RESEARCH ON REGRESSION MODELING OF PROFIT RELATED TO MILK YIELD IN DAIRY FARMING

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1 Scetfc Papers Seres Maagemet, Ecoomc Egeerg Agrculture ad Rural Developmet Vol. 14, Issue 4, 014 PRINT ISSN , E-ISSN RESEARCH ON REGRESSION MODELING OF PROFIT RELATED TO MILK YIELD IN DAIRY FARMING Agatha POPESCU, Lva DAVID Uversty of Agrcultural Sceces ad Veterary Medce Bucharest, 59 Marast, Dstrct 1, Zp code , Bucharest, Romaa, Phoe: /3, , , Fa: , Correspodg author: Abstract The paper amed to establsh a correspodg regresso model reflectg the relatoshp betwee proft, as the ma barometer of ecoomc effcecy ad mlk yeld dary farmg usg a sample of 8 farms operatg the Souther Romaa. Two regresso models were compared: the lear regresso ad the quadratc ft. Average mlk yeld regstered 6, kg/cow ad had just 9.4 % varato amog farms. Proft per cow recorded Le, average wth a very hgh varato from a farm to aother ( 46.0%). The correlato coeffcet betwee mlk yeld ad proft per cow, r y = 0.91, reflected a strog postve lk betwee the two ecoomc dcators. The regresso model had the form Y= , wth the stadard error S est = ad the parabolc ft was Y= ,50 havg a hgher stadard error S est = 18, From ths comparso, the lear regresso model proved to be the most sutable oe to reflect the relatoshp betwee proft per cow ad mlk yeld wth the hghest accuracy. Accordg to ths model, t was estmated that for a aual 500 kg ga mlk yeld, proft per cow could be hgher by Le 79 per year wth a deep mpact o farm proftablty. Key words: dary farmg, regresso modelg, proft, mlk yeld INTRODUCTION Mlk yeld has a deep mpact o the ecoomc results dary farmg beg ts tur flueced by techologcal aspects, maly regardg cow feedg, but also breedg herd structure, reproducto ad atural codtos. Mro ad Lup (013) affrmed how mportat s dary farm sze determg ecoomc effcecy. [8] Kopecek 00, usg the cost fucto, otced that the costs for marketed mlk for oe feedg day of a cow have a lower growth compared to mlk yeld ad usg the epese fucto he determed the mamum proft per ltre of marketed mlk, mamum proft per cow ad year ad the terval of proftablty for mlk producto. [6] Grgorou (008) proposed a ew method for establshg the threshold average marketed mlk producto for assurg proftablty dary farms Romaa. [4] Betwee mlk yeld, varable cost ad gross marg per cow s a close relatoshp wth major results for farm proftablty as metoed by Prvutou ad Popescu Agatha 01. [10] The correlato betwee mlk yeld ad proft per cow s a strog postve oe, as foud by Popescu Agatha ad Gyeres Stefa 1989 [15] Ecoomc performace terms of mlk yeld ad the facal performace terms of gross marg are closely related to farm sze as affrmed by Popescu Agatha 009 ad 010. [11,1] Proft varato depeds o marketed mlk ad producto cost as metoed by Kopecek 00 ad Popescu Agatha 014. [6,14] A ga of 100 kg mlk producto could crease mlk cost by Le 0.0 per mlk klogram ad farmers proft by Le per cow ad year as obtaed by Popescu Agatha 014 Romaa. [14] The relatoshp betwee mlk cost, retur ad proftablty dary farmg was put to evdece by Popescu Agatha (014b) [15] 11

2 Scetfc Papers Seres Maagemet, Ecoomc Egeerg Agrculture ad Rural Developmet Vol. 14, Issue 4, 014 PRINT ISSN , E-ISSN The relatoshp betwee mlk yeld ad ecoomc dcators dary farmg was studed usg varous modelg techques. Popescu Agatha 010 used lear regresso fucto gross marg forecast based o mlk yeld.[1,13] Murphy et al. 014 used olear autoregressve model wth eogeous put, a statc eural etwork ad a multple lear regresso model for predctg daly mlk yeld per herd over varous forecast horzos. He cocluded that the o lear autoregressve model wth eogeous put s the more accurate soluto to covetoal regresso techques for short-term predcto of mlk yeld. [8] Ramsbottom et al. 011 used lear ad quadratc models to determe the correlato betwee dary cow geetc mert terms of ecoomc breedg de, mlk yeld, fat ad prote cotet, calvg terval ad facal dcators: come per cow, cost per cow, ad proft commercal sprg calvg dary farms. [18] Hase et al. 005 measured the facal performace dary farms close relatoshp wth mlk producto. [5] The correlato coeffcet s largely used to reflect the relatoshp betwee varous varables as affrmed by Colto 1974, [], Pearso 1985, [9], Spoaugle et al. 014, [0]. Lear regresso s used to reflect the relatoshp ad evoluto tred betwee dfferet varables whch deped oe to aother as affrmed by Murphy et al. 014 [6], Popescu Agatha 010 [1], Sokal et al [19]. Quadratc models are also used to characterze the lk betwee dfferet varables ad ther depedece oe to aother as metoed by Popescu Agatha ad Gyeres Stefa 1989 [16], Ramsbottom et al. 011 [18]. Stadard error of lear regresso, quadratc ft ad other mathematcal models assures the hghest accuracy of the predcto [19]. For ths reaso, t s commoly used the decso what mathematcal model should be chose to reflect the best way the lk betwee varous dcators or varables ad to 1 predct ther future evoluto wth the hghest precso. Also, the determato coeffcet or R squared s used to epla how much of the total varato of the depedet varable s gve by the depedet varable as metoed by Bolboaca [1], Dufour et al. 011 [3]. I ths cotet, the preset paper amed to test two mathematcal models: lear regresso ad quadratc ft the aalyss of mlk yeld mpact o proft dary farmg Romaa order to establsh the most sutable modelg techque proft predcto based o average mlk producto. MATERIALS AND METHODS I order to set up ths paper, the prmary data were collected from a sample of 8 dary farms stuated the Souther Romaa the year 013. The ecoomc dcators take to cosderato were dvded to two categores of varables: () depedet varables, ths case X-mlk yeld/cow/year, ad () depedet varables symbolzed Y, as follows: Y 1 -mlk producto/farm, Y - producto epeses/cow/year, Y 3 -mlk cost, Y 4 -proft/cow/year, ad Y 5 -proft/farm. For each ecoomc dcators, the followg statstcal parameters have bee determed: (a)average of the varable, X, usg the well kow formula: X1 X... X X (1) (b)varace of varable, S, accordg to the formula: S ( X X ) 1 1 () (c)stadard Devato, S, based o the formula:

3 Scetfc Papers Seres Maagemet, Ecoomc Egeerg Agrculture ad Rural Developmet Vol. 14, Issue 4, 014 PRINT ISSN , E-ISSN S = 1 ( X X ) 1 (3) (d)varato Coeffcet, V %, usg the formula: S V% X 100 (4) The correlato coeffcets betwee mlk yeld ad each of the other ecoomc dcators: mlk producto/farm, producto epeses/cow/year, mlk cost, proft/cow/year ad proft/farm were determed usg Pearso product-momet correlato coeffcet, r y, whose mathematcal formula s: y y y y ry (5) The ecoomc optmzato was based o the estmato of proft per cow/year, the depedet varable, Y 4, reflectg the best maer the results of the actvty dary farmg, related to mlk yeld, X, cosdered the depedet varable. I order to establsh whch mathematcal model s sutable to the evoluto of ths par of dcators, two regresso fuctos were tested: - Lear regresso, whose formula s: y = a +b, (6) where y = the depedet varable ad = the depedet varable, Least Square Method of Regresso Aalyss allowed to calculate the values of the coeffcets a ad b, solvg the system of the two ormal equatos gve below: y a b y a b (7) ad usg the formulas: a b y y ( ) y y ( ) (8) (9) The stadard error of the estmate, S est, was also requred to be determed as a measure of the accuracy of predctos, usg the formula gve below: S est ( Y Ycalc ) = (10) N where Y s the actual value, Y cal s a predcted value, ad N s the umber of pars of values. Also, the determato coeffcet or R squared, R, was calculated usg the formula: R 1 1 ( Y Y ) 1 calc ( Y Y) (11) -Quadratc or Parabolc Ft, whose formula s: y = a +b + c, (1) where y = the depedet varable ad = the depedet varable. Least Square Method of Regresso Aalyss allowed to calculate the values of the coeffcets a, b ad c solvg the system of the ormal equatos gve below: y a y a y a 4 3 b b b 3 c c c (13) b b 4ac where = (14) a The formulas for the parameters a, b ad c are gve below: (15) [ ( ) ] y [ ] y [ ( ) ] y a

4 Scetfc Papers Seres Maagemet, Ecoomc Egeerg Agrculture ad Rural Developmet Vol. 14, Issue 4, 014 PRINT ISSN , E-ISSN [ ( ] y [( ) ] y [ ] y b [ ( ) ] y [ ] y [ ( ) ] y c where [ ( ) ] [ ] [ ( ) ] ad. (16) 1 Also, the stadard error ad R squared were calculated for the parabolc fucto. The most adequate regresso fucto was chose to forecast proft per cow usg the regresso model havg the lowest stadard error for assurg the hghest predcto ad a 500 kg/cow ga terval for mlk yeld. Table 1.The ecoomc dcators by farm the year 013 Farm Number of dary cows Mlk yeld kg/cow Mlk producto per farm Kg/farm RESULTS AND DISCUSSIONS The ecoomc dcators characterzg each farm are preseted Table 1. Producto Epeses per cow Le/cow Mlk cost Le/kg Proft/cow Le/cow Proft per farm Le/farm F1 5 5, ,000 7,030 1,0 1,135 8,375 F 30 5, ,500 6,696 1,13 1,505 45,150 F3 18 6, ,660 6,76 1,06 3,06 55,116 F4 6, ,00 7,096 1,08 3,089 67,958 F5 8 6, ,440 7,35 1,08 3,079 86,1 F6 34 5, ,000 7,034 1,8 1,089 37,06 F8 50 5,630 68,000 7,198 1,34 1,717 85,850 F9 0 5,115 10,300 7,19 1, ,000 Source: Farm bookkeepg the Souther Romaa, 013 [] The average, varace, stadard devato ad varato coeffcet. Mlk yeld regstered a average of 6, kg/cow wth a varato from the mmum 5,115 kg/cow case of F8 ad 6,730 kg/cow case F5. The varato coeffcet was 9.4 % reflectg a low varato from a farm to aother.(table ). Table. Average ad varato coeffcet of each ecoomc dcator Idcator MU X S S V% Mlk yeld Kg/cow/year 6, , Mlk producto per farm Kg/farm 175,400,718,65, , Producto epeses per Le/cow 7, , cow Mlk producto cost Le/kg Proft per cow Le/cow, , Proft per farm Le/farm 57, ,1, , Source: Ow calculatos Mlk producto per farm recorded 175,400 kg average, varyg from the lowest level case of F5, 10,300 kg, ad the hghest level case of F8, 68,000 kg. The varato of ths dcator amog farms was very hgh, 14

5 Scetfc Papers Seres Maagemet, Ecoomc Egeerg Agrculture ad Rural Developmet Vol. 14, Issue 4, 014 PRINT ISSN , E-ISSN %, beg determed by the umber of cows rased farms ad ther mlk yeld. Producto epeses per cow accouted for Le 7,007.9 per dary cow, ragg betwee Le 6,696 case of F, the mmum level, ad Le 7,198 case of F8. The varato coeffcet reflected a small varato amog farms regardg ths ecoomc dcator,.78 %. Mlk producto cost was Le 1.19 per mlk klogram, varyg betwee Le 1.06 case of F3, the lowest level ad Le 1.40 case of F8, the hghest level. The varato of mlk cost amog farms was a mddle oe, as the varato coeffcet dcated, %. Proft per cow recorded Le, average wth a varato betwee Le 900, the lowest level regstered by F9, ad Le 3,089, the hghest value regstered by F4. Ths dcator had a very hgh varato from a farm to aother, as the varato coeffccet cofrmed, 46.0%. Proft per farm comg from mlk was Le 57,955.9 average, varyg betwee Le 18,000 case of F9, the lowest value, ad Le 86,1 case of F5, the hghest value. The varato regardg ths dcator was very large, the coeffcet of varato beg %.(Table ) The the correlato coeffcets betwee mlk yeld ad the other fve ecoomc dcators take to cosderato are preseted Table 3. per farm. Ths could be eplaed by the fact that mlk producto s flueced by the umber of dary cows whch vared from a farm to aother ad also by mlk cosumpto for calves up to weag. Betwee mlk yeld ad producto epeses s was foud a egatve low correlato, r y = , reflectg a large varety of factors fluecg producto costs per cow, besdes average mlk producto. The correlato coeffcet betwee mlk yeld ad proft per cow, r y = 0.91, reflected a strog postve lk betwee the two ecoomc dcators. Therefore, the hgher mlk yeld, the hgher proft per cow. Also, betwee mlk yeld ad proft per farm comg from mlk, t was foud a postve hgh correlato, r y = 0.647, showg that a hgher mlk yeld could lead to a hgher proft. Takg to accout that the strogest postve correlato was foud betwe mlk yeld ad proft per cow, r y = , t was cosdered that proft per cow s the ma ecoomc dcator whch should be optmzed close relato to average mlk producto per cow. Comparatve results for the lear regresso ad quadratc ft regardg the formulas, the values for the parameters a, b ad c ad, the stadard error ad the R squared case of proft per cow related to mlk yeld are preseted Table 4. Table 3. Pearso product-momet correlato coeffcets betwee mlk yeld ad the other ecoomc dcators Pars of ecoomc dcators take to accout PPMCC, correlato coeffcet, r y Mlk yeld Mlk producto per farm Mlk yeld Producto epeses per cow Mlk yeld Mlk producto cost Mlk yeld Proft per cow Mlk yeld Proft per farm comg from mlk Source: Ow calculatos A egatve weak correlato, r y = was foud betwee mlk yeld ad mlk producto Table 4.Comparatve aalyss betwee lear regresso ad quadratc ft Lear regresso Quadratc Ft y = a +b + c y = a +b Regresso Model Y= , Y= ,50 Stadard error , Pearso productmomet correlato coeffcet R ( R squared) a coeffcet b coeffcet -7, c coeffcet 14,50 Source: Ow calculatos 15

6 Scetfc Papers Seres Maagemet, Ecoomc Egeerg Agrculture ad Rural Developmet Vol. 14, Issue 4, 014 PRINT ISSN , E-ISSN As oe ca easly see, the lowest stadard error was regstered case of the lear regresso model, S est = compared to S est = 18, recorded case of the quadratc ft. Therefore, oly the lear regresso model assures the hghest accuracy predctg the proft related to mlk yeld. The graphcal represetato of the two regresso models s show Fg.1. ad, respectvely, Fg.. Forecast of proft per cow based o mlk yeld for a 500 kg ga. Takg to accout the lear regresso model, Y= ,508.66, assurg the lowest stadard error, that s the hghest precso, t was estmated proft per cow for a terval of mlk yeld ga of 500 kg/cow. The results are preseted Table 5 ad showed that for a creased mlk yeld by 500 kg per year, proft per cow wll grow by Le 79/year. Fg.1.Lear regresso betwee mlk yeld ad proft per cow Fg.. Parabolc ft betwee mlk yeld ad proft per cow 16

7 Scetfc Papers Seres Maagemet, Ecoomc Egeerg Agrculture ad Rural Developmet Vol. 14, Issue 4, 014 PRINT ISSN , E-ISSN Table 5.Estmated proft per cow based o mlk yeld usg the lear regresso model Y= , Mlk yeld, X Estmated Proft per cow, Y est , ,000 1, ,500, ,000 3, ,500 4, ,000 5, ,500 5, ,000 6, ,500 7, ,000 8, Source: Ow calculatos CONCLUSIONS Average mlk yeld regstered 6, kg/cow ad had a reduced varato amog farms ( 9.4 %). Proft per cow recorded Le, average wth a very hgh varato from a farm to aother (46.0%). Proft per cow s deeply flueced by mlk yeld as Pearso product-momet correlato coeffcet proved ( r y = 0.91), estg a strog postve relatoshp betwee these two ecoomc dcators. The comparso betwee the two regresso models: the lear regresso ad the quadratc ft had the followg mathematcal represetato: Y= , wth the stadard error S est = ad the parabolc ft was Y= ,50 wth the stadard error S est = 18, The lear regresso model proved to be the most sutable oe to reflect the relatoshp betwee proft per cow ad mlk yeld wth the hghest accuracy as ts stadard error was the lowest oe. For ths reaso, based o the lear regresso model, t was estmated that for a crease of 500 kg mlk yeld, proft per cow could grow by Le 79 per year. As a cocluso, the most mportat dcators wth a deep mpact o farm proftablty dary farmg are mlk yeld ad proft per cow ad the most adequate mathematcal model for reflectg the lk betwee them s the lear regresso. ACKNOWLEDGMENTS The authors thak the eght dary farmers for ther kdess to provde the producto ad facal data as ths research work to be carred out. REFERENCES [1]Bolboaca Soraa, Correlato ad Lear Regresso, []Colto, T., Statstcs Medce, 1974, Lttle Brow ad Compay, New York [3]Dufour Jea-Mare, 011, Coeffcets of determato, CIRANO, McGll Uversty, Motreal [4]Grgorou, E, 006, Method for establshg the average threshold marketed mlk producto dary farms, Scetfc Papers Seres Maagemet, Ecoomc Egeerg Agrculture ad Rural Developmet, Vol.6, pp [5]Hase, B. G. ad G. Stokstad (005). Measurg facal performace o Dary Farms, Acta Agrcultural Scadavca, Secto C-Food Ecoomcs, Jue 005, vol., Issue : [6]Kopecek Petr, 00, Aalyss of the mlk yeld effect o the ecoomcs of mlk producto, Agrc. Eco., 48 (10): [7]Mro Llaa, Lup Aurel, 013, Aalyss of the structure of the agrcultural farms by sze ad the share of the lvestock amog them. A argumet for more helpg for the small farms, Vol.13(): [8]Murphy, M.D., Mahoy, M.J.O., Shallo, I., Frech, P., Upto, J., 014, Comparso of modellg techques for mlk-producto forecastg, Joural of Dary Scece, Vol.97)(6): [9]Pearso Karl, 1985, Notes o regresso ad hertace the case of two parets, Proceedgs of the Royal Socety of Lodo, 58: 40 4 [10]Prvutou, Io, Popescu, Agatha, 01, Research Cocerg Stadard Gross Marg Depedg o Yeld Dary Farmg, Scetfc Papers: Amal Scece & Botechologes, Vol. 45():339 [11]Popescu Agatha, 009, Aalyss of mlk producto ad ecoomc effcecy dary farms, Scetfc Papers Amal Scece ad Botechologes, Tmsoara, vol. 4 (1): [1]Popescu Agatha, 010a, Research Cocerg the Use of Regresso Fucto Gross Marg Forecast, Bullet UASVM Hortculture, 67():197-0 [13]Popescu Agatha, 010b, Research cocerg gross marg forecast based o mlk yeld usg the least square method of regresso aalyss, Vol.10(): [14]Popescu Agatha, 014a, Research o proft varato depedg o marketed mlk ad producto cost dary farmg, Scetfc Papers Seres 17

8 Scetfc Papers Seres Maagemet, Ecoomc Egeerg Agrculture ad Rural Developmet Vol. 14, Issue 4, 014 PRINT ISSN , E-ISSN Maagemet, Ecoomc Egeerg Agrculture ad Rural Developmet, Vol. 14():3-9 [15]Popescu Agatha, 014b, Research o mlk cost, retur ad proftablty dary farmg, Scetfc Papers. Seres Maagemet, Ecoomc Egeerg Agrculture ad rural developmet, Vol. 14(): 19- [16]Popescu Agatha, Gyeres Stefa, 1989, Research regardg the harmozato of techcal optmum wth ecoomc optmum cow mlk producto. Noveltes the Techology of Domestc Amals, Vol.XV, Cluj Napoca, pp [17]Quadratc Least Square Regresso, calbrato-trag/1-quadratc-least-squaresregresso-calb.pdf [18]Ramsbottom, G., Crome, A. R., Hora, B., Berry, D. P. 011, Relatoshp betwee dary cow geetc mert ad profto commercal sprg calvg dary farms, Amal (01), 6:7, pp [19]Sokal, R.R., Rohlf, F.J., 1995, Bometry, Freema, New York [0]Spoaugle Brta, 014, Pearso Product-Momet Correlato: A Relatoshp Measuremet Tool, [1]Stats Tutoral - The Regresso Le/Stats Tutoral - Errors the Regresso Equato, Tutoral/ErrRegr.html []Valuable bookkeepg data for the year 013 from 8 dary farms stuated the Souther Romaa 18

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: