IMPACT OF STOCK CONTROL ON PROFIT MAXIMIZATION OF MANUFACTURING COMPANY. Keywords: Stock, Profit Maximization, Manufacturing Company, Nigeria.

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1 IMPACT OF STOCK CONTROL ON PROFIT MAXIMIZATION OF MANUFACTURING COMPANY AJAYI Boboye L.1, and OBISESAN Oluwaseun G.2 Department of Bankng and Fnance, Faculty of Management Scences, Ekt State Unversty, Ado Ekt, Ngera ABSTRACT Ths study examned the mpact of stock control on proft maxmzaton of manufacturng company wth the man of determnng the mpact of stock control on proftablty of manufacturng company. The data collected was spanned from 2005 to The study employed the use of panel data regresson for the purpose of analyss usng proft after tax (PAT) as endogenous varable whle stock value (STV), frm sze (SIZE) and current rato (CRR) were regressed as exogenous varables. The result of the analyss explored that stock value (STV) and frm sze (SIZE) were sgnfcantly related to proft after tax whle current rato was negatvely related to proft after tax of manufacturng companes. The study essentally concluded that stock control sgnfcantly mpact proft maxmzaton of selected manufacturng companes n Ngera. Based on the concluson the study recommended that the sales and marketng department of the company should pay closer attenton to the growth pattern of nventory usage and ncorporate t n sales forecastng technque Keywords: Stock, Proft Maxmzaton, Manufacturng Company, Ngera. INTRODUCTION Stocks or nventory s one of the largest and most valuable current assets of any tradng or manufacturng concern. These are tems of value held for use or sale by an enterprse and nclude goods awatng sale, sometmes called fnshed good stocks; goods n the course of producton, also called work n progress or process and goods to be consumed n the course of producton, called raw materal stocks. Conversely, t excludes long term assets subject to deprecaton, called fxed assets and those subject to amortsaton, called ntangble or fcttous assets. Nonetheless, nventory of manufacturng concerns consttutes the second largest tem after fxed assets n the balance sheet n terms of monetary value; hence t s paramount to attach mportance to the control of the stock and ts usage by the management (Syanbola, 2012). Page 176

2 The survval and growth of any organzaton greatly depends on ts effcency and effectveness of nventory management ths mples that organzaton that does not keep nventory s prone to loss customers and techncally sales declne s nevtable. When management s prudent enough to handle nventory t mnmzes deprecaton plferage and wastages whle ensurng avalablty of the materal as at when requred (Ogbadu, 2009). Proper nventory management result n enhancng compettve ablty and market share of small manufacturng unts (Chalotra, 2013) well managed nventores can gve companes a compettve advantages and result n superor fnancal performance (Isaksson and Sefert, 2014). Inventory control determnes the extent to whch stock holdng of materals equally makes t possble for materals manager to carry out accurate and effcent operaton of the company through decouplng of ndvdual segment of the total operaton and t entals the process of assessng of stock nto the store house largest cost of the company especally for the tradng frm wholesalers and retalers. It s a ple of money on the shelf n normal crcumstance t conssts of 20% - 30% of the company total nvestment. Most organzatons, especally manufacturng ndustry, now operate at lower measure whch makes t extremely dffcult for such organzatons to control stock. Qute often management s faced wth stock problems such as nadequate raw materals; obsolute materals; hgh storage cost etc. Stocks are nfluence by both nternal and external factor and are balanced by the creaton of the purchase order request to keep supples at a reasonable or prescrbed level. Stock control s use to show how much stock a frm has at any tme, and how you keep track of t, t apples to every tem you use to produce a product or servces from raw materals to fnshed goods. Ths covers stock at every stage of the producton, purchase and delvery to usng and reorderng the stock. Effcent stock control allow the frm to have amount of stock n the rght place and at the rght tme n ensurng that captal s not ted up unnecessarly, and protect producton f problem arse wth the supply chan. However researches showed that many organzatons do not mantan effcent stock management process whch creates a gap for the current research on the mpact of stock control on proft maxmzaton of manufacturng company. In lne wth the dentfed problems the followng research questons are guded for the study. Wll stock control have sgnfcant mpact on proftablty of a manufacturng company?. What are the prncples and method for effectve stock control?. Can stock control have sgnfcant mpact on frms proft and effcency? METHODOLOGY The model of the study s specfed wth reference to the work of Ashok (2013) wth modfcaton replacng operatng proft wth Proft after tax, and ncludng stock values to the set Page 177

3 of explanatory varables. Hence the model of the study proxes proftablty usng proft after tax (PAT), along explanatory varables such as stock value (STKV), Frm sze (SIZE), and Current Rato (CRR) The model can as well be specfed n lnear form as: ) Where: PAT=Proft After Tax STKV=Stock Value SIZE=Frm Sze CRR=Current Rato U=Stochastc error term = cross-sectonal varable from 1,2, 3, 4 t = tme seres varable form 1, 2, 3, 10 α0, α1, α2, α3 are parameter estmates correspondng to the explanatory varable and the constant term, s the cross sectonal unt effect, whle s the dosyncratc error term Method of Data Analyss The study employed both descrptve and nferental statstcal analyses. The Descrptve analyss shows the measure of central locaton and measure of dsperson, normalty status, skewness, kurtoss of all the varables ncluded n the model of the study. However panel estmatons ncludng fxed and random effect estmatons were conducted n the study for nferental purpose. Estmaton Technques The study shall adopt the panel data regresson analyss to analyze the mpact of merger and acquston on the performance of some selected bankng frms n Ngera. Page 178

4 The Fxed Effect Model The term fxed effect s due to the fact that although the ntercept may dffer among frms, each frm s does not vary overtme, that s tme-varant. Ths s the major assumpton under ths model.e. whle the ntercept are cross-sectonal varant, they are tme varant. Wthn-Group Fxed Effects In ths verson, the mean values of the varables n the observatons on a gven frm are calculated and subtracted from the data for the ndvdual, that s; Y t Y k 2 ( X jt X j _ ) ð(t - t) E t _ - E (3.1) And the unobserved effect dsappears. Ths s known as the wthn groups regresson model. Frst Dfference Fxed Effect In the frst dfference fxed effect approach, the frst dfference regresson model, the unobserved effect s elmnated by subtractng the observaton for the prevous tme perod from the observaton for the current tme perod, for all tme perods. For ndvdual n tme perod t the model may be wrtten: Y t k j2 X j jt ðt E t (3.2) For the prevous tme perod, the relatonshp s k j2 (3.3) Subtractng (3.3) from (3.2) one obtans. k Yt-1 j X jt 1ð(t -1) Et- 1 Yt jx jt ðet Et- 1 j2 (3.4) and agan unobserved heterogenety has dsappeared. Least Square Dummy Varable Fxed Effect Page 179

5 In ths thrd approach known as the least squares dummy varable (LSDV) regresson model, the unobserved effect s brought explctly nto the model. If we defne a set of dummy varables A, where A s equal to 1 n the case of an observaton relatng to frm and 0 otherwse, the model can be wrtten Y t k j2 X j jt ðt n t1 A E t (3.5) Formally, the unobserved effect s now beng treated as the co-effcent of the ndvdual specfc dummy varable. Random Effect Model Another alternatve approach known as the random effects regresson model subject to two condtons provde a soluton to a problem n whch a fxed effects regresson s not an effectve tool when the varables of nterest are constant for each frm and such varables cannot be ncluded. The frst condton s that t s possble to treat each of the frst unobserved Zp varables as beng drawn randomly from a gven dstrbuton. Ths may well be the case f the ndvdual observatons consttute a random sample from a gven populaton. If Y X ð E X ð (3.6) t j k j2 j jt t t where: µt = + Et The unobserved effect has been dealt wth by subsumng t nto the dsturbance term. The second condton s that the Zp varables are dstrbuted ndependently of all the Xj varables. If ths s not the case,, and here µ, wll not be uncorrelated wth Xj varables and the random effects estmaton wll be based and nconsstent. In order to provde a complete analyss of the mpact of stock control on proft maxmzaton of a manufacturng company, the study shall be developng Panel Data usng the followng methods: Pooled Ordnary Least Square (OLS) regresson model, the Fxed Effect or Least Square Dummy Varable (LSDV) Model and the Random Effect Model. However, t would be recalled that there are three (3) manufacturng companes (cross sectons) and there are four (4) varables such as Proft After Tax (PAT), Stock value (STV), Frm sze (SIZE) and Current rato (CRR). Hence, ths study shall be analyzng the relatonshp between k j2 j jt t t Page 180

6 Proft After Tax (PAT) and the three (3) explanatory varables such as Stock value (STV), Frm sze (SIZE) and Current rato (CRR). The data for ths study spanned from So, the observatons would be 33 (.e of 3 manufacturng ndustres). ANALYSES AND RESULTS Pooled OLS Regresson Model In the pooled OLS regresson model, we pull all the 33 observatons and run the regresson model, neglectng the cross secton and tme seres nature of data. The result of the pooled OLS regresson model s presented n Table 4.1 below: Extract from the Pooled OLS Regresson Model Result Dependent Varable: PAT Varable Coeffcent Std. Error t-statstc Prob. C STV SIZE CRR R-squared Adjusted R-squared Durbn-Watson stat F-statstc Prob(F-statstc) Source: Author s Computaton from EVews 7 Estmated Pooled OLS Regresson Model PAT *STV *SIZE *CRR (4.1) The result of the pooled OLS regresson model s shown above. It s evdent from the estmated pooled regresson model that only the dependent varable (PAT) s negatve however t s statstcally sgnfcant to explanng the behavor of the stock control n manufacturng company. Furthermore, STV and SIZE varables were postve and statstcally sgnfcant at 5% level of sgnfcance wth the excepton of CRR whch s postve but nsgnfcant. Snce CRR s nsgnfcant, hence t cannot explan the behavor of the dependent varable - PAT. The result thereby mples that one percent change n STV and SIZE wll sgnfcantly ncrease PAT by 51% and 72%. However, the major problem wth ths model s that t does not dstngush between the varous manufacturng ndustres that the study has. Conversely, by combnng the three (3) manufacturng companes by poolng, the study deny heterogenety or ndvdualty that may Page 181

7 exst among the three manufacturng companes selected for analyss n ths study, therefore, t s mperatve to carry out the remanng two regresson models. The R 2 coeffcent s very mpressve (94.16%) connotng the degree of varaton of the dependent varable as explaned by the explanatory varable. However, the model s statstcally sgnfcant n ts overall lookng at the sgnfcance of the F-statstcs from t probablty value. Furthermore, snce the study assumed that all the three (3) manufacturng companes are the same, whch normally does not happen, hence, the study cannot accept ths model because all the manufacturng companes are not the same. Fxed Effect or LSDV Model The fxed effect or LSDV model allows for heterogenety or ndvdualty among the three manufacturng companes by allowng havng ts own ntercept value. The term fxed effect s due to the fact that although the ntercept may dffer across manufacturng ndustres, but ntercept does not vary over tme, that s, t s tme nvarant. The result of the fxed effect model s presented n Table 4.2. Table 4.2: Extract from the Fxed Effect or LSDV Regresson Model Result Dependent Varable: PAT Varable Coeffcent Std. Error t-statstc Prob. C STV SIZE CRR Cross-secton fxed (dummy varables) R-squared Adjusted R-squared Durbn-Watson stat F-statstc Prob(F-statstc) Source: Author s Computaton from EVews 7. PAT *STV * SIZE * CRR -----(4.2) Presented n Table 4.2 s the fxed effect regresson model. It can be seen n the estmated model that explanatory varables such as stock value and frm sze depct postve relatonshp wth the dependent varable whle currency rato depcts negatve relatonshp wth proft after tax. However, only the CRR varable s negatve and statstcally nsgnfcant wth the dependent varable PAT. Ths s because the probablty value of the estmated coeffcent of CRR varable s greater than 5%. Ths mples that one percent change n the STK and SIZE varables wll further ncrease sgnfcantly the value of PAT by 71% and 66% respectvely. The thrd model Page 182

8 (random effect model) wll hence be analysed below as earler specfed. The R 2 value shows that 97.73% of the varaton n PAT s explaned by the explanatory varables whle the remanng 2.27% s accounted for by the error term. In ts overall, the model s statstcally sgnfcant owng to the statstcal sgnfcance of ts F-statstcs. Random Effect Model In the case of the random effect model, the three (3) manufacturng ndustres used for the purpose of analyss n ths study are assumed to have a common mean value for the ntercept. The result of the random effect model s presented n Table 4.3. Extract from the Random Effect Regresson Model Result Dependent Varable: PAT Varable Coeffcent Std. Error t-statstc Prob. C STV SIZE CRR Effects Specfcaton S.D. Rho Cross-secton random Idosyncratc random Weghted Statstcs R-squared Adjusted R-squared Durbn-Watson stat F-statstc Prob(F-statstc) Unweghted Statstcs R-squared Mean dependent var Sum squared resd Durbn-Watson stat Source: Author s Computaton from EVews 7. PAT *STV *SIZE *CRR ----(4.3) The estmated random effect model s presented n equaton 4.3. The result showed that, only the STV and SIZE varables are statstcally sgnfcant to explanng the dependent varable s behavor PAT; ths s evdent from the probablty value of the varables as t s less than 5% as shown n Table 4.3. However, CRR became postve but statstcally nsgnfcant wth PAT. Page 183

9 Hence, one percent change n the value of STV and SIZE wll brng about a statstcally sgnfcant ncrease n the value of PAT by 51.53% and 71.32% respectvely. The weghted R 2 value of 94.17% mples the varable of the dependent varable as accounted for by the explanatory varables whle the remanng percentage s ascrbed to the stochastc error term. The random effect model s statstcally sgnfcant n ts overall owng to the sgnfcance of the model s F-statstc value. To ascertanng the approprateness of ether of these estmated models, the study shall employ the Hausman Test. Hausman Test Haven estmated the three models above; the study shall have to decde whch model s good to accept. To check t, the study shall use the Hausman Test to check whch model s sutable to accept. Hausman Test Hypothess: H0: Random effect model s approprate H1: Fxed effect model s approprate NB: If the probablty value s statstcally sgnfcant, the study shall use fxed effect mode, otherwse, random effect model. Table 4.4: Extract from the Hasuman Test Result Correlated Random Effects - Hausman Test Test Summary Ch-Sq. Statstc Ch-Sq. d.f. Prob. Cross-secton random Source: Author s Computaton from EVews 7. Lookng at the Ch-square value of the cross-secton random n Table 4.4, the probablty value of the ch-square statstc s % whch s more than 5%, ths mples that, the study cannot reject the null hypothess; rather, we accept the null hypothess. Ths mples that, the random effect model s the approprate model to accept. Nonetheless, lookng at the estmated random effect model Table 4.3, t s evdent that stock value and frm sze (STV and SIZE) varables are statstcally sgnfcant to explan the behavor of the dependent varable Proft After Tax (PAT); ths result s theoretcally expected. Conversely, the result further showed that the coeffcent of the current rato varable n the model (.e. CRR) depcts postve and theoretcally expected relatonshp wth the dependent varable; however, ths relatonshp s statstcally nsgnfcant to explanng the behavor of the dependent varable. Page 184

10 Analyss of t-statstcs (t-test) The t test; the rato of estmated parameter to ts standard error s used to test for the ndvdual sgnfcance of the parameters estmated n the model. Gven values of the t-statstc from the random effect model result shown n Table 4.3 above are t-calculated. For t-tabulated at 5% level of sgnfcance wth observaton , t tabulated at 5% s usng the two tal test. The decson rule states that; f t-calculated s greater than t-tabulated (t-cal>t-tab), the parameter estmate s statstcally sgnfcant, vce versa. The nsgnfcance of the parameters estmated presupposes that the varable wth such parameter do not have any sgnfcant effect on Proft After Tax (PAT). The t-test hypothess are as follows: H0:1=2=3=0 H1: Table 4.5 Summary of t-test (Extract from Estmated Random Effect Model) Varable T-tabulated at 5% level T-calculated Decson STV Reject H0 SIZE Reject H0 CRR Do Not Reject H0 Source: Author s Computaton The summary of t-test above further affrmed the statstcal sgnfcance of the STV and SIZE varables n the model snce t fulflled the t-test crtera. Ths mples that, the behavour of Proft After Tax (PAT) s mostly nfluenced by stock value and frm sze (STV and SIZE) Test for the Overall Sgnfcance (f-test) The f-test s used to test for the overall sgnfcance of the model and to test the hypothess that the estmated parameters are smultaneously equal to zero. F calculated = F tabulated = Page 185

11 Snce F cal > F tab, hence, ths mples that, the estmated random effect model s statstcally sgnfcant n ts overall. Implcaton of Fndngs Owng to the fact that an emprcal analyss makes no meanng f t s not nterpreted for polcy purpose, ths secton therefore presents the polcy mplcatons of all the fndngs earler dscussed n ths secton. From the accepted pooled OLS regresson result (random effect model) shown n Table 4.3, t was showed that all the ndependent varables n the model depct postve relatonshp wth the dependent varable. However, only the stock value and frm sze varables were statstcally sgnfcant enough to explan the behavor of proft maxmzaton of manufacturng companes as measured by proft after tax. Ths mples that, the most credble asset and tool to enhancng the performance of manufacturng companes n the Ngeran economy s the degree of stock value avalable at a tme and how the frm has been able to expand n ts sze. CONCLUSION Ths study examned the mpact of stock control on proft maxmzaton of manufacturng company wth the man of determnng the mpact of stock control on proftablty of manufacturng company. The data collected spanned 3 manufacturng companes from 2005 to The study employed the use of panel data regresson for the purpose of analyss usng proft after tax as endogenous varable whle stock value frm sze and current rato were regressed as exogenous varables. The result of the analyss explored that stock value and frm sze were sgnfcantly related to proft after tax whle current rato was nsgnfcantly related to proft after tax of manufacturng companes. The study therefore concluded that stock control sgnfcantly mpact proft maxmzaton of selected manufacturng companes n Ngera under the study revew. Ths s n consstence and n relatonshp wth the work of Mwang and Nyambura (2015), Muhaymana (2015) and Syanbola (2012) n ther work on stock control and proftablty of manufacturng companes and found that manufacturng companes sgnfcantly mproved ther proft maxmzaton. RECOMMENDATIONS Haven examned the mpact of stock control on proft maxmzaton of manufacturng companes; these emprcal fndngs have sgnfcant mplcatons for manufacturng ndustres and ts stakeholders. Hence, the study therefore suggests the followng recommendatons: Page 186

12 .. Economc order quantty model because has been placed to be n the best nterest of manufacturng companes to mantan an optmal level of materals n store such that t mnmzes total cost of nvestment n nventory. To acheve ths successfully, dfferent costs whch are assocated wth nventory should be dfferentated and accumulated n such a way that EOQ can be easly determned. In the analyss we mentoned that there s a postve relatonshp between the stock value and productvty of a company. Ths does not mply that nventory automatcally determnes producton cost or sales. However, t does shows that nventory levels can be a useful ndcaton of what level of sales to expect. It s thus recommended that the sales and marketng department of the company should pay closer attenton to the growth pattern of nventory usage and ncorporate t n sales forecastng technque. Materals management unt should also pay attenton to sales growth made over the years and thus be takng nto consderaton as aganst the expected sales n current tme. REFERENCES Syanbola, T. T. (2012). Impact of Stock Valuaton on Proftablty of Manufacturng Industres. Internatonal Journal of Advanced Research n Management and Socal Scences, 1(2), Ogbadu, E. E. (2009). Proftablty through Effectve Management of Materals. Journals of Economcs and Internatonal Fnance, 1(4), Chalotra, V. (2013). Inventory Management and Small Frms Growth: An Analytcal Study n Supply Chan. Vson, 17(3), Isaksson, O. H. D. & Sefert, R.W. (2014). Inventory Leanness and the Fnancal Performance of Frms. Producton Plannng & Control. The Management of Operatons, 25(12), Mwang, W. & Nyambura, M.T. (2015). The Role of Inventory Management on Performance of Food Processng Companes: A Case Study of Crown Foods Lmted Kenya. European Journal of Busness and Socal Scences, 4(04), Muhaymana, V. (2015). Inventory Management Technques and Its Contrbuton on Better Management of Manufacturng Companes n Rwanda. European Journal of Academc Essays, 2(6), Page 187

13 APPENDIX I DATA PRESENTATION DANGOTE CEMENT PLC Year PAT STOCK VALUE FIRM SIZE CURRENT RATIO ,429,884 6,523,543 9,291, ,377,481 8,793,788 7,977, ,607,128 11,105,588 27,762, ,941,068 45,941,611 34,995, ,392,230 69,136,138 60,660, ,605,409 84,916, ,648, ,415,513 97,707, ,698, ,925, ,326, ,309, ,262, ,892, ,614, ,814, ,583, ,950, ,819, ,610, ,927, Source: Annual Statement of Account varous ssue LAFARGE CEMENT PLC Year PAT STOCK VALUE FIRM SIZE CURRENT RATIO ,321,830 5,423,743 7,211, ,387,400 5,105,000 6,017, ,607,108 11,105,588 27,762, ,941,068 45,941,611 34,995, Page 188

14 ,392,230 69,136,138 60,660, ,605,409 84,916, ,648, ,415,513 97,707, ,698, ,925, ,326, ,309, ,262, ,892, ,614, ,814, ,583, ,950, ,819, ,610, ,927, Source: Annual Statement of Account varous ssue GLAXOSMITHKLINE NIG PLC Year PAT STOCK VALUE FIRM SIZE CURRENT RATIO ,816,000 2,177,000 16,896, ,498,000 2,437,000 18,215, ,310,000 3,062,000 17,399, ,712,000 3,010,000 17,937, ,669,000 4,064,000 20,988, ,853,000 3,837,000 20,800, ,458,000 3,873,000 20,055, ,744,000 3,969,000 18,537, ,628,000 3,900,000 17,920, ,831,000 4,231,000 15,683, ,372,000 4,716,000 15,070, Source: Annual Statement of Account varous ssue Page 189

15 APPENDIX II RESULTS POOLED LEAST SQUARE RESULT Dependent Varable: PAT Method: Panel Least Squares Date: 12/11/16 Tme: 04:54 Sample: Perods ncluded: 11 Cross-sectons ncluded: 3 Total panel (unbalanced) observatons: 33 Varable Coeffcent Std. Error t-statstc Prob. C STV SIZE CRR R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regresson Akake nfo crteron Sum squared resd Schwarz crteron Log lkelhood Hannan-Qunn crter F-statstc Durbn-Watson stat Prob(F-statstc) FIXED EFFECT OR LSDV MODEL Dependent Varable: PAT Method: Panel Least Squares Date: 12/11/16 Tme: 05:00 Sample: Perods ncluded: 11 Cross-sectons ncluded: 3 Total panel (unbalanced) observatons: 33 Varable Coeffcent Std. Error t-statstc Prob. C STK FRM CRR Page 190

16 Cross-secton fxed (dummy varables) Perod fxed (dummy varables) Effects Specfcaton R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regresson Akake nfo crteron Sum squared resd Schwarz crteron Log lkelhood Hannan-Qunn crter F-statstc Durbn-Watson stat Prob(F-statstc) RANDOM EFFECT MODEL RESULT Dependent Varable: PAT Method: Panel EGLS (Perod random effects) Date: 12/11/16 Tme: 05:01 Sample: Perods ncluded: 11 Cross-sectons ncluded: 3 Total panel (unbalanced) observatons: 33 Swamy and Arora estmator of component varances Varable Coeffcent Std. Error t-statstc Prob. C STK FRM CRR Effects Specfcaton S.D. Rho Perod random Idosyncratc random Weghted Statstcs R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regresson Sum squared resd F-statstc Durbn-Watson stat Prob(F-statstc) Unweghted Statstcs R-squared Mean dependent var Sum squared resd Durbn-Watson stat Page 191

17 HAUSMAN TEST RESULT Correlated Random Effects - Hausman Test Equaton: Unttled Test perod random effects Test Summary Ch-Sq. Statstc Ch-Sq. d.f. Prob. Perod random Perod random effects test comparsons: Varable Fxed Random Var(Dff.) Prob. STK FRM CRR Perod random effects test equaton: Dependent Varable: PAT Method: Panel Least Squares Date: 12/11/16 Tme: 05:03 Sample: Perods ncluded: 11 Cross-sectons ncluded: 3 Total panel (unbalanced) observatons: 32 Varable Coeffcent Std. Error t-statstc Prob. C STK FRM CRR Perod fxed (dummy varables) Effects Specfcaton R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regresson Akake nfo crteron Sum squared resd Schwarz crteron Log lkelhood Hannan-Qunn crter F-statstc Durbn-Watson stat Prob(F-statstc) Page 192