A MODEL TO MEASURE THE PERFORMANCE OF HUMAN RESOURCES IN ORGANISATIONS

Transcription

1 DOI: /sues A MODEL TO MEASURE THE PERFORMANCE OF HUMAN RESOURCES IN ORGANISATIONS Lecturer Magnola Tlca PhD Vasle Goldş Western Unversty of Arad E mal: tlca.magnola@uvvg.ro Elsabeta Mare SMART APPS & SOLUTIONS, Baa Mare, Romana E - mal: sales@smartapps.ro Assocate Professor Anca Apatean PhD Techncal Unversty of Cluj Napoca E mal: anca.apatean@gmal.com (Receved: December 2017; Accepted March 2018) Abstract: The economc crss, demography, technology, globalzaton etc. are all factors whch wll nfluence the organzatonal structures and busness strateges. A new busness strategy wll requre, among others, that passve Human Resources Management (HRM) change nto an actve one wth a decsve nfluence upon busness. The vson of an actve HRM requres that HR nformaton (IT) dedcated systems assst human resources managers n ther decson-makng. The estng IT systems predomnantly manage the salary calculatons and, possbly, the employee's professonal development, two of the tasks that a human resources manager has to pursue. However, tasks such as assstng, consultng and engagng the human resources n the organzaton are equally mportant. IT systems must also develop nto these drectons. The present paper proposes a soluton to measure the performance of human resources by creatng an employee performance ndcator (EPI). The paper frst descrbes the economc phenomenon nvolved n the HR performance process, then the mathematcal model s formulated, the algorthm s mplemented, the soluton of the model s analysed from a techncal and economc pont of vew, and fnally the decson s made. We use the weghted arthmetc mean to compute the EPI ndcator and the correlaton formula to establsh the degree of relevance between the EPI ndcator and the varables nvolved n the model. An mplementaton n R s gven. Key Words: ongong performance management, key performance ndcators, multple lnear regresson, statstcal R envronment J.E.L. CODES: C15, C60, M53 1. Introducton Nowadays, performant nformaton systems (IS) are able to assst almost the entre actvty of an organsaton: servces, producton, sales, customer management, 57

2 employees, management, decsons and so on. The new busness strateges nvolve the human resources management (HRM) more and more n the decson process. It s about the performance management (PM) that conssts n all of the processes that managers use to effectvely lead, mange, develop, reward and assess employees (Garr, 2011). Most estng HRM nformaton systems are mplemented to manage the salary calculatons and only few of them manage the employee's professonal development. In order to acheve performance management (PM), an ongong supportng performance module was lately mplemented n an HRM nformaton system. Ths module s based on the contnuous performance management prncples and proved to be more effcency than other performance management software: companes lke Mcrosoft, Google, Adobe, PWC, Cargll and so on, who have recently (2012) adopted ths knd of modules, ncreased ther productvty and profts as a result of mprovng employees performance. Management nformaton systems dedcated to ongong performance management are n a contnuous development. The managers are searchng to mprove the crtera of measurng employees performance and the software developers are havng dffculty fndng the concrete formula that measures performance n varous stuatons. We propose a soluton to measure the human resources performance by creatng an employee performance ndcator (EPI) based on the defned performance crtera of each job. The frst secton descrbes some economc aspects regardng the effcency of the HR process. In the second secton, we gve the mathematcal soluton of ths effcency process. We use the weghted arthmetc mean to compute the EPI ndcator and the correlaton formula to establsh the degree of relevance between the EPI ndcator and the varables nvolved n the model. The soluton of the model s analysed from a techncal and economc pont of vew and fnally the decson s made. The model s mplemented usng R statstcal envronment. 2. Prelmnary notes In modern organsatons, performance management s management (Garr, 2011). Many organsatons treat performance management as a yearly event. Garr proposes an ongong performance management framework whch contans all of the actvtes ncluded n a regular performance management, but the process s contnuous. Garr s research shows that companes wth an ongong focus on performance management have better employees, talent and busness results: 45% are more lkely to have above-average fnancal performance and 46% are more 58

3 lkely to be effectve at holdng costs at the same level or below the level of compettors. In lterary revew, the topc of shftng the tradtonal performance management to contnuous one s qute new and t s dscussed by researchers and developers at dfferent levels: Garr, analyst of the HR communty of Bersn by Delottes [1], desgned a new Performance Management Framework to help HR organsatons performance management from an event to a powerful ongong busness actvty (Garr, 2011), Gandh (Gandh, 2017) underlnes, n Chef Learnng Offcer [2], the mportance of adoptng an ongong performance management; eperts for IT developers stes, such as Atm (A-team) [3], propose 10 tps for an Ongong Performance Management Framework and ther advantages (Atm, 2017); Robertson, manager specalsts of Step Two[4], talks about nformaton management that t s not just a technology, but a busness processes and practces that underpn the creaton and use of nformaton (Robertson, 2005), studes done by researchers from Brandon Hall Group (Brandon Hall Group, 2015) and so on. Armstrong and Baron defne performance management (PM) as a strategc and ntegrated approach to delverng sustaned success to organzatons by mprovng the performance of the people who work n them and by developng the capabltes of teams and ndvdual contrbutors. (Armstrong & Baron, 1998) Ongong performance management establshed the term contnuously to weekly, daly. The most compellng reasons are underlned by Hansen (Hansen, 2017): the annual revew s neffcent, managers and employees need more feedback, ongong feedback actually saves tme, feedback s most effectve when gven n real-tme, as t mproves engagement and performance. Whle performance management s askng How do we manage the strategy we have put n place? performance measurement asks How do we track the progress of the strategy we ve put n place? Performance measurement encompasses the assessment of performance and results acheved by ndvdual employees, groups of employees or teams, and entre organzatons (OPM.gov, 2016). Performance measurement uses performance ndcators. Performance Indcators (or Key Performance Indcators KPI) are the quantfable masses, both fnancal and nonfnancal, of the performance of those tasks, operatons or processes whch are essental for busness. Tracked contnuously and together wth strategc objectves of the organsaton, HR performance ndcators mprove ongong performance management. HR performance ndcators generally measure employee engagement, performance ratngs, retenton/turnover, hgh potental employees (HIPO) [5], employees development plans, readness for job, nternal hre age, dversty of workforce, 59

4 level of competence and so on. Some HR performance ndcators are quantfable, whle others are qualtatve ndcators. A glossary of employee performance ndcators dvded nto key subject areas can be studed at the ICAEW s page (ICAEW, 2017). Ongong performance management n a human resource management contet s the supervson of an employee's work through one-to-one dscussons and ongong feedback from supervsors and regularly scheduled check-ns (Rouse, 2016). In ths regard, Performance Factors and Behavour Indcators are ntended to clarfy for employees and supervsors what performance or behavour s epected. There are descrbed seven unversal performance factors and four management performance factors (UC Rversde, 2016), wth fve ratng levels for each factor: from eceptonal to unsatsfactory performance. If employees clearly understand ther assgnments, know what level of performance s consdered acceptable and receve consstent feedback then employees are successful performers. Technology s especally mportant n supportng the delvery of the necessary nformaton regardng rated factors. Technology s drvng the evoluton of ongong performance management. The power of developng performant management nformaton systems allowed bg companes to mplement ther management actvtes regularly nstead of sporadcally. Thus, ongong performance management could become part of the human resources everyday role. A human resource nformaton system (HRIS) [6] s a sute of software, databases and cloud computng whch provde an all-encompassng soluton for managng every aspect of a workforce (Retsema, 2016). HRISs nclude modules for classcal human resources management lke contact nformaton, work progress, pay hstory, hours worked, beneft trackng and so on. Recently, HRISs were mplemented for employee goal trackng whch enable employees to set goals collaboratvely (algn wth the organzaton), see n real tme ther progress and receve feedback from managers (see Clear Revew software). 3. Methodology secton Problem framework As performance management systems are contnuously developng, the present artcle proposes a model to measure the effcency of human resources performance whch may be mplemented n HRIS. Beng known such evaluaton crtera for employee that the number of achevements of the crteron may be determned, n order to evaluate the employee performance correlated wth gven crteron, we defne the rate of apprecaton as nteger number between 0 and 100, less ratngs meanng great apprecaton, bg 60

5 ratngs meanng poor apprecaton. Multplyng the number of achevements of each crteron wth the rate of apprecaton we obtan an evaluaton of each crteron. Further, by assgnng each crteron wth the rate of the mportance n crtera, we can compute the value of mportance rate of the evaluaton of each crteron. Fnally, to determne the performance of an employee, we compute the weghted mean average of rate of the mportance n crtera weghted by the evaluaton of each crteron. The employee performance ndcator EPI Defnton 1. Beng known n evaluaton crtera for employee and the number of achevements of each crteron k, =1,,n, the employee performance ndcator s defned as weghted mean average (1) EPI n 1 n v p where p : k r, 1,..., n s the evaluaton of each crteron wth o k, =1,,n denotes the number of achevements of each crteron (an nteger postve number) and o r, =1,,n denotes the rate of apprecaton (a number between 0 and 100, less ratngs meanng great apprecaton, bg ratngs meanng poor apprecaton), v, 1,..., n s the rate of the mportance n crtera (a real postve number between 0 and 10). Observaton 1. The formula (1) has sense as denomnator s not null. Indeed, the case of all achevements to be zero ( k 0, 1,..., n ) s ecluded, not beng a real case. Proposton 1. The employee performance ndcator EPI takes real values between 0 and 10. Proof: We have followng nequaltes: (2) 0 k ma( k), 1,..., n, wherek (3) 0 r 100, 1,..., n, wherer (4) 0 v 10, 1,..., n, wherev R Multplyng nequaltes (2) and (3) we have 1 p 61

6 0 p 100 ma( k), 1,..., n, where p : k r N. Thus (5) (6) n 0 p 100 nma( k) or 1 n 1 0 p v 1000 nma( k). p v 1 Dvdng (6) and (5) and takng nto account Observaton 1, n p Observaton 2. a. If all the mportance rates are equal, then EPI has the value of mportance rate. b. If the mportance rates have the same value, 10, then EPI has mamum value. Proof. Indeed, f v1... vn v then EPI n 1 n 1 vp p n 1 v. If the manager establshes the entre mportance rate to be 10, or 0, then EPI has the mamum value, 10, respectvely the mnmum value, 0. EPI s applcablty To llustrate the applcablty of the EPI ndcator we take a very smple eample. Consder the tranng program of employees, a mandatory program n any organzaton. Human resources managers determne when tranng s necessary and the type of tranng necessary to mprove performance and productvty. Human resource managers are responsble for conductng the tranng program. Consder the set of 3 crtera on trackng the tranng progress of an employee: C1: the number of courses employee attended C2: the number of graduated courses C3: the number of absences from courses For a certan employee, there are known the number of achevements for each crteron: k 1 =6 courses attended 62

7 k 2 =4 courses graduated k 3 =1 absence The manager prevous apprecates each crteron as follows: r 1 =20 r 2 =30 r 3 =50 The manager prevous sets the rate of mportance n crtera: v 1 =8 v 2 =10 v 3 =2.5 Applyng formula (1), the employee performance ndcator has the value 8(620) 10(430) 2.5(1 50) EPI A score of 7.88 ndcates that employee successfully meets performance epectatons. Now, consderng the case when all the courses are graduated (k 2 =6) and there s no absence (k 3 =0), n the same ratng values, the EPI s 9.2 that means the employee made an eceptonal performance. On the other sde, f employee graduated only one course (k 2 =1) and gets 8 absences (k 3 =8), EPI s 4.08 that means the performance needs mprovement. EPI s nterpretaton Ratng scale EPI measures the performance of employee. The feedback s based on the followng ratng scale: an EPI rated between 10 and 9 means an eceptonal performance, between 9 and 8 the employee eceeds performance epectatons, between 8 and 7 the employee successfully meets performance epectatons, a rate between 7 and 5 means that the performance needs mprovement, a rate between 5 and 1 denotes an unsatsfactory performance. The strength of the assocaton between the EPI ndcator and the varables nvolved n the model EPI ndcator depends on three sets of varables: number of achevements, rate of apprecaton and rate of mportance of each crteron. Because each varable contans n values, the total number of ndependent varables s n 3. Thus a multple lnear regresson s necessary to apply. Multple lnear regresson s a statstcal tool that eamnes how multple ndependent varables are related to a dependent varable. The ndependent varables are the n 3 varables nvolved n the EPI defnton: 63

8 the number of achevements: k 1, k 2,, k n the rate of apprecaton: r 1, r 2,, r n the rate of mportance of each crteron: v 1, v 2,, v n Proposton 2. The equaton of lnear multple regresson s y... (7) where EPI 0 1,1 k1 1,2 k2 1, n kn... 2,1 r1 2,2 r2 2, n rn... 3,1 v1 3,2 v2 3, n,...,,,...,,,..., are the ndependent varables correspondng to k1 kn r1 rn v1 vn the number of achevements, the rates of apprecaton, respectvely the rates of the mportance; y s the dependent varable correspondng to EPI; EPI 0 s the ntercept;, j, 1,2,3, j 1,..., n are the regresson coeffcents; s the resdual standard devaton. Proposton 3. Knowng data for the ndependent varables X collected from N subjects and N observatons for the dependent varable Y, equaton (7) becomes (7) Y X. T The regresson coeffcents are obtaned as 1 where Y y1 y2 y3... y N T N T T X X X Y, (Hervé, 2007) 1 1, k 1 1, k , k 1, 1 1, , 1, 1 1,... n r r r n v v 2 1, vn 1 2, k 1 2, k , k 2, 1 2, , 2, 1 2,... n r r r n v v 2 2, vn X N, k1 N, k2 N, kn N, r1 N, r2 N, rn N, v1 N, v2 N, vn ,1 1, n 2,1 2, n 3,1 3, n The values and regresson analyses come from statstcal software. The regresson analyses gve the correlaton coeffcent whch establshes the degree of relevance between the EPI ndcator and the varables nvolved n the model. T 64

9 Proposton 4. The correlaton coeffcent s the percentage of varaton n the response EPI that s eplaned by the regresson. The hgher the value, the better the regresson fts the data. The correlaton coeffcent s always between 0% and 100%. Observaton 3. It s known that multple correlaton coeffcent always ncreases (or stays the same) as more ndependent varables are added to multple lnear regresson model, even f the ndependent varables added are unrelated to the dependent varable (PennState, 2017). However, the multple lnear correlaton may be appled to nvestgate how much EPI s related to the ndependent varables f there s used a larger sample of data correspondng to more than 40 predcted EPI values (MnTab Epress support, 2016). 4. Fndngs In order to compute the value of the employee performance ndcator and to determne the ntensty of the relaton between employee performance ndcator and ts varables, the statstcal R software s used. R s a free and powerful envronment language and software for statstcal calculaton and graphcs whch contans lnear and non-lnear modellng technques. There s a varety of data types ncludng vectors, matrces, lsts and data wndows. R provdes facltes for mplementng regressons usng functons from R packages. In (Tlca & Bojor, 2016), R was used to study the outcomes generated by three dfferent types of regresson: lnear, splne and B-splne regresson. Now we use R to mplement the formula of EPI ndcator and to nterpret the multple lnear regresson and correlaton. A comple study about the correlaton of the regresson varables may be appled startng from the paper (Precup, 2015). The R algorthm s descrbed below. Input data: n the number of crtera The R algorthm s descrbed below. Input data: n the number of crtera c c[1]... c[ n] strng vector of crtera r r[1]... r[ n] v v[1]... v[ n] nteger values vector of the rate of apprecaton real values vector of the mportance rate k k[1]... k[ n] nteger values vector of the number of the achevements Output data: EPI the employee performance ndcator real number Y EPI the predcted value of EPI real number 65

10 R 2 square multple correlaton coeffcents Step 1. Insertng the gven values Step 2. Computng the EPI usng the weghted mean formula Step 3. Computng the predcted values EPI usng the multple lnear regresson Step 4. Computng the multple correlaton coeffcent Step 5. Dsplayng the results The algorthm was mplemented n R, n ScrptCode.R fle. The R-functons used n algorthm are: R-functon Used to cat( ) - prnt the nformaton on-screen; readlne(prompt=, "\\,")[[1]]- read a lne from the termnal; as.numerc(.) - convertng a factor to numerc; read.deln( fle.tt, - read n delmted fles, where data s header=true, organzed n data matr wth coma- set=,, dec=. ) lm(y~model,data) separated elements whch has header; - create a lnear (smple or multple) regresson model gven some formula, n the form of Y~X; summery(model) - summarse the results of model fttng functons; coeffcents(model) - etract model coeffcents; ftted(model) - compute the predcted values of the model; runf(n,mn=m,ma=m) - generate random numbers wth a unform dstrbuton; floor(n) - round a number. The code from ScrptCode.R fle s dvded n four parts: - frst part mplements the employee performance ndcator EPI formula, - second part mplements the multple lnear regresson model wth data mported from tet fle, - thrd part mplements the multple lnear regresson model wth random data, - forth part gves conclusons. The ScrptCode.R fle s called n R Console, by tastng source( ScrtCode.R ) (the ScrptCode.R fle has to be n the current workng drectory of the R process). Data nput: the number of crtera, the number of achevements, the rate of apprecaton and the rate of mportance. The code computes the EPI value for nput data. The nterpretaton of the employee 66

11 performance regardng the nvestgated crtera s dsplayed n the thrd part Conclusons. Fgure 1. The code of the EPI computaton Source: the author s smulaton n R Data nput necessary n the second part of the code need to be organzed n a smple ForRegresson.tt fle. The fle must contans at least 10 dfferent values of EPI correspondng to 10 employees evaluatons. Data are organzed n 10 9 matr wth elements comma separated. The data are loaded n R usng the read.delm(.)functon and used n regresson formula lm(.)and summary(.). Thus, the ScrptCode.R fle returns the regresson results: the values of regresson coeffcents ( vector), the predcted values of EPI (y vector), resdual values of the predcted values ( vector) and the correlaton coeffcent (multple R-squared R 2 ). Fgure 2. The code of the lnear regresson predcted values EPI and R-squared coeffcent computaton usng gven set of data* Source: the author s smulaton n R * Here, the lm(.)functon s appled for 9 ndependent varables The thrd part uses data randomly generated. Consderng a suffcently large number of employees performance evaluatons (between 40 and 90), the code wll automatcally compute the predcted EPI values and the correlaton coeffcent R 2 usng random data. Fgure 3. The code of the regresson predcted values EPI and R-squared coeffcent computaton usng random data Source: the author s smulaton n R Forth part of the code dsplays conclusons about - the EPI value and the nterpretaton of the employee performance and 67

12 - the degree of relevance between the EPI ndcator and the varables nvolved n the model and the correspondng nterpretaton. Fgure 4. The code of the R-squared nterpretaton Source: the author s smulaton n R 5. Conclusons The evaluaton of the employee performance s a constant concern for human resources department. The managers are searchng to mprove the crtera of measurng employees performance and the software developers are havng dffculty fndng the concrete formula that measures performance n varous stuatons. The soluton proposed n ths artcle measures human resources performance. The employee performance ndcator (EPI) s based on the defned performance crtera of each job together wth numercal values: the number of achevements, the rate of apprecaton and the rate of mportance for each crteron. The queston s how well EPI formula s defned? Are the varables and EPI suffcently related? An algorthm of multple lnear regresson computaton s mplemented n R n order to ndcate the assocaton between dependent varable EPI and ndependent varables. Applyng the ScrptCode.R fle we obtan the followng conclusons: Fgure 5. The nterpretatons of the results Source: the author s smulaton n R 1. for the same values as n prevous secton, the employee performance ndcator EPI s 7.88 (the rounded of ); 2. for the same values as n prevous secton, the multple correlaton coeffcent between EPI and the varable nvolved n formula s R-squared 68

13 = a very good correlaton; ths means that 93.39% of the varaton of the EPI ndcator s eplaned by the varaton of the varables (here 9 varables were consdered: each of three crteron has three varables); 3. for random generated values of the number of evaluated employees N, the number of crtera n and the values for varables k, r, v, the multple correlaton coeffcent between EPI and the varable nvolved n formula, R-squared = a good correlaton; ths means that 68.67% of the varaton of the EPI ndcator s eplaned by the varaton of the varables (here n 3 varables were random generated); the generated number of the eperments (evaluated employees number) s 84 and 3 crtera. Other elements of the regresson analyss are: the resduals of the predcted EPI values vary between and 0.71 very good predctons; the resdual standard error beng small ndcates that the regresson equaton s relevant p-value >0.05 ndcates that the predcted EPI are not statstcal sgnfcant, but a large number of data wll generate more trusted predcted values; thus, for 84 observed data and the 3 crtera, the predcted EPI values are sgnfcant because p-value s 6.938e-08. Followng these results, the varables (the number of achevements, the rate of apprecaton and the rate of mportance for each crteron) nvolved n EPI formula are mportant (sgnfcant) n the defnton of employee performance ndcator. Thus, the EPI ndcator, contnuously evaluated, may be consdered a HR performance ndcator n ongong performance management. Notes [1] Bersn by Delotte delvers research-based people strateges desgned to help leaders drve eceptonal busness performance [2] Chef Learnng Offcer a multmeda publcaton focused on the mportance, benefts and advancements of a properly traned workforce [3] A-team an enterprse goals & contnuous performance management platform [4] Step two ste for plannng and desgnng soluton for the workplace and workforce [5] Hgh-Potental Employee s an ndvdual wth ablty, aspraton and engagement to rse to and succeed n more senor, crtcal postons. [6] HRIS s known as HRMS - Human Resource Management Systems or HCM - Human Captal Management software 69

14 References 1. Adnan, S. & Mohamed, Y., Performance Evaluaton Methods and Technques Survey. Internatonal Journal of Computer and Informaton Technology, 3(5), pp Armstrong, M. & Baron, A., Performance Management Handbook. London: IPM. 3. Atm, Learn About Goals Settng, OKR framework and Team Performance. [Onlne] Avalable at: [Accessed 30 September 2017]. 4. Brandon Hall Group, The Value of Ongong Performance Managemen. [Onlne] Avalable at: Ongong-Performance-Manangement.pdf [Accessed 30 September 2017]. 5. Gandh, V., Managers, Get Ready for Ongong Performance Conversatons. [Onlne] Avalable at: [Accessed 30 September 2017]. 6. Garr, S., The Performance Management Framework: Evolvng Performance Management to Ft the Modern Workforce. [Onlne] Avalable at: [Accessed 30 September 2017]. 7. Hansen, J., Why Ongong Feedback vs. Annual Performance Revews?. [Onlne] Avalable at: hs_automaton&utm_medum=emal&utm_content= &_hsenc=p2anqtz- _DNnMuDLSywt0dwSKqF2mrtWs8jIH1KSuQ-TfOuzMOLAMX7PZ8p [Accessed 5 Octomber 2017]. 8. Hearn, S., What s Contnuous Performance Management?. [Onlne] Avalable at: [Accessed 5 October 2017]. 9. Hervé, A., Multple Correlaton Coeffcent. In: A. Hervé, ed. Encyclopeda of Measurement and Statstcs. Dallas: Nel Salknd Ed CAEW, Employee key performance ndcators (KPI). [Onlne] Avalable at: [Accessed 2 October 2017]. 11. MnTab Epress support, Interpret the key results for Multple Regresson. [Onlne] Avalable at: [Accessed 11 October 2017]. 12. O Bren, J. & Marakas, G., Management nformaton systems. A busness unt of The McGraw-Hll Companes, Volume McGraw-Hll/Irwn. 70

15 13. OPM.gov, Performance Management - Measurng. [Onlne] Avalable at: [Accessed 6 October 2017]. 14. PennState, The Multple Lnear Regresson Model. [Onlne] Avalable at: [Accessed 4 October 2017]. 15. Precup, M., What Drves Prvate Equty Investments In R. Studa Unverstats "Vasle Golds" Arad Economcs Seres, 25(4), pp Prodan, A. & Aruște, C., Managementul resurselor umane. [Onlne] Avalable at: Rațu-Sucu, C., Luban, F., Hîncu, D. & Ccou, N., Modelare economcă. Bucureșt: Edtura ASE. 18. Retsema, D., Understandng HRIS, HRM, HCM. [Onlne] Avalable at: [Accessed 2 October 2017]. 19. Robertson, J., prncples of effectve nformaton management. [Onlne] Avalable at: [Accessed 30 September 2017]. 20. Rouse, M., Contnuous performance management. [Onlne] Avalable at: [Accessed 2 October 2017]. 21. Tlca, M. & Bojor, M., Comparatve study of dfferent types of regresson appled to unemployment n Maramures County of Romana. Studa Unverstats Vasle Golds Arad. Economcs Seres, 26(3), pp UC Rversde, Performance Factors & Behavor Indcators, Calforna: Human Resources - Unversty of Calforna. 23. wkhow, How to Measure Performance. [Onlne] Avalable at: [Accessed ]. 24. Wkpeda, Multple correlaton. [Onlne] Avalable at: [Accessed ]. Append A Fg. A.1. Sample of nput data Source: own results generated by ScrptCode.R fle 71

16 Fg.A.2. Sample of observed data from ForRegresson.tt fle Source: own results generated by ScrptCode.R fle Fg.A.3. Multple lnear regresson analyss usng gven set of data Source: own results generated by ScrptCode.R fle Fg.A.4. Multple lnear regresson analyss usng random set of data Source: own results generated by ScrptCode.R fle Fg.A.5. Code of the EPI computaton wth data read from termnal Source: own results generated by ScrptCode.R fle 72

17 Fg.A.6. Code for the multple regresson/correlaton wth mported data Source: own results generated by ScrptCode.R fle Fg.A.7. Code for the multple regresson/correlaton wth random data Source: own results generated by ScrptCode.R fle 73