151 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 © Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ Statistical Analysis of Vehicular Registration in Lagos, Nigeria Based on Ownership and Type Kehinde Adigun a *, Oluwasesan Adewusi b , Abiodun Adigun c a,b Department of Statistics, Ekiti State University, Ado-Ekiti, Nigeria c Department of Economics, Federal University of Technology, Akure, Nigeria a Email: kabimbola2@gmail.com b Email: adewusiadeoye2008@gmail.com c Email: abiodunoladele24@yahoo.com Abstract This paper examined the vehicular registration in Lagos state, Nigeria between the years 1998-2015. Time series analysis was employed to analyze the data, to compute the seasonal variation and fluctuations in the number of motor vehicles that was registered between the periods of 16 years in the state. The least square method was also used in forecasting the number of vehicles that will be registered in the next 10years in the state. It was discovered that the number of private, commercial and government registered vehicles will be increased over the years. . Based on the fact of the analysis made, we were able to conclude that the rate at which vehicles were registered in Lagos – State fluctuates over the time. Keywords: Vehicles; Licensing stations; time series; National Motor Vehicle Administration Agency. 1. Introduction Vehicle registration in Nigeria began over 100 years ago, the record have been essentially manual, which in turn has not helped to raise efficiency of general or automotive services in recent years [1]. Today computer has been discovered as a very efficient instrument, which has played a very significant role in adequate management of information. Every vehicle kept or used on public roads must be registered and an appropriate vehicle license fee must be paid in respect. This is done by applying for a motor vehicle license. The board of internal revenue which is known to be the revenue division of the ministry of finance is the authority responsible for the insurance of vehicle in the state. ------------------------------------------------------------------------ * Corresponding author American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 151-159 152 This board has motor licensing in various local government areas and the licensing offices in the various local government areas gives the monthly report to the state board [2]. The vehicles owner is required to go through several government agencies to completely have a license to ply the vehicle on roads. National agencies such as; National Motor Vehicle Administration Agency (NMVAA), Federal Road Safety Corps (FRSC), and Vehicle Inspection Officers (VIO) [3]. Lagos State Commissioner for Transportation has exempted all private vehicles from obtaining its compulsory number plates before plying the state roads. It announced that private and commercial vehicles in the state would be mandated to use the state's number plates. Number-plates are unified all over the federation. The state never made any pronouncement that vehicles with other states’ number plates had been banned from plying Lagos roads, only vehicles operating as commercial public transport will have to obtain the state’s number plates before being allowed to operate in and on Lagos roads. This is necessary to enable the government to have adequate information about such vehicles and also to ensure the safety and security of residents [4]. 2. Materials and method Time series can be defined as the recording or measurement of variable over a period of time. It is also described as a qualitative forecasting technique which uses forms of mathematical or statistical analysis on past data arranged in a chorological order. It has been a veritable tool applied in various fields like Agriculture, Engineering, Business and Economics, Geophysics, Medical Science, Quality Control, Statistics and Social Science etc [5]. 2.1 Model in time series Additive Model: This can be written mathematically as; (1) Then its seasonal variation at time t is; (2) Multiplicative Model: This can also be written mathematically as; (3) And its seasonal variation at time t is; ⁄ Where; is the original observation is the trend movement is the seasonal movement American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 151-159 153 is the cyclical movement is the irregular movement 2.2 The least Square Method The least square estimates a curve that approximately fits a given data point by minimizing the sum of the square errors or deviation from the mean. A linear relationship between the given sets of data points and some independent variables (t) must be sufficiently established before the least square method can be used to estimate the trend line T [6]. If a linear relationship exists between the time series values, and time t then the linear method is given as; (4) t = 1,2,3,… where; a = the intercept of the Y axis. b = slope, et = error term The general formula for estimating the trend line is given below; b = (5) 3. Results 3.1 Based on Ownership 20 15 20 14 20 13 20 12 20 11 20 10 20 09 20 08 20 07 20 06 20 05 20 04 20 03 20 02 20 01 20 00 19 99 19 98 250000 200000 150000 100000 50000 0 Year p ri v a te MAPE 32 MAD 20754 MSD 703272208 Accuracy Measures Actual Fits Variable Trend Analysis Plot for private Linear Trend Model Yt = -248 + 14099*t Figure 1: Graph of private owned vehicles American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 151-159 154 Interpretation: the number of private registered vehicles increases by 14099 except for a very sharp decrease in 2005. 20 15 20 14 20 13 20 12 20 11 20 10 20 09 20 08 20 07 20 06 20 05 20 04 20 03 20 02 20 01 20 00 19 99 19 98 50000 40000 30000 20000 10000 0 Year c o m m e r c ia l MAPE 58 MAD 4141 MSD 26949757 Accuracy Measures Actual Fits Variable Trend Analysis Plot for commercial Linear Trend Model Yt = -5462 + 2932*t Figure 2: Graph of commercial owned vehicles Interpretation: the number of commercial registered vehicles increases by 2932 except for a very sharp fall in 2003 and 2004. 20 15 20 14 20 13 20 12 20 11 20 10 20 09 20 08 20 07 20 06 20 05 20 04 20 03 20 02 20 01 20 00 19 99 19 98 1200 1000 800 600 400 200 0 Year Go ve rn m en t MAPE 71.4 MAD 220.4 MSD 81681.4 Accuracy Measures Actual Fits Variable Trend Analysis Plot for Government Linear Trend Model Yt = 211 + 25.2*t Figure 3: Graph of Government owned vehicles Interpretation: the number of government registered vehicles increases by 25.2 and decreases in year 2013, 2014 and 2015. 3.2 By Type American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 151-159 155 20 15 20 14 20 13 20 12 20 11 20 10 20 09 20 08 20 07 20 06 20 05 20 04 20 03 20 02 20 01 20 00 19 99 19 98 300000 250000 200000 150000 100000 50000 0 Year S a lo o n / S ta ti o n w a g o n / je e p MAPE 33 MAD 23617 MSD 827730690 Accuracy Measures Actual Fits Variable Trend Analysis Plot for Saloon/Station wagon/jeep Linear Trend Model Yt = 143 + 15022*t Figure 4: Graph of saloon, station wagon and jeep type of vehicle Interpretation: the cumulative of saloon, station wagon and jeep type of vehicles increases by 15022 except for a very sharp fall in 2003 and 2004. 20 15 20 14 20 13 20 12 20 11 20 10 20 09 20 08 20 07 20 06 20 05 20 04 20 03 20 02 20 01 20 00 19 99 19 98 35000 30000 25000 20000 15000 10000 5000 0 Year M in ib u s MAPE 37 MAD 3439 MSD 18365645 Accuracy Measures Actual Fits Variable Trend Analysis Plot for Minibus Linear Trend Model Yt = 1053 + 1565*t Figure 5: Graph of Minibus vehicles Interpretation: the number of Minibus type of vehicle increase by 1565 except for a very sharp fall in 2004 and 2011. 3.3 Trend Table Seasonal Variation (Additive Model) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 151-159 156 Forecast, Forecasting = Table 1: Table for private owned vehicles Year Private( ) T Trend( ) Seasonal( ) 1998 10073 1 13851 -3778 1999 11260 2 27950 -16690 2000 25944 3 42049 -16105 2001 107555 4 56148 51407 2002 121646 5 70247 51399 2003 91669 6 84346 7323 2004 53322 7 98445 -45123 2005 67246 8 112544 -45298 2006 109436 9 126643 -17207 2007 138592 10 140742 -2150 2008 181632 11 154841 26791 2009 153781 12 168940 -15159 2010 186429 13 183039 3390 2011 196987 14 197138 -151 2012 237697 15 211237 26460 2013 245332 16 225336 19996 2014 225361 17 239435 -14074 2015 242,456 18 253534 -11078 Table 2: Commercial T Year commercial( ) Trend( ) Seasonal( ) 1 1998 1057 -2530 3587 2 1999 1544 402 1142 3 2000 2270 3334 -1064 4 2001 13078 6266 6812 5 2002 15651 9198 6453 6 2003 9700 12130 -2430 7 2004 5879 15062 -9183 8 2005 5766 17994 -12228 9 2006 17446 20926 -3480 10 2007 19484 23858 -4374 11 2008 28425 26790 1635 12 2009 32490 29722 2768 13 2010 32978 32654 324 14 2011 43641 35586 8055 15 2012 40758 38518 2240 16 2013 45668 41450 4218 17 2014 43198 44382 -1184 18 2015 43,965 47314 -3349 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 151-159 157 Table 3: Government T Year Government( ) Trend( ) Seasional( ) 1 1998 87 236.2 -149.2 2 1999 86 261.4 -175.4 3 2000 204 286.6 -82.6 4 2001 320 311.8 8.2 5 2002 373 337 36 6 2003 148 362.2 -214.2 7 2004 216 387.4 -171.4 8 2005 268 412.6 -144.6 9 2006 571 437.8 133.2 10 2007 1061 463 598 11 2008 651 488.2 162.8 12 2009 1170 513.4 656.6 13 2010 892 538.6 353.4 14 2011 445 563.8 -118.8 15 2012 618 589 29 16 2013 478 614.2 -136.2 17 2014 274 639.4 -365.4 18 2015 231 664.6 -433.6 Analysis by type Table 4: Saloon/Station Wagon/Jeep T Year Saloon/Station wagon/jeep( ) Trend( ) Seasonal( ) 1 1998 10529 15165 -4636 2 1999 12104 30187 -18083 3 2000 27729 45209 -17480 4 2001 112600 60231 52369 5 2002 127446 75253 52193 6 2003 95326 90275 5051 7 2004 57826 105297 -47471 8 2005 70496 120319 -49823 9 2006 118099 135341 -17242 10 2007 156858 150363 6495 11 2008 202042 165385 36657 12 2009 166207 180407 -14200 13 2010 188515 195429 -6914 14 2011 218528 210451 8077 15 2012 253404 225473 27931 16 2013 264286 240495 23791 17 2014 236873 255517 -18644 18 2015 252,497 270539 -18042 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 151-159 158 Table 5: Table for Minibus T Year Minibus( ) Trend( ) Seasonal( ) 1 1998 1573 2618 -1045 2 1999 1920 4183 -2263 3 2000 3175 5748 -2573 4 2001 14529 7313 7216 5 2002 15469 8878 6591 6 2003 10897 10443 454 7 2004 6292 12008 -5716 8 2005 6988 13573 -6585 9 2006 14290 15138 -848 10 2007 17124 16703 421 11 2008 19244 18268 976 12 2009 22351 19833 2518 13 2010 30232 21398 8834 14 2011 20420 22963 -2543 15 2012 19424 24528 -5104 16 2013 21807 26093 -4286 17 2014 28859 27658 1201 18 2015 31,950 29223 2727 From the estimation of the time series components, trend was used to normalize the trend which gives a varying or different regression equation over the categories of vehicles registered over the period e.g. Private owned vehicles has a trend of Tt = -248 + 14099(t) which shows that the number of private owned vehicles registered in Lagos State over the period increased by 14099 while that of commercial increased by 2932 and that of government by 25.2. And this makes private registered vehicles the most registered vehicle under vehicles registered by ownership. The trend analysis was obtained and the graph shows an irregular variation also, the prediction shows fluctuations in the future occurrence. From the estimation of the time series components, trend was used to normalize the trend which gives a varying or different regression equation over the categories of vehicles registered over the period e.g. Private owned vehicles has a trend of Tt = -248 + 14099(t) which shows that the number of private owned vehicles registered in Lagos State over the period increased by 14099 while that of commercial increased by 2932 and that of government by 25.2. And this makes private registered vehicles the most registered vehicle under vehicles registered by ownership. The trend analysis was obtained and the graph shows an irregular variation also, the prediction shows fluctuations in the future occurrence. 4. Conclusion and Recommendations From the time series analysis that was carried out, we can see that time series is a good statistic for analysing American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 151-159 159 vehicular registration data. Relevant predictions can be made which serves as a link to the future and the influence of statistics have been spread to all areas of life because of its usefulness and refuge in its operations. Furthermore, we could see that the use of trend to forecast is an example of what statisticians could call adaptive forecast prediction. The Lagos state government should employ competent hands in the registration exercise so as to avoid fraudulent act and also enhance their registration data base for more accurate and precise estimate of registered vehicles. The Government should also use the data on the estimate of vehicles registered to improve the state roads and also strikes balance between ratios of good road networks to registered vehicles and vehicles in use in the country so as to reduce traffic on the state roads. And there should be an improved scheme whereby the Government provides a suitable, comfortable and conducive public transportation to reduce the number of private owned vehicles plying her roads to reduce traffic congestions and can also serve as source revenue for the country. References [1] K. Adeniji. “Transport subsidies in Nigeria: A Synopsis of Workshop Proceedings”, in NISER, Ibadan and Friedrich Ebert Foundation, Germany, 1993. [2] Vehicle registration plate, Driver's license, Vehicles Pages: 88 (12149 words) Published: September 23, 2014 [3] S.T Ahmed. “Essentials of Vehicle Registration in Nigeria”. University press limited, Ibadan, 1991 [4] T. Agboola. “Perspective planning: the urban and regional planning dimensions” The Nigerian Journal of Economic and Social Studies, Vol. 31, 1989. [5] M.S Bartlett. “Some aspect of the time series correlation problems regards to test of significance@ in Journal of the Royal Statistical Society, 1935. [6] G.B. Gupta. Introduction to statistical method (9 th edition) Vicas publish prentices hall int. Inc, 1973.