Page - 106 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 3442 values that is, thedifferencebetweentheactualandmeanandthedifferencebetweentheestimated andthemeangives theR2value. 1−R2={SSR/SST} SSRrefers to theresidual sumofsquaresandSSTrefers to the total sumofsquares. The standarderrorof theestimate is thedistancebetween theestimatedand theactualvalue. Theconstantvalue isactually the ‘y’ interceptof the line. The independentvalue is theslopeof the regression line; since the line is linear theslope isalsoconstant. Thesignificance is theactual ‘p’values. StandardError ( √ n)=σ whereσ refers to thestandarddeviation,nrefers to thesamplesize. 3.1.1. Population As depicted in Table 1, the constant value is−591,193.3447. The independent value that is, the slope of the regression line is 959,469.219; since the line is linear the slope is also constant. Theregressionequationusually framesapredictionandtheprecisionof theprediction iscalculatedby meansof thestandarderror. Italsomeasures thescatterordispersionof theobservedvaluesaround theregression line. Y=959,469.219X−591,193.347 is theregressionequation. Table1.Summaryof themodelwithPopulationas thevariable. Ind.Variable RSquare Std. Error Constant Slope Significance Population 0.845 89,127.342 −591,193.347 959,469.219 0.000 3.1.2.GDP Asillustrated inTable2, theconstantvalue is53,096.385. The independentvalue that is, theslope of theregression line is417,965.826; since the line is linear theslope isalsoconstant. Y=417,965.826X−53,096.385 is theregressionequation. Table2.Summaryof themodelwithGDPas thevariable. Ind.Variable RSquare Std. Error Constant Slope Significance GDP 0.957 46,784.201 53,096.385 417,965.826 0.000 3.1.3.GDPperCapita Theconstantvalue is−2457.344. The independentvalue that is, theslopeof theregression line is 959,469.511; since the line is linear theslope isalsoconstantas inTable3. Y=546.511X−2457.344 is theregressionequation. Table3.Summaryof themodelwithGDPpercapitaas thevariable. Ind.Variable RSquare Std. Error Constant Slope Significance GDP/Capita 0.951 50,234.297 −2457.344 546.511 0.000 WhenweforecastTotalElectricityConsumption(TEC)usingthreevariables, theGDPplaysan important roleanditpredictsbetter theTotalElectricityConsumptionthantheGDPperCapitaand thepopulation. TheR2value forGDPandTECis0.957whereasbetweenGDPpercapitaandTEC it is only0.951. WhencomparedwithPopulationandTECit is evenas loweras0.845. Hence it is concludedthatGDPforeseesTECbetter. The loweststd. error,46,784.201ofall the three isalsowith theGDP. 106