Internatonal Symposum on Computers & Informatcs (ISCI 05) A Panel Date Model of Cell Phone Internet Influencng on Undergraduates Score Lrong A, Shpeng Chen and Shengpng Jn,# Wuhan Insttute of Shpbuldng echnology, Wuhan, 430050, Chna Department of Statstcs,Wuhan Unversty of echnology, Wuhan, 430070,Chna Abstract Cell phone nternet nfluence on undergraduate s examnaton score s an mportant research ssue n the educaton feld n unverstes. he panel data model of cell phone nternet nfluencng on undergraduate s mark s bult based on the theory of probablty and statstcs. Data of undergraduate studyng on nternet s obtaned from QQ contact group by usng the moble phone Internet. Accordng to the statstcal method, the nfluence factors weght of the regresson on score s calculated, and results show that Cell Phone Internet affects undergraduates scores sgnfcantly n unverstes. Keywords: cell phone nternet, theory of probablty, QQ contact group, panel data.. Introducton Usng nternet by cell phones s becomng a part lfe for undergraduates n unverstes. Cell phone nternet refer to nternet can be used by cell phones, or moble phones. Whether undergraduate s examnaton score affected by cell phone nternet or not can be analyzed by the data collected from contact QQ group. Panel data refers to selected a number of sample data on the secton of specfc factor sequence[]. Panel data has many advantages such as t can control ndvdual heterogenety data, and can provde more nformaton from sample, and reduce lnear collnearty, and provde more degrees of data freedom, and adjustment process of ndvdual effects and tme effects. Nowadays the panel data research s quckly development on the theory and applcaton. Snce 960, scholars began to pay attenton to panel data econometrcs. In early 986, Hsao[] wrote a monograph about the research of panel data model, and publshed second edton n 003. Wooldrdge[], Arellano[3], Baltag[4] descrbed many aspects of the panel data model. In recent years, a lot of researchers around the world set up a great study on the panel data model, such # Correspondng author: spjn@whut.edu.cn 05. he authors - Publshed by Atlants Press 998
as nonlnear panel data model, the nonconstraned statonary panel data [5] model, dynamc panel data model, and varable structure model[6] and so on. hs paper wll research moble phone nternet whch affects on undergraduates examnng mark by usng panel data theory. In Secton, panel data model s ntroduced. Secton 3 dscrbed the estmaton of parameters n panel data. And n Secton 4, the nfluencng of cell phone nternet on undergraduates score s analyzed by panel data model. And Secton 5 gves some concluson remarks.. Panel data model Support y t s repones varable, or observaton for undergraduate examnaton score, and suppose Xt = ( x t, xt,..., xkt ) s k explanatory varable,or the observaton probablty of undergraduate usng cell phone nternet. b= ( b, b,..., bk ) s k coeffcent vector, u t s random error term whch satsfed mutually ndependent, zero mean, and same varances. he sngle equaton panel data model can be wrtten as: y = a+ xb+ u, =,,..., N, t=,,..., () t t t Accordng to the matrces termnology, let: y x x... xk X u y x x... xk X Y = X u = = U.................. =... y x, x... xkt X u, Y X U a Y X U a Y =, X =, U =, a =, Z = IN e, Y N X N U N a N Where I N s the dentty matrx of order N, e s the vector of ones of dmenson, and denotes Kronecker product. he panel data can be represented by metrx equaton: Y = Za + Xb + U () he number of sample observaton value of panel data s N. If N =, the panel data model of Eq. becomes one dmenson observaton data. 999
3. Estmaton of the parameters n panel data We consder short tme panel data analyzed by usng OLS estmaton method[]. he dfferent value of panel data wth ts average data s calculated, and then estmate the parameters n the model for the probablty of undergraduate usng cell phone nternet. he average of Eq. are: y = yt, x = xt, t= (3) t= So that the average formula are: y = a + xb + u, =,,..., N (4) From above Eq. 3 and Eq. 4, we have ( ) ( ) y y = x x b+ u u (5) t t t By applyng OLS estmaton method[], we have parameter estmator from Eq. 5 f b s a sclar: b = N = t= N = t= ( xt x )( yt y ) ( xt x )( xt x ) If b s a vector, the estmaton of b can also be easy to calculated by the multvarate lnear regresson. It s called OLS estmatve value, and s unbased estmator, and estmatve value of a can be from the formula as aˆ = y xbˆ. Let RSS = Wyy, W xy, W xx, Wxy, be the resdual sum of squares for group, =,,, N, where ( ) ( ) W = x x x x xx, t t t= xy, = t t t= ( ) ( ), W ( ) yy, = yt y W x x y y And denote N N N W = W, W = W, W = W t=, xx xx, xy xy, yy yy, = = = hen the whole resdual sum of squares for our model and other statstcs are 000
N = RSS, S Wyy = S =, S = W WW W 3 yy xy xx xy We can show below theorem. heorem [4] If x t s panel data, we have below conclusons: () S σu ~ χ N( k ) () S σ χ N ( k + ) 3 u ~ (3) ( S S ) σ χ ( N )( k+ ) 3 u ~ S S σ s ndependent wth S σ (4) ( ) (5) (6) F 3 u = u ( S3 S) ( N )( k+ ) S N( k ) ( )( + ) ( ) ( S S) ( N ) k ~ ( ), ( ) S N( k ) ~ F N k, N k F = F N kn k N et N = t= N e DD e LM = = ( ) N ee et = t= (7) ( ) ( ) LM χ( ) ~ where e t s resdual of lnear regresson, e and D are matrces of t. 4. Affect examnaton score model and calculaton hrough the QQ contact group, a total of 438 undergraduates, from freshmen to senor grades, are nvestgated. he undergraduates come from engnnerng colleges, transportanton colleges or shp buldng colleges. Some of them come from the countrysde, or mountanous area, whch famly ncome are not hgh. Some of them come from ctes, or economcally developed areas, whch famly ncome are relatve hgher. Accordng to the followng standards, the famly ncome are dvded nto 5 categores. 0 500,50-5000,500 75000,7500--00000, >00000, From the undergraduate s famly ncome dstrbuton, whch s depcted n Fg., we fnd that most undergraduate s famly ncome s less than 500. 00
Fg. dstrbuton for the student s famly ncome 4. Estmaton of the parameters Applyng Evews software, we calculate Hausman estmatve value shown n the able. able Hausman estmatve value est Summary Ch-Sq. Ch-Sq. d.f. Prob. Cross-secton random 4.55475 0.0000 Cross-secton random effects test comparsons: Varable Fxed Random Var(Dff.) Prob. PO 0.0094 0.000895 0.000000 0.0000 From able, the Hausman estmatve value s 4.55475, fxed ndvdual parameter estmaton value s 0.0094, random parameter estmaton value s 0.000895. Fllng YD n the Cross secton Specfc coeffcents of Evews software, and choose fxed effects n the wndow of ntercept, we get coeffcent of undergraduate s probablty shown n the able. In the table, Std. Error s parameter normal error, t-statstc s t value of t statstc. able fxed effects model(ols)estmatve value Varable Coeffcent Std. Error t-statstc C -5.05 57.80-7.63354 BJ--POBJ 0.057 0.000 7.78737 SH--POSH 0.06 0.0009 3.49879 J--POJ 0.054 0.00095 7.8738 GZ--POGZ 0.097 0.000796.5904 NJ--PONJ 0.08890 0.0006 8.368066 CS--POCS 0.06079 0.0080 4.7494 CD--POCD 0.0367 0.000584 6.8546 HF--POHF 0.0367 0.00090 4.73353 WH--POWH 0.06376 0.0069 5.45473 ZZ--POZZ 0.0005 0.00043 4.43437 XA--POXA 0.0400 0.000893 4.705909 Y--POY 0.08906 0.00706 5.9903 LZ--POLZ 0.75 0.0034 3.59843 00
he goodness of fttng regresson equaton, F statstc and DW statstc value ndex and other statstcs are lsted n the able 3. able 3 fxed model(ols)estmatve results R-squared 0.940960 Mean dependent var 5.803 Adjusted R-squared 0.98308 S.D. dependent var 33.05 S.E. of regresson 89.4364 Akake nfo crteron 6.60438 Sum squared resd.0e+04 Schwarz crteron 7.5655 Log lkelhood -0.537 Hannan-Qunn crter. 6.8867 F-statstc 74.37568 Durbn-Watson stat 0.99090 wo lays regresson model s doubled n ths paper as below: z= ay+ ay + ay+ ay +ε 3 3 4 4 Where z s all grad student regresson examnaton score, y k s kth grade undergraduate examnaton score represented by: y = a0 + ax + ax + a3x3 + a4x 4 +a5x5 + ε y = a 0 + a x + a x + a 3x 3+a 4x 4 +a 5x 5 + ε y3 = a30 + a3x3 + a3x3 + a33x 33+a34x 34 +a35x35 + ε3 y = a + a x + a x + a x +a x +a x + ε 4 40 4 4 4 4 43 43 44 44 45 45 4 By usng data, we easy obtan regresson equaton of examnaton score z s z = 0.5y+ 0.3y + 0.7y3+ 0.5y4 y = 77 0.0x + 0.3x +0.33x 3+0.36x 4 +0.04x5 y = 73 0.3x + 0.04x +0.7x 3+0.40x 4 +0.0x5 y3 = 70 0.03x3 + 0.30x 3 +0.84x 33+0.7x 34 +0.x35 (6) y4 = 69+0.4x4 + 0.04x 4 +0.68x 43+0.5x 44 +0.6x 45 From above formula, we fnd that cell phone affects more on frst year to thrd year undergraduate. For students from poor ncome famles, the affectve degree s decrease wth the tme of undergraduate n the unversty. For other undergraduates, the cell phone nternet s benefcal to examnaton score. In ths calculaton, the sum square resdue s 0.34, the R-square s 0.94, see able 4. able 4 estmatve results of regresson R-squared 0.94090 Mean dependent var 57.803 Adjusted R-squared 0.9838 S.D. dependent var 339.05 S.E. of regresson 9.4364 Akake nfo crteron 6.60438 Sum squared resdue 0.304 Schwarz crteron 7.5655 Log lkelhood -0.537 Hannan-Qunn crter. 6.8867 F-statstc 4.3568 Durbn-Watson stat 0.99090 003
4. Dagnoss of the model he dagnoss of the frst regresson of Eq.(6) s as followng by usng the R software. Coeffcents: Estmate Std. Error t value Pr(> t ) (Intercept) 75.099 0.07039 065.9 <e-6 *** group 0.6 0.086 4.07 <e-6 *** group3 0.33797 0.09444 33.3 <e-6 *** group4 0.707 0.9 8.6 <e-6 *** group5 0.84 0.5740 3.5 <e-6 *** --- Sgnf. codes: 0 *** 0.00 ** 0.0 * 0.05. 0. Resdual standard error: 0.9955 on 995 degrees of freedom Multple R-squared: 0.5535, Adjusted R-squared: 0.557 F-statstc: 308.4 on 4 and 995 DF, p-value: <.e-6 We can see from the dagnoss results that the affectng factors are all sgnfcants, and the whole model s sgnfcants also. So our nference n Secton 4. s credble. Fg. s the graph of Model checkng plots for the frst equaton of regresson of Eq.(6). It shows that the model assumpton s reasonable. Resduals vs Ftted Normal Q-Q -3-3 8 5 55-3 - 3 555 8 75.0 76.0 77.0 78.0-3 - - 0 3 0.0 0.5.0.5 5 8 55 Scale-Locaton -3-3 Cook's dstance Resduals vs Levera 976 967 995 75.0 76.0 77.0 78.0 0.000 0.005 0.00 0.05 0.0 Fg. Model checkng plots for the frst equaton of regresson of Eq.(6) he same dagnoss for other equatons of Eq.(6) are smlar to the above and s ommted, other checkng tests by usng heorem are not gven here for savng the space. 004
5. Conclusons he moble phone has been developed rapdly on usng Internet, undergraduates are an mportant group of moble phone access to the Internet, so the research on Moble Phone Internet nfluence on undergraduates s nprotant project. Accordng to the undergraduate s grade at the Unversty and ther famly ncome, we have constructed a -D panel data model and calculate parameter n the OLS model. he results show that the moble phone access to the Internet has a great nfluence on undergraduate examnaton scores and s also benefcal to examnaton score. Acknowledgements he research work was supported by Natonal Natural Scence Foundaton of Chna under Grant No.57949, No.57947, No.539005 and Chna natonal educaton department doctoral foundaton under Grant No. 00433000. References [] Hsao C. Analyss of Panel Data (second edton)[m]. Be Jng: he PeKng Unversty Press, (003). [] Wooldrdge J.M. Econometrc Analyss of Cross Secton and Panel Data [M], Massachusetts, he MI Press, (00). [3] Arellano M. Panel data econometrcs[m]. Oxford: Oxford Unversty Press. (003). [4] Baltag B.H. Econometrc Analyss of Panel Data [M].New York:Johu Wley&Sons,(005). [5]Ye Xaoqng, Estmator for nonlnear panel data model wth nteractve fxed effects[j], Statstcal Research, Vol. 0, (04), 97-0 [6] Hubrch K., erasvrta. hresholds and smooth transtons n vetor autoregressve model[r], CREASS research paper,(03). 005