Page - 107 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 3442 3.2.MultipleLinearRegression Toforecast theTECofelectricityfor2030,multiple linearregressionmethodisusednow,takingin account the yearlyGDPper capita, GDPandhistorical populationdata, as in the case of Turkey. Duringmostof thesituations,multiple independentvariablesmightbeusedtopredict thesignificance of a dependent variable forwhichweusemultiple regression. Inmultiple regression, GDP and Populationare takensimultaneouslyas thepredictingvariables.Multiplevariable regressionanalysis establishes a relationshipbetween adependent variable (in thisworkTotal EnergyConsumption (TEC))andtwoorevenmore thantwoindependentvariables that is, thepredictors,populationand GDPutilizedanapplication techniqueforyearlyconsumptionforecastingalgorithmonthesmartnew intelligentelectronicdevicesusingmultiple regressionmethodwhich isput intopractice inaddition torecursive least square. TEC=(332,023.240)Population+(302,638.253)GDP−185,039.015is theregressionequationfrom Table4. Table4.Summaryof themodelwithbothPopulationandGDPas thevariable. Ind.Variable RSquare Std. Error Constant Slope Significance Population 0.986 27,442.309 −185,039.015 332,023.240 0.000 GDP 0.986 27,442.309 −185,039.015 302,638.253 0.000 Withone independentvariable ofpopulation theR2 is 0.845 andwith that ofGDP it is 0.957, whereaswith twoindependentvariablesGDPandpopulationcombined, inmultiple linear regression theR2 increases to0.986. Thestandarderrorof46,784.201withonevariable,GDPdrops to27,442.309 withtwovariables. Lowerisbetter. TheGDP’sstandarderrorisalmostlessthanhalfofthepopulation’s error. SoGDPisagain thebetterpredictor in termsofLinearMultipleRegression. 3.3. CorrelationAnalysis Almostall the independentvariablesexhibitahigherdegreeofcorrelationagainst thedependent variables, the analysis of correlation fromTable 5 illustrates that there is positivehigh correlation betweenpopulationandTEC.ThePearsoncorrelationcoefficientisfoundtobe0.919. FromFigures6–8, theanalysisofcorrelationbetweenGDPandTECproves that there isaveryhighpositivecorrelation. ThePearsonCorrelationCoefficient is found tobe0.978Whereas the correlationbetweenGDPper capitaandTECdemonstrates that there isapositivecomparatively lowcorrelationbetweenGDPand TEC.TheCoefficient is foundtobe0.975. Table5.CorrelationMatrix. Variables TEC Outcome Direction Population 0.919 Highcorrelation Positive GDP 0.978 Veryhighcorrelation Positive GDP/Capita 0.975 Highcorrelation Positive 107