 441.47 68.03 5.00 – 6.00 5 19 2.0291 9 492.02 63.3 6.00 – 7.00 6 19 2.0291 9 501.98 64.26 7.00 – 8.00 7 20 2.1213 8 329.77 82.2 8.00 – 9.00 8 20 2.1213 8 479.58 82.18

12.00 – 1.00 9 20 2.1213 8 418.78 79.99 1.00 – 2.00 10 20 2.1213 8 425.2 77.01 5.00 – 6.00 11 20 2.1213 8 319.42 75.79 6.00 – 7.00 12 20 2.1213 8 325.91 73.65 7.00 – 8.00 13 21 2.0534 12 297.02 80.91 8.00 – 9.00 14 21 2.0534 12 439.07 80.59

12.00 – 1.00 15 21 2.0534 12 410.96 75.4 1.00 – 2.00 16 21 2.0534 12 426.45 74.41 5.00 – 6.00 17 21 2.0534 12 448.44 73.54 6.00 – 7.00 18 21 2.0534 12 430.23 74.23 7.00 – 8.00 19 22 1.9141 7 305.59 71.99 8.00 – 9.00 20 22 1.9141 7 446.81 70.99

12.00 – 1.00 21 22 1.9141 7 423.1 73.91 1.00 – 2.00 22 22 1.9141 7 398.79 71.06 5.00 – 6.00 23 22 1.9141 7 416.53 75.62 6.00 – 7.00 24 22 1.9141 7 374.44 73.06 7.00 – 8.00 25 23 1.9441 6 327.42 72.32 8.00 – 9.00 26 23 1.9441 6 476.08 71.22

12.00 – 1.00 27 23 1.9441 6 455.08 73.95 1.00 – 2.00 28 23 1.9441 6 436.34 71.75 5.00 – 6.00 29 23 1.9441 6 444.78 75.52 6.00 – 7.00 30 23 1.9441 6 392.51 73.26

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RESULT S OF THE MULTIPLE LINEAR REGRESSION ANALYSIS

SUMMARY OUTPUT

Appendix D

Regression Statistics

Multiple R 0.998737008 R Square 0.997475612 Adjusted R Square 0.960251583 Standard Error 0.106653138 Observations 30

Coefficients Standard Error t Stat P-value Intercept 0 #N/A #N/A #N/A

AP 0.021232017 0.009533646 2.227061546 0.034474931HTV 0.75 + GAP 1.25 0.000705917 0.000273406 2.58193706 0.015571332

85th PS 0.021002698 0.00178282 11.78060468 3.78097E-12

ANOVA df SS MS F Significance F Regression 3 121.3548779 40.45162597 3556.220702 4.33145E-34 Residual 27 0.307122081 0.011374892 Total 30 121.662

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RESULT OF THE VALIDATION OF THE PREDICTION MODEL Coefficient of Determinant

Regression Statistics

Multiple R 0.998737

R Square 0.997476

Adjusted R Square 0.960252

Standard Error 0.106653

Observations 30

R-square :

R square 0.5 1

R2= 0.997

Rating Poor Perfect

T-Test :

ANOVA df SS MS F Significance F Regression 3 121.3549 40.45163 3556.220702 4.33145E-34 Residual 27 0.307122 0.011374892 Total 30 121.662

(From Microsoft Excel)

6340.590113749.0

45163.40==T ; Critical value, t = 1.706

T>t : The model is significant and can be used for prediction

Explanatory Variable t-stat

|t Stat| “>”or “<”

Critical value Significance of coefficient AP 2.227061546 >1.706 Significance

HTV 2.58193706 >1.706 Significance 85th PS 11.78060468 >1.706 Significance

(From Microsoft Excel)

Residual Output

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Observation Predicted ln(APW)0.5 Residuals 1 1.799147918 0.22998983 2 1.907716702 0.121421046 3 1.923810197 0.105327551 4 1.931542738 0.09759501 5 1.867884071 0.161253677 6 1.895077591 0.134060157 7 2.129068045 -0.007794842 8 2.234401379 -0.113128176 9 2.145485733 -0.02421253 10 2.08742968 0.033843523 11 1.987134515 0.134138688 12 1.946770142 0.174503061 13 2.16378386 -0.110347716 14 2.257338471 -0.203902327 15 2.128491151 -0.075055007 16 2.118633131 -0.065196986 17 2.115883893 -0.062447749 18 2.117521011 -0.064084866 19 1.876329418 0.037723873 20 1.955016284 -0.040962993 21 1.999606875 -0.085553584 22 1.922588351 -0.00853506 23 2.030883615 -0.116830324 24 1.947404673 -0.033351382 25 1.877441934 0.066677404 26 1.959276975 -0.015157637 27 2.001787359 -0.057668022 28 1.942356591 0.001762746 29 2.027496252 -0.083376914 30 1.943130436 0.000988902