Statistical Analysis of Electricity Generation in Nigeria Using Multiple Linear Regression Model and Box-Jenkins Autoregressive Model of Order 1

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1 Iteratoal Joural of Eergy ad Power Egeerg 7; 6(3: do:.648/j.jepe.763. ISSN: X (Prt; ISSN: 36-96X (Ole Statstcal Aalyss of Electrcty Geerato Ngera Usg Multple Lear Regresso Model ad Box-Jeks Autoregressve Model of Order Imo Eodem Ebukaso, Chukwu Beedct Chd, Abode Iocet Iraoghua Departmet of Electrcal/Electroc ad Computer Egeerg, Faculty of Egeerg, Uversty of Uyo, Uyo, Ngera Departmet of Electrcal/Electroc Egeerg Imo State Polytechc, Umuagwo, Owerr, Ngera Emal address: (I. E. Ebukaso To cte ths artcle: Imo Eodem Ebukaso, Chukwu Beedct Chd, Abode Iocet Iraoghua. Statstcal Aalyss of Electrcty Geerato Ngera Usg Multple Lear Regresso Model ad Box-Jeks Autoregressve Model of Order. Iteratoal Joural of Eergy ad Power Egeerg. Vol. 6, No. 3, 7, pp do:.648/j.jepe.763. Receved: Jauary 8, 7; Accepted: Jauary 8, 7; Publshed: Jue 7, 7 Abstract: Ths study presets statstcal aalyss of electrcty geerato Ngera usg two dfferet statstcal models, amely; multple lear regresso model ad box-jeks autoregressve model of order. Two clmatc varables (rafall ad temperature were used as the explaatory varables. Data o electrcty geerato Ngera betwee ad 4 were obtaed from the Cetral Bak of Ngera Statstcal Bullet whle Data o rafall ad temperature betwee ad 4 were extracted from the Natoal Bureau of Statstcs (NBS abstract. Test of model ftess ad forecastg accuracy were doe usg geerc statstcal approach whch clude coeffcet of determato ad root mea square error. The predcto accuracy of the two statstcal models was compared ad the best model was selected. Furthermore, correlato betwee power geerato ad the two clmatc varables (rafall ad temperature, were carred out ad the result reveals that the amout of rafall has sgfcat ad postve relatoshp wth power geerato Ngera. Specfcally, rafall has correlato value of r =.97 wth the power geerato at probablty, p =. ad the relatoshp was sgfcat at % (p<.. However, temperature although t s postvely correlated, does ot sgfcatly affect power geerato. Temperature has correlato value of t =.36 wth power geerato at probablty, p =.658 (p>.5 ad the relatoshp was sgfcat at 5% (p<.5. Amog the two statstcal models, multple lear regresso model was selected as the best model as t gave the hghest value of coeffcet of determato (r =99.77% ad the least Root Mea Square Error (6.7%. Keywords: Electrcty, Box-Jeks Autoregressve Model, Electrcty Geerato, Multple Lear Regresso Model, Statstcal Aalyss of Electrcty. Itroducto Electrcty geerato ad supply s dspesable moder lvg ay dustral or commercal socety. Electrcty producto Ngera over the years vared from gas fred, ol fred, hydroelectrc power statos to coal-fred wth hydroelectrc power system ad gas fred system takg precedece [-4]. Presetly, Ngera mostly employs gas-fred ad hydroelectrc turbes for bulk geerato, ol beg too expesve ad coal-fred statos havg goe morbud. Ngera beg rapdly growg developmet, dustry ad commerce, s battlg wth the problems of cotually expadg cosumpto ad crease demad for electrcty. Madueme [5] observed that Ngera, the atoal peak demad for electrc eergy s o the crease as a result of may developmet actvtes. He wet further to state that spte of ths, the total power geerato has ot matched ths crease. It s a fact that most commutes Ngera regard the costructo of access roads, stallato of ppe bore water, buldg of tow halls ad so forth as the rudmets to ther developmet, yet electrcty promotes statly ther socal ad ecoomc lfe as may servces ad facltes become readly avalable [6].

2 9 Imo Eodem Ebukaso et al.: Statstcal Aalyss of Electrcty Geerato Ngera Usg Multple Lear Regresso Model ad Box-Jeks Autoregressve Model of Order I ths regard, adequate electrcty geerato costtute a cetral developmet ssue whch caot be over-emphaszed [7-]. Apart from servg as the pllar of wealth creato Ngera, t s also the ucleus of operatos ad subsequetly the ege of growth for all sectors of the ecoomy. Ths study exames how the power geerato wll be affected by clmate chage or varables such as temperature ad rafall whch s regarded as oe of the greatest threat to humaty the st cetury. Cosderable efforts have bee made assessg the causal lk betwee eergy cosumpto ad ecoomc growth, but very few studes have examed how evrometal challeges such as the cdece of clmate chage wll sgfcatly mpact eergy producto whch s regarded as the bae of ecoomc growth. Most researches the aspect of mpacts of clmate chage o the eergy sector are form of techcal reports; some others exame how the eergy sector cotrbutes to clmate chage ad ot so much o how the eergy sector wll be affected by the cdece of clmate chage. Ths study wll attempt to fll ths gap addto to examg the bvarate relatoshp betwee two clmate varables (rafall ad temperature ad electrc power geerato Ngera betwee ad 4, coductg statstcal aalyss of electrc power geerato Ngera betwee ad 4 based o two dfferet statstcal models usg rafall ad temperature as the explaatory varables.. Methodology I ths study, aalytcal ad smulato research methodologes are used. I the aalytcal method, statstcal models are developed for aalysg ad predctg electrcty geerato Ngera. Specfcally, two dfferet statstcal models are used ths study. These models are multple lear regresso model [-4] ad Box-Jeks autoregressve model of order [5-9]. It also provdes the source ad method of data collecto... Source ad Method of Data Collecto The source of data collecto for ths study s secodary. Data o electrcty geerato Ngera betwee ad 4 were obtaed from the Cetral Bak of Ngera statstcal bullet [] whle data o rafall ad temperature were extracted from the Natoal Bureau of Statstcs (NBS abstract []... Multple Lear Regresso The multple lear regresso ca be represeted mathematcally as: G = + R + T + e ( Makg the resdual the subject equato ( gves; e = G R T ( The sum of square error (S s gve as; S = ( G R T = ( ( G R T (3 (4 = ( [ R ( G R T ] (5 = ( ( RG R R RT = T ( G R T ( Tg T T R T = (6 To fd estmate of the parameters (,,, equatos (3, (5, (6 are set to zero. The, G R T = (7 RG R R RT = (8 TG T T R T = (9 Rearragg equatos (7, (8 ad (9 gves; + R + T = ( R + R + R T = RG ( G T + TR + T = TG ( Solvg the systems of the equatos, to, gve the estmate of the parameters of the model..3. Box Jeks Autoregressve Model of Order The Box Jeks Autoregressve Model of Order ca be expressed mathematcally the form: g = γ + γ g + e (3 The resdual term e ca be obtaed from Equato ( as: e = g ( γ + γ g (4 e = ( g γ γ g (5

3 Iteratoal Joural of Eergy ad Power Egeerg 7; 6(3: The sum of square error ca be expressed as: RMSE = MSE (6 S 4 = e = ( g γ γ g (6 MSE = ( ˆ G G (7 = Dfferetatg the Equato (6 wth respect to γ, γ 4 = ( g γ γ g (7 γ 4 = g ( g γ γg (8 γ 4 = gg γ g γ g γ (9 To obta the parameters ( γ, γ we set the partal dervato wth respect to each parameter to. The: γ + = ( γ γ g g g + γ g = gg ( Solvg the set of equatos -, wth two ukows ( γ, γ, ths wll gve the estmates of the model parameters..4. Test of Model Ftess.4.. Coeffcet of Determato SST s the sum of square total whch s gve as; Where SST= ( G G ( G s the electrcty geerated durg the year SS (Error = SS (Regresso = ˆ ( G G ˆ ( G G (3 (4 Coeffcet of Determato (r s gve as; SSR r = (5 SST Where G ad Ĝ are the mea ad estmated electrcty geerato..4.. Root Mea Square Error (RMSE The root mea square error was used to assess the forecastg accuracy of the four models. The RMSE s defed as: Where G ad Ĝ are the electrcty geerated durg the year ad estmated electrcty geerato ad s the umber of observato. 3. Results ad Dscusso The data o electrcty geerato obtaed from cetral bak of Ngera statstcal bullet ad the two clmatc varables (rafall ad temperature extracted from Natoal Bureau of statstcs abstract betwee ad 4 were aalysed based o the two dfferet statstcal models. Correlato betwee power geerato ad clmatc varables was carred out. Graphpad prsm 5. Ecoometrc Vew (E-Vew software was used to plot the graph of actual ad predcted power geerato Ngera betwee ad 4 for the two statstcal models. Geerc statstcal approach was used to assess the goodess of ft ad forecastg accuracy of the two models. The predcto accuracy of the two models was compared ad the best model was selected. Table shows the result of bvarate relatoshp betwee power geerato ad the clmatc varables. The result reveals that the amout of rafall was foud to be sgfcatly related wth power geerato (r =.97, p =., p<.. The relatoshp was sgfcatly postve whch meas that as the amout of rafall creases, power geerato also creases. Also, the relatoshp betwee the temperature ad power geerato was also postve but ot sgfcat (t =.36, p =.658, p>.5. Ths relatoshp was ot sgfcat at 5 percet (p<.5. Table. Correlato betwee power geerato ad clmatc varables. G R T G R.97 ** (. T.36 ( (.73 G = Power geerato, R = rafall, T = temperature. ** Sgfcat at % (p<., *sgfcat at 5% (p< Multple Lear Regresso Table shows that the parameters of the multple lear regresso are as follows: =-69.78, =.46, = Therefore, the estmated model for power geerato based o the multple lear regresso s: G = R T (8 The coeffcet of determato s Ths dcates that rafall ad temperature explaed for 99.77% of the varato power geerato whle the remag.3

4 3 Imo Eodem Ebukaso et al.: Statstcal Aalyss of Electrcty Geerato Ngera Usg Multple Lear Regresso Model ad Box-Jeks Autoregressve Model of Order percet of the varato power geerato could be due to other varables ot accouted for the multple lear regresso model. Furthermore, the coeffcet of rafall ( =.46 s postve meag that as rafall creases, power geerato also creases. Table. Summary result of the estmates of the multple lear regresso model. Model Parameters SSR SST r-square RMSE (% Costat Rafall.46 Temperature = coeffcets, SSR = regresso sum of square, SST = Total Sum of Square, RMSE = Root Mea Square Error. Table 3. Actual ad Predcted power geerato Ngera betwee ad 4 usg multple lear regresso model. Year Actual geerato (MWh Predcted geerato (MWh Fgure. Graph of actual ad predcted power geerato Ngera betwee ad 4 usg multple lear regresso model. 3.. Box Jeks s Autoregressve Model of Order The Box s Jek s AR ( model for power geerato s: G t = G t- (9 From Table 4, Box Jek s AR ( model gave a r value of 98.45% whch meas that the model explaed percet of the varato power geerato Ngera. The coeffcet of power geerato at oe perod lag ( =.773 s postve whch meas that power geerato wll crease wth tme. The Box s Jek s AR ( model for power geerato s: G t = G t- (3 From Table 4, Box Jek s AR ( model gave a r value of 98.45% whch meas that the model explaed percet of the varato power geerato Ngera. The coeffcet of power geerato at oe perod lag ( =.773 s postve whch meas that power geerato wll crease wth tme. Table 4. Summary result of the estmates of the box Jeks s autoregressve model of order. Model Parameters SSR SST r-square RMSE (% Costat G t-.773 = coeffcets, SSR = regresso sum of square, SST = Total Sum of Square, RMSE = Root Mea Square Error. Table 5. Actual ad Predcted power geerato Ngera betwee 3 ad 4 usg box s Jeks autoregressve model of order. Year Actual geerato (MWh Predcted geerato (MWh

5 Iteratoal Joural of Eergy ad Power Egeerg 7; 6(3: Actual Predcted 34 Power geerato(mwh Year Fgure. Graph of actual ad predcted power geerato Ngera betwee 3 ad 4 usg box s Jeks autoregressve model of order Comparso of the Forecastg Accuracy of the Two Models Table 6. Comparso of the forecastg accuracy of the two models. S/N Models r-square (% RMSE Rak Multple lear regresso Box-Jeks s Autoregressve Model of order Based o the result Table 6, the multple lear regresso model has the hghest coeffcet of determato (r-square = 99.77% ad least root mea square error (RMSE = 6.7. Hece, the multple lear regresso model s recommeded as the best of the two competg models. 4. Cocluso I ths study, correlato betwee power geerato ad two clmatc varables are preseted. The result reveals that the amout of rafall has sgfcat ad postve relatoshp wth power geerato Ngera. The relatoshp was sgfcatly postve whch meas that as the amout of rafall creases, power geerato also creases. However, temperature although postve, does ot sgfcatly affect power geerato. From the results obtaed from model shows that the two depedet varables (rafall ad temperature explaed for 99.77% of the varato electrcty geerato. The multple lear regresso model was selected as the best model as t gave the hghest value of coeffcet of determato (r =99.77% ad the least root mea square error (6.7%. Refereces [] Wara, S. T. (. Electrcty Provso Ad Maageme I Ngera: Challeges Ad Prospects. [] Oj, J. O., Idusuy, N., & Kareem, B. (. Coal power utlzato as a eergy mx opto for Ngera: a revew. Amerca Academc & Scholarly Research Joural, 4 (4,. [3] Aumaka, M. C. (. Scearo of Electrcty Ngera. Iteratoal Joural of Egeerg ad Iovatve Techology (IJEIT, (6, [4] Aumaka, M. C. (. Scearo of Electrcty Ngera. Iteratoal Joural of Egeerg ad Iovatve Techology (IJEIT, (6, [5] Madueme, T. I. (. Aalyss of Electrcty Load Demad Ngera. Ngera Joural of Egeerg Maagemet. 3 (: 76. [6] Ogumodede O. B. (5. Cosumers Expectatos o Servce Delvery of PHCN: A Study of Lagos ad Ibada Metropols. Upublshed MBA Thess, Imo State Uversty. [7] Ayodele, A. S. (4. Improvg ad sustag power (electrcty supply for soco-ecoomc developmet Ngera.

6 33 Imo Eodem Ebukaso et al.: Statstcal Aalyss of Electrcty Geerato Ngera Usg Multple Lear Regresso Model ad Box-Jeks Autoregressve Model of Order [8] Loel, E. (3. The dyamc aalyss of electrcty supply ad ecoomc developmet: Lessos from Ngera. Joural of Sustaable Socety, (, -. [9] Wara, S. T., Abayom-All, A., Umo, N. D., Oghogho, I., & Odkayor, C. (9. A mpact assessmet of the Ngera power sector reforms. I Advaced Materals Research (Vol. 6, pp Tras Tech Publcatos. [] Egboh, H. I. (. Clea eergy Norway: a case study for Ngera electrcty developmet. [] Iwayem, A. (8. Ivestmet electrcty geerato ad trasmsso Ngera: ssues ad optos. Iteratoal Assocato for Eergy Ecoomcs, [] Hma, J., & Hckey, E. (9. Modelg ad forecastg short-term electrcty load usg regresso aalyss. Joural of IIsttute for Regulatory Polcy Studes [электронный ресурс]. [3] Cho, H., Goude, Y., Brossat, X., & Yao, Q. (3. Modelg ad forecastg daly electrcty load curves: a hybrd approach. Joural of the Amerca Statstcal Assocato, 8 (5, 7-. [4] Safa, M., Alle, J., & Safa, M. (4, Jauary. Predctg Eergy Usage Usg Hstorcal Data ad Lear Models. I ISARC. Proceedgs of the Iteratoal Symposum o Automato ad Robotcs Costructo (Vol. 3, p.. Vlus Gedmas Techcal Uversty, Departmet of Costructo Ecoomcs & Property. [5] Adhkar, R., & Agrawal, R. K. (3. A troductory study o tme seres modelg ad forecastg. arxv preprt arxv: [6] Roke, R. M., & Badr, M. A. (6. Tme Seres Models for Forecastg Mothly Electrcty Peak Load for Duba. Chacellor's Udergraduate Research Award. [7] Beett, C., Stewart, R. A., & Lu, J. (4. Autoregressve wth exogeous varables ad eural etwork short-term load forecast models for resdetal low voltage dstrbuto etworks. Eerges, 7 (5, [8] Sgh, A., & Mshra, G. C. (5. Applcato of Box-Jeks method ad Artfcal Neural Network procedure for tme seres forecastg of prces. Statstcs Trasto ew seres, (6, [9] Mohamed, Z., & Bodger, P. S. (4. Forecastg electrcty cosumpto: A Comparso of models for New Zealad. [] CBN. (6. Cetral Bak of Ngera, Statstcal Bullet, Vol. 7. [] NBS. (. Natoal Bureau of Statstcs Abstract Avalable at: Accessed o th November 6.

Chapter Business Statistics: A First Course Fifth Edition. Learning Objectives. Correlation vs. Regression. In this chapter, you learn:

Chapter Business Statistics: A First Course Fifth Edition. Learning Objectives. Correlation vs. Regression. In this chapter, you learn: Chapter 3 3- Busess Statstcs: A Frst Course Ffth Edto Chapter 2 Correlato ad Smple Lear Regresso Busess Statstcs: A Frst Course, 5e 29 Pretce-Hall, Ic. Chap 2- Learg Objectves I ths chapter, you lear: