Predict Global Earth Temperature using Linier Regression

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1 Predict Globl Erth Temperture using Linier Regression Edwin Swndi Sijbt ( ) Progrm Studi Mgister Informtik Sekolh Teknik Elektro dn Informtik ITB Jl. Gnesh 10 Bndung 40132, Indonesi Abstrct Globl wrming is globl issue of the world nowdys. Every yer globl erth temperture tends to increse nd dt bout it recorded continuously. This dt cn be used to get more vluble informtion. Predicting is one point tht we cn do. This pper discuss bout how dt bout globl erth temperture cn be used to pproximte the dt tht not recorded or how the dt cn be used to predict bout the next globl erth temperture. This cn be done by implementing linier regression. Keywords component; globl erth temperture, prediction, linier regression. I. INTRODUCTION Globl wrming is one issue tht needs to be considered becuse this issue cn ffect world society. This issue cn be very lrge disster becuse it cn ffect system in erth. Incresing of globl erth temperture is the result of the development of industry. The use of mchine tht hs dnger wste is growing fst. Pollution levels lso increse. This issue ffects system in erth. Every yer, NASA nlyzes this issue nd recodes the informtion. Observtion result shows tht temperture in our erth tends incresing. NASA hs recorded dt from 1880 to The recorded informtion shows tht 2016 is yer when erth surfce hs highest verge temperture. They predict, globl erth temperture will be highest in the next yer. To support the prediction, we need to develop method tht cn predict globl erth temperture using recorded dt. We cn use mthemticl pproch. We cn develop prediction method by using linier regression. By using this method, we try to look correltion between yer nd globl erth temperture. We cn predict by getting pproximte vlue before doing direct observtion. We lso cn pproximte missing vlue of dt recorded. II. METHODOLOGY A. Dtset One of the most importnt in this pper is dtset. From dtset, we cn get more informtion. In this cse, we use globl erth temperture dt. Dt is tken from NASA website. Dt is collected from institute tht clled NASA's Goddrd Institute for Spce Studies (GISS). Dt contin informtion bout globl erth temperture from 2000 to TABLE I. GLOBAL EARTH TEMPERATUR DATASET No Yer Temperture (⁰C) NASA's Goddrd Institute for Spce Studies (GISS) B. Regression Regression is method to get functionl reltionship between vrible nd the other vrible [1]. In this cse we wnt to know globl erth temperture in yer. By using regression, we lso cn mtch curve tht hs low ccurcy dt. Low ccurcy dt cn be obtined from observtion, lbortory experiment, nd sttistic dt. There re two kinds of vrible, response or dependent vrible nd explntory or predictor vrible. Response vrible is vrible tht contin vlue we wnt to know. Predictor vrible is vrible tht will be used to find the response vlue. C. Simple Linier Regression Simple linier regression is linier regression tht hs one predictor. This method is suitble for use becuse dtset is

2 sttisticl dt tht hs low ccurcy [2]. We only using vrible yer to get pproximte globl erth temperture. In linier regression, there is linier line through set of dt. This linier function is using to predict vlue of when is known. The eqution is simplified gin + + Or + + These equtions re linier eqution nd we cn write it in mtrix form. We cn find vlue of nd by solving linier eqution system [3]. Fig. 1. Linier Regression Curve In Fig 1, there re severl nodes tht we hve known vlue of x nd y respectively, except. We just know vlue of. By using linier regression, we cn pproximte vlue of using vlue is given by linier function. We cn mke linier eqution tht gives pproximte vlue for. The true vlue is contin error, so eqution must be written with ( ) = ( ) + = 1,2,3,, From eqution (1), ( ) is true vlue nd is error every node. In linier regression, we form linier eqution s ( ) = + As explin before, ( ) only gives pproximte vlue. There is devition vlue between true vlue nd pproximte vlue. Devition is clculted by eqution = ( ) = ( + ) = Vlue of nd lso cn be computer by eqution = ( ) = To know how good our pproximte function is, we cn mesure RMS error (root-men-squre error). The smller the function. = ( ) the better pproximte vlue of the III. EXPERIMENT In this section we wnt to implement liner regression to get informtion of globl erth temperture in yer. This is eqution for squre of totl devition. = ( ) To get minimum of, we must mke differentil of. = 2 ( ) = 0 = 2 ( ) = 0 Ech of differentils from eqution (5) nd eqution (6) divided by -2 ( ) = ( ) = Fig. 2. Globl erth temperture dt Distribution dt in Crtesin digrm is shown by Fig.1. This digrm shows us tht nodes form line of set of dt. This mkes us ssume tht globl erth temperture cn be predicted by using linier regression.

3 For strting the experiment, the dtset is divided in to two. 15 rows of them to be dt trining, nd other 2 rows re used s dt testing. Dt trining is used to mkes model or function nd dt test is used to test function. TABLE II. DATA TRAINING No Yer Temperture (⁰C) TABLE III. DATA TESTING No Yer Temperture (⁰C) By this experiment we wnt to mke pproximte function from dt trining nd try to predict dt vlue of dt testing. First, mke tble tht contins,,, nd. i TABLE IV. DATA FOR NORMAL EQUATION i x = y = 9.87 x = x y = Second, we mke mtrix to solve linier eqution system. Mtrix denoted s mtrix A b = By implementing linier eqution system, we cn get vlue of nd. = ; = By getting vlue function. f(x) = + bx f(x) = x nd, now we hve clculte the Now, we try to predict vlue for dt test. We hve 2 dt test nd here the prediction vlue. TABLE V. PREDICTION FOR DATA TEST i ( ) = + error We lso need to know how good the pproximte function is. Now, we wnt to mesure the Root Men Squre Error. We compre vlue of with vlue of ( ). We lso mesure devition nd squre of devition. TABLE VI. i ( ) = + DATA FOR ROOT MEAN SQUARE ERROR

4 i ( ) = By using dt from tble, we cn mesure the RMS error for knowing how good the function is. The function is good if it hve smll vlue. E = f(x ) y / i = ( ) = ( ) ln ( ) = ln ( ) = E = f(x ) y / Now, we must find vlue of system. nd. We use linier eqution E = / E = From experiment bove, we get vlue nd the vlue is smll. The smller, the better result will be obtined. There re severl non linier functions tht we cn use for comprison. 1) Simple Power Eqution Eqution for this method is = We cn chnge tht non liner eqution to linier eqution. By chnge the non linier eqution, we cn use it in linier regression. Now, we try to chnge the form. = ln( ) = ln( ) + ln ( ) We mke new vribles nd form new eqution = ln( ) ; = ln( ) ; = ln( ) ; = So we cn form it to linier regression form. = + TABLE VII. DATA FOR = EQUATION i = ( ) = ( ) b = By implementing linier eqution system, we cn get vlue of nd. So, we cn get vlue of. = ; = = = TABLE VIII. PREDICTION FOR DATA TEST USING = EQUATION i ( ) = error ) Exponentil Model Eqution for this method is = We cn chnge tht non liner eqution to linier eqution. By chnge the non linier eqution, we cn use it in linier regression. Now, we try to chnge the form. = ln( ) = ln( ) + ln( ) ln( ) = 1 We mke new vribles nd form new eqution = ln( ) ; = ln( ) ; = ; = So we cn form it to linier regression form. = +

5 TABLE IX. DATA FOR = EQUATION i = = ( ) Y = Now, we must find vlue of elimintion nd. We use Guss b = By process of Guss elimintion we found vlue of vlue of. So, we cn get vlue of. = ; b = = = TABLE X. PREDICTION FOR DATA TEST USING = EQUATION i ( ) = error ) Sturted growth rte model Eqution for this method is nd y = = + Define new vribles Y = ; = ;b = ;X = So we cn form it to linier regression form. = + TABLE XI. DATA FOR = EQUATION i = = Y = Now, we must find vlue of elimintion nd. We use Guss b = By process of Guss elimintion we found vlue of vlue of. = ; b = So, we cn get vlue of. C = 1/ = d = = TABLE XII. PREDICTION FOR DATA TEST USING = EQUATION i ( ) = + error nd

6 IV. CONCLUTION In this pper, we wnt to show wht correltion between globl erth temperture nd yer is. Globl erth temperture tends incresing every yer. This dt forms set of nodes tht tends to be linier. By this sitution, we cn mke prediction using linier regression. Experiment is done with four pproches. First, we use linier regression. Second, we use simple power eqution. Third, we use exponentil model. Fourth, we use sturted growth rte model. Approch tht genertes smllest error is exponentil model. [4] ccessed on My, 10 th 2017 STATEMENT I hereby declre tht this pper is written by me in my own words, not n dpttion or trnsltion of nother pper, nd certinly not result of plgirism. Bndung, 29 April 2012 REFERENCES [1] S. Chtterjee nd A. S. Hdi, Regession Anlysis By Exmple, 5th ed. Hoboken, New Jersey: John Wiley & Sons, Inc., [2] R. Munir, Metode Numerik. Penerbit Informtik, [3] S. C. Chpr, Applied Numericl Methods, 3rd ed Avenue of the Americs, New York: McGrw-Hill, EdwinSwndi Sijbt