FACTORS FACTORS AFFECTING THE VARIABILI VARIABILITY TY OF ENROLLMENT ENROLLMEN T RATE IN BASIC EDUCATION OF THE PHILIPPINES
A study presented to Ms. Angela D. Nalica Professor, Stat 136
In partial fulfilment of the reuirements for S!A! 136" Introduction to #egression Analysis $ni%ersity of the Philippines, Diliman, &ue'on (ity
Danan, #ustico I) Ing*ing, +ugene (reely )itug, )itug, Marianne
April -1
1
I. ABSTRACT
!his paper aims to e/plain the factors affecting the %aria0ility of the enrolment rate in 0asic education of the Philippines. $sing SAS, the enrolment as regressed on 1 %aria0les that ha%e 0een initially considered as indicators in the enrolment rate. In coming up ith the 0est model, the researchers ha%e detected pro0lems ith outliers. #emedial measures such as deletion and transformation transformation of %aria0les ere performed performed to %erify the compliance compliance of the model ith the regression assumptions. !he %aria0les that shoed a positi%e linear relationship ith enrolment rate are percentage percentage of teachers, teachers, !otal !otal 2inancial 2inancial #esources, Percentage of 2ully Immuni'ed Immuni'ed children 451 months and Percentage of pri%ate motor %ehicles hile (ohort Sur%i%al #ate shoed a negati%e linear relationship. !he resulting model had an # %alue of -.477 here all fi%e %aria0les are significant predictors of the enrolment rate in 0asic ed ucation. II. INTRODUCTION
!he Philippine has committed itself to 8 Millennium De%elopment 9oals MD9 0y -1. :ne of hich is to pro%ide uni%ersal access to primary education. !he go%ernment ac*noledges the potential of 0asic education as an empoering process that capacitates the indi%idual to function, to achie%e, to 0e la5a0iding, participate intelligently in elections, and ha%e a 0etter sense of nation and community Sen, 1444. ;oe%er, according to the Philippine Midterm Progress report on MD9 that as released last --<, the go%ernment assessed the pro0a0ility of attaining 1--= enrolment rate in primary institution to 0e lo. Also, according to $NDP, from a near uni%ersal rate of 4<= in 1444>---, as measured 0y net enrolment rate N+#, participation in elementary education dropped to 83.= in --6>-<, the loest o%er the last to decades. ?hile increasing marginally in --< at 87.8=, 87.8=, the rate rate of progre progress ss is %ery minimal minimal in order order to achie%e achie%e uni%er uni%ersal sal access access to 0asic 0asic education 0y -1. . :n the other hand, as released 0y $NI(+2 last --, the net enrollment rate of secondary education reached 6-.<= from 66.1=.
Although the compulsory minimum education la is already enforced, there are still other factors that affect the said rate. According to a study conducted 0y !ullao and #i%era --4, it suggests that the factors affecting enrolment rate in 0asic education can 0e di%ided into @Supply and Demand factors. Supply factors include the capa0ility of the go%ernment to cater
2
pupils and students, the num0er of teachers, school facilities, num0er of 0oo*s, school supplies and other educational inputs !ullao, #i%era, --4. Moreo%er, the demand factors refer to the householdBs decision to a%ail educational ser%ices. !his can 0e measured through household income, cost of education, and health factors. Coo*ing at the pro%incial le%el, these factors can 0e measured through total financial resource, the num0er of pri%ate cars and num0er of fully immuni'ed children. It is also important to note the (ohort Sur%i%al #ate per pro%ince as one of the indicators that might affect the enrolment rate. !o address the pro0lems in enrolment rate, the researchers aim to pro%ide a model that ill ill determi determine ne and e/plain e/plain the signif significa icant nt factor factorss that that e/plain e/plainss the %aria0 %aria0ili ility ty.. Also, Also, the researchers aim to relate this model to the recently implemented 51 educational system. III. RELATED LITERATURE
Cast Cast Septem0 Septem0er er ---, ---, Phili Philippin ppinee go%ernm go%ernment ent is one of the 184 mem0er mem0er states states that committed to achie%e 8 Millennium De%elopment 9oals MD9 0y -1. :ne of these goals is to achie%e uni%ersal access to primary education. !he +ducation plays a significant significant in economic de%elopment. de%elopment. It is idely ac*noledged ac*noledged that education increases the inno%ati%e capacity of an economy and facilitates the diffusion, adoption, and adaptation of ne ideas. More specifically, education increases the amount of human capital a%aila0le, there0y increasing producti%ity and ultimately output. +ducation is especially important in a rapidly e%ol%ing economic en%ironment here a rapid rate of Eo0 destruction and creation might otherise lead to a gap 0eteen the s*ills demanded in the la0or mar*et and the s*ills of Eo05see*ers Fap, Fap, -1. !he Department of +ducation recei%es one of the 0iggest 0udget allocations among other sectors and agencies in the Philippines. !his allos the go%ernment to create more schools, increase the num0er of teachers, 0oo*s and impro%e educational facilities. Gasing from the Philippine Net enrolment ratio in primary education for 0oth se/es, during 144-Bs, the rate as consistently high going up to 4<= then there as a decrease in year --1, ith only 4.<=. !he loest rate for the last to decades as reported to 0e 83.= last --<. In the case of the secondary education, education, last year ---, the enrolment rate is .6= that e%entually e%entually increased to 6-= last --.
3
Alth Althou ough gh the the 0udg 0udget et allo allocat catio ion n to 0asi 0asicc educa educati tion on remai remains ns to 0e the the 0igg 0igges est, t, and and compulsory education la is already enforced, family decision still affects the a0ility of the children to go to school ing, 1483. !he family demand for human capital can 0e attri0uted to different economic and demographic factors !ullao, #i%era, --4. As cited 0y (aHete n.d., Maligalig Maligalig and Al0ert --8 presented presented in their analysis analysis of the -- and --7 APIS the different reasons for nonattendance in school of school5age children as follos" a (annot cope ith school or* 0 ;igh cost of education c Illness and>or disa0ility d Cac* of personal interest e Schools are far or there is no school ithin the 0arangay f 2inished schooling g ;ouse*eeping chores h No regular transportation from house to school and others. Poor health as also pointed out to 0e one of the factors that negati%ely affect the school participation is the poor health of pupils. (urrently, different programs are 0eing implemented to remedy the pro0lems in the enrolment rate. :ne of the programs is called @Pantaid Pamilyang Pilipino Program. !he aim of 7P is to pro%ide pro%ide human de%elopment de%elopment capital to eradicate eradicate intergenerati intergenerational onal po%erty cycles 0y granting poor families that complied to different conditions. !hese conditions include sending children to school and *eeping them healthy. Also, the go%ernment launched the J1 program to 0etter ensure the uality of the primary education here in the Philippines. !his program also aims to prepare e%ery 2ilipino citi'ens to 0e more glo0ally competiti%e, in the hope of eradicating, if not lessening, po%erty.
4
IV. METHODOLOGICAL SKETCH Framework
Ecoom! E"#ca$%o 2amily Income Percentage of !eachers !eachers (onsumer Price Inde/ (ohort Sur%i%al #ate Po%erty Incidence Num0er of Pu0lic Schools Ero&me$ Ra$e Pri%ate Gan* Deposit ith respect to the total population of the pro%ince
Go(erace Hea&$' 2inancial #esourcesSafe ?ater Supply Inde/ed (rime Num0er of Sanitary !oilet !oilet 2ully Immuni'ed
O$'er) !elephone !elephone Cine Su0scri0ers
5
!he researchers chose to include 1 independent %aria0les in the model50uilding process 0ased on the re%ie of related literature ith the constraint of the a%aila0ility of the data. !he indepen independen dentt %aria0 %aria0les les consid considere ered d in the study study ere ere groupe grouped d into into fi%e fi%e catego categorie riess namely namely"" education, economy, go%ernance, health, and others communication, transportation, energy. !he data under the categories ere 0ased on the same reference year --4. !he data on the %aria0les ere o0tained from the Philippine Statistical Authority 5 National Statistical (oordination Goard NS(G e0site and Department of +ducation Dep+d. !he %aria0 %aria0les les ith ith their their descri descripti ptions ons and>or and>or proced procedura urall defini definitio tions ns and their their la0els la0els are the folloing" De*e"e$ Var%a+&e, +nrolment #ate of pu0lic elementary and secondary schools +N#:C
!his !his refers refers to the percentage percentage of the sum of go%ernm go%ernment ent elemen elementar tary y and seconda secondary ry enrolees ith respect to the total population in each pro%ince. In the year --4, a total of 1,<<,7-7 enrolees as collected in the country. I"e*e"e$ Var%a+&e), Var%a+&e), Ecoom! •
2amily Income IN(:M+ K a%erage family annual income o0tained 0y di%iding the total income of families 0y the total num0er of families. It includes primary income and receipts from other sources recei%ed 0y all family mem0ers during the calendar year as participants in any economic acti%ity or as recipients of transfers, transfers, pensions, grants, etc.
•
(onsumer Price Inde/ (PI K indicator of the change in the a%erage prices of a fi/ed 0as*et of goods and ser%ices commonly purchased 0y households relati%e to a 0ase year
6
Po%erty Incidence of 2amilies P:) 5 proportion of families hose annual per capita
•
income fall 0elo the annual per p er capita po%erty threshold Pri%ate Gan* Deposit GAND+P K total pri%ate commercial 0an* deposits in million
•
pesos E"#ca$%o
Percentage of !eachers !+A(; 5 percentage of the sum of go%ernment elementary and
•
secondary teachers ho engaged in actual teaching of a group of pupils>students on full5 time or part5time 0asis ith respect to the total population of the pro%ince (ohort Sur%i%al #ate (:;:#! 5 percentage of enrolees at the 0eginning grade or year
•
in a gi%en school year ho reached the final grade or year of the elementary>secondary le%el •
Num0er of Pu0lic Schools P$G+ 5 num0er of pu0lic schools in the pro%ince
Go(erace
2inancial #esources 2IN#+S 5 total financial resources in each pro%ince in million
•
pesos Percentage of Inde/ed (rime (#IM+ 5 percentage of the total inde/ crime ith respect
•
to the total num0er of crime Hea&$' •
•
Safe ?ater ?ater Supply ? ?A A!+# 5 num0er of households ho useholds ith access to clean ater Num0er of Sanitary !oilet !:IC+! 5 num0er of sanitary toilet in the pro%ince. Sanitary toilet is a co%ered installation, hether pu0lic or pri%ate, used for the disposal of aste.
•
Percentage of 2ully Immuni'ed (hildren IM$ 5 percentage of fully immuni'ed children from 4511 months ith respect to the population of the pro%ince
7
O$'er) -Comm#%ca$%o Tra)*or$a$%o Eer/!0 •
Percent Percentage age of !elepho elephone ne Cine Cine Su0scr Su0scri0e i0ers rs P;:N+ P;:N+ 5 percent percentage age of teleph telephone one line line su0scri0ers ith respect to the total population of the pro%ince
•
Pri%ate Motor )ehicles percentage (A#S K percentage of registered pri%ate motor %ehicles not to 0e used for hire under any circumstances ith respect to the total num0ers of registered motor %ehicles in the pro%ince
•
Num0er of +nergi'ed Garangays +N+#9 K total num0er of energi'ed 0arangays in the pro%ince !he researchers chose --4 data due to a greater degree of a%aila0ility. :0ser%ations ith
missing cells ere deleted prior to importing in the statistical pac*age. A remaining total of < o0ser%ations pro%inces, 1 independent %aria0les ere organi'ed in a spreadsheet and ere included in the de%elopment of the model. !he full model used in the study to determine hich predictor %aria0les significantly e/plain the %ariation in the response %aria0le, the enrolment rate of pu0lic elementary and secondary schools +N#:C, is gi%en 0elo"
ENROL= β 0+ β1 INCOME INCOME + β 2 BANKDEP + β 3 CPI + β 4 CARS + β 5 ENERG + β 6 TEACH + β 7 PHO , !o determine the adeuacy of the full model, it as su0Eected to an AN:)A AN:)A 25test for the significance of at least one of the predictor %aria0les that sufficiently e/plains the %ariation in the response %aria0le. !he researchers set the le%el of significance to 0e -.-. !hrough a stepise selection procedure, the reduced model as o0tained. 2urther diagnostic chec*ing of the reduced model model as done done to %alida %alidate te assump assumptio tions ns using using SAS. !his !his includ includes es the multic multicoll olline ineari arity ty,, nonlinearity, nonnormality, nonnormality, heteros*edasticity, identification identification of outlier and its deletion, influential o0ser%ation, and autocorrelation. !he researchers then proposed an estimated regression function to represent and summari'e all of these results.
8
V. RESULTS AND DISCUSSION
Initially, percentage of enrolled students in pu0lic elementary and high schools as regres regressed sed using using the follo folloing ing %aria0 %aria0les les"" A%erag %eragee family family annual annual income income,, total total pri%at pri%atee 0an* deposi deposit, t, consum consumer er price price inde/, inde/, percent percentage age of pri%at pri%atee motor motor %ehicl %ehicles, es, num0er num0er of energi' energi'ed ed 0arangays, percentage of teachers, percentage of telephone line su0scri0ers, total financial resource, resource, num0er of households households ith access to clean ater, num0er of sanitary sanitary toilets, po%erty gap, percentage of inde/ed crimes, cohort sur%i%al rate, num0er of pu0lic schools and percentage of fully immuni'ed childrenfrom - to 4 months.
Figure 1. SAS Output of the Full Model Dependent Variale! "#$O% "#$O% Anal&'i' of Varian(e Sour(e
Su) of S*uare'
DF
Model "rror 0orre(ted 0orre(te d otal
15 56
Mean S*uare
F Value
8-41.4242 5-6.-4-5 467.7178 8.351-8 71 -4-.134-8
+r , F
71.37
/.1
$oot MS" 2.88--8 $S*uare .-53 Dependent Mean 27.3254 Ad $S* .-37 0oe Var 1.6-74 +ara)eter "'ti)ate' %ael
nter(ept #0OM" A#D"+
nter(ept 1 25.-1442 13.71744 1.8.641 #0OM" 1 .1823 .1427 1.28 .26A#D"+ 1 .5-8 .31- .1.8521
CPI
CPI
0A$ "#"$9 TEACH
+:O#"
FINRES
;A"$ O%" 0$M"
+ara)eter Standard DF "'ti)ate "rror
Variale
COHORT
+<" IMU
+OV
1
0A$ "#"$9
-0.19485
1 1
TEACH FINRES
1
1
IMU
+OV
.155.155-
1
1
-2.03
2.48649
.554
0.00222
1 .786 1 .84 1 .1338 .1338
COHORT COHORT
+<"
24.45408
1
;A"$ ;A"$ O%" 0$M"
0.09621
+r , t
0.0476
.853 .4363 .4363 1.85 .72 .-835 .167 .54 .58-3 1
+:O#"
t Value
1
2.28500
.--32
<.0001
.77-4
0.00096923
2.29
0.0260
.664 1.18 .2412 .635 1.27 1.27 .213 .4273 .31 .7553
-0.20181
.255
9.83
.28
.2-
0.04034
1.22
0.54931
.5785 .5785
1.72
-5.00
<.0001
.2272
4.16
0.0001
.-16
Sinc Sincee the the 2 )alue lue is rela relati ti%el %ely y high high,, then then this this sugg sugges ests ts that that ther theree is at leas leastt one one independent %aria0le in the model that can e/plain the %aria0ility of the percentage of enrolment. Also, 4.-3= can 0e e/plained 0y the model as seen in the %alue of # .
-
Gased on the independent %aria0lesB p5%alues using .- as alpha, the significant %aria0les are the folloing" (PI, !+A(;, 2IN#+S, (:;:#! and IM$. !he researchers used Stepise )aria0le Selection Procedure to identify the independent %aria0les that ill 0e included in the reduc ed model.
2igure . SAS :utput for )aria0le )aria0le Selection All =ariale' left in the )odel are 'igni>(ant at the .1 le=el. #o other =ariale )et the .5 'igni>(an(e le=el for entr& into the )odel.
Su))ar& of Step?i'e Sele(tion Variale Variale Step "ntered $e)o=ed 1 2 3 4 5
"A0: M< 0O:O$ F#$"S 0A$
#u)er +artial Model %ael Var' n $S*uare $S*uare 0@p
F Value +r , F
"A0: 1 .855- .855- -4.3347 415.7- /.1 M< 2 .424 .8-83 48.5626 28.77 /.1 0O:O$ 3 .27 .-1- 27.2116 17.41 /.1 F#$"S 4 .148 .-338 12.5716 14.-5 .3 0A$ 5 .75 .-413 6.1276 8.43 .5
$sing stepise selection, the %aria0les that are suggested to 0e included in the model are !+A(;, IM$, (:;:#!, 2IN#+S and (A#. !he researchers regressed the percentage of enrolment to the %aria0les suggested 0y the %aria0le selection procedure.
2igure 3. SAS :utput for the #educed Model Dependent Variale! "#$O% "#$O% Anal&'i' of Varian(e
Sour(e
DF
Model
5
Su) of S*uare' 8856.83842
Mean S*uare
F Value
1771.36768
+r , F
211.68
/.1
1
"rror 0orre(ted 0orre(te d otal
66
552.2-656 8.36813 71 -4-.134-8
$oot MS" 2.8-277 $S*uare .-413 Dependent Mean 27.3254 Ad $S* .-360oe Var 1.717 +ara)eter "'ti)ate' Variale
%ael
+ara)eter Standard DF "'ti)ate "rror
t Value
+r , t
nter(ept nter(ept 1 2.-3143 3.73332 .7.4351 "A0: "A0: 1 24.15-75 24.15-75 2.21674 1.- /.1 M< M< 1 2.25222 .45582 .45582 4.-4 /.1 0O:O$ 0O:O$ 1 .1785 .3125 5.47 /.1 F#$"S F#$"S 1 .1-3 .5-288 3.26 .18 0A$ 0A$ 1 .111 .37-3 .37-3 2.- .5
Gased on the # , 47.13 = of the %aria0ility of the percentage of enrolment can 0e e/plained 0y the reduced model. !he full model # decreased 0y around 1= hich is %ery minim minimal al implyi implying ng that that the unsele unselecte cted d %aria0 %aria0les les didnBt didnBt contri contri0ut 0utee much much on e/plain e/plaining ing the %aria0ility of the dependent %aria0le. !he reduced model has to undergo diagnostic chec*ing in order for the researchers to ma*e sure that the assumptions are not %iolated. MULTICOLLINEARITY
2igure 7. SAS :utput for )ariance )ariance Inflation, (ondition Inde/ and Proportion of )ariation )ariation +ara)eter "'ti)ate' +ara)eter Var Varia ial le e "'ti "'ti)a )ate te
Standard Varian(e 0ondition "rr "rror t Value alue +r , t nBa nBati tion on "ige "igen= n=al alue ue nde ndeC C
nter(ept 2.-3143 3.73332 .7.4351 5.54181 1. "A0: 24.15-75 2.21674 1.- /.1 3.878-7 .2475 4.7-77M< 2.25222 .45582 4.-4 /.1 4.322 .173-6 .173-6 5.64413 0O:O$ .1785 .3125 5.47 /.1 1.5637 .2142 16.8425 F#$"S .1-3 .5-288 3.26 .18 .18 1.27644 .1668 18.2288 0A$ .111 .37-3 2.- .5 1.11116 .538 32.-414 0ollinearit& Diagno'ti(' +roportion of Variation #u)er nter(ept "A0: M< 0O:O$ F#$"S 1 2 3 4 5 6
.26347 .144 .6-5 .321 .2427 .-653
.12 .264.134.134.74283 .74283 .1-45 .1-45 .2573 .2573
.135 .246.81-1 .76458 .835.438-
.65372 .231 .2342 .117 .565- .3876
0A$
.554 .4177 .5-1-1 6.3-7-4"7 .1-31.1-31.874 .13-62 .13-62 .252 .1-4 .1-4 .28631 .533 .533 .67-53
11
Gase Gased d on the the %ari %arian ance ce infl inflat atio ion, n, none none of the the %ari %aria0 a0le less are are susp suspec ecte ted d to ha%e ha%e multicollinearity pro0lem since all of the )I2Bs L 1-. ;oe%er, one %alue of the condition inde/ is greate greaterr than than 3-. !he resear researcher cherss then then chec*ed chec*ed the propor proporti tion on of %ariat %ariation ion for possi0le possi0le multicollinear %aria0les. Although (A# has a proportion of %ariation greater than -., there is no other %aria0le ithin the same line that has proportion of %ariation greater than -.. 2rom these o0se o0ser% r%at atio ions ns,, the the rese researc arche hers rs concl conclude uded d that that ther theree is no mult multic icol olli line neari arity ty 0ete 0eteen en the the independent %aria0les in the reduced model. NONLINEARITY
2igure . SAS :utput for Partial #egression Plot
!he residual plot shos that the points are randomly scattered in a hori'ontal 0and ith a fe outliers. 2rom this the assumption of linearity is %erified.
NONNORMALITY
2igure 6. SAS :utput for Statistics of !ests !ests for Normality e't' for #or)ali t& e't
Stati'ti(
p Value
Shapiro;il ; .--338 +r / ; .-716 ol)ogoro=S)irno= ol)ogoro=S)irno= D .3-828 +r , D ,.15 0ra)er=on Mi'e' ;S* .14527 +r , ;S* ,.25
12
Ander'onDarling
AS* .1354-1
+r , AS* ,.25
Since the P5%alues for olmogoro%5Smirno%, (ramer5%on Mises and Anderson Darling are all greater than .-, there is no sufficient e%idence to conclude that the error terms are not normally distri0uted. !he Shapiro ?il* !est pro%es that the input data %alues comprise a random sample from a normal distri0ution since 15PPrL? .-87 is less than .- and its !est Statistic ? is %ery close to 1.
HETEROSKEDASTICITY
2igure <. SAS :utput for Partial #esidual Plots
13
14
Since all residual plots are neither diamond nor funnel shape, then heteros*edasticity might not 0e present among all independent %aria0les in the reduced model. !o ma*e sure, the researchers used ?hiteBs !est for homos*edasticity.
2igure 8. SAS :utput for ?hiteBs !est !est for homos*edasticity
:etero'(eda'ti(it& e't "*uation
e't
Stati'ti(
"#$O%
;hiteE' e't
DF
31.17
+r , 0hiS* 2
Variale'
.53
0ro'' of all =ar'
Gased from the P5%alue hich is greater than .- then there is no sufficient e%idence to conclude that the %ariances of the error terms are not constant.
OUTLIERS1INFLUENTIAL OBSERVATIONS
2igure 1-. SAS :utputs for Detection of :utliers Dependent Variale! "#$O% "#$O% Anal&'i' of Varian(e Sour(e
DF
Model "rror 0orre(ted 0orre(te d otal
5 66
Su) of S*uare'
Mean S*uare
F Value
8856.83842 1771.36768 552.2-656 8.36813 71 -4-.134-8
+r , F
211.68
/.1
$oot MS" 2.8-277 $S*uare .-413 Dependent Mean 27.3254 Ad $S* .-360oe Var 1.717 +ara)eter "'ti)ate' Variale
%ael
+ara)eter Standard DF "'ti)ate "rror
t Value
+r , t
nter(ept nter(ept 1 2.-3143 3.73332 .7.4351 "A0: "A0: 1 24.15-75 24.15-75 2.21674 1.- /.1 M< M< 1 2.25222 .45582 .45582 4.-4 /.1 0O:O$ 0O:O$ 1 .1785 .3125 5.47 /.1 F#$"S F#$"S 1 .1-3 .5-288 3.26 .18 0A$ 0A$ 1 .111 .37-3 .37-3 2.- .5 Output Stati'ti('(ONLY INCLUDES OUTLIERS) Dependent +redi(ted Std "rror Std "rror Student 0ooE' O' Variale Value Mean +redi(t $e'idual $e'idual $e'idual 21 1 2 16 22.--75 17.2267
.6124
5.778
25 23.-2-7 2-.54-
.8367 5.61-3
2.827
2.41
2.76- 2.2-
D
.33 .63
15
32 22.267 28.74
1.12 6.5333
2.714 2.47
.131
36 35.833 3.13
.-78
5.73
2.725
2.13
.-4
62 7-.7616 72.727
1.5-85
7.58-
2.411
2.-28
.628
Output Stati'ti(' :at Diag 0o= O' $Student : $atio 16 2.-28 .448 .775-
DFFS .4533
25 2.7-8
.837
.8125
.6284
32 2.513
.11-8
.7174
.-227
36
2.164
.1126
.8147
.76-6
62
3.1148
.353
.6847
2.651
Output Stati'ti('
DF"AS O' nter(ept "A0: M< 0O:O$ F#$"S 16
0A$
.8--
.453
.72
.2235
.1421
.235
25 .1846
.3317
.2--7
.461
.173
.1-84
32
.267
.7176
.8223
.2144
.173
.415
36 .484
.316
.-53
.4754
.1588 .1588
.48-7 .48-7
62 .5
.2111
.846
.1875
.5257
.1-5
2rom this SAS output, the o0ser%ations ith a0solute %alues of student residuals greater than are 16, , 3, 36 and 6. !he 6nd o0ser%ation has the highest (oo*Bs D. Meaning it has the highest influence influence among the o0ser%atio o0ser%ations. ns. 2or the D22I!S, only o0ser%ation o0ser%ation no. 6 e/ceed the cut5off. No o0ser%ation e/ceeds e/c eeds the cut5off for the D2G+!AS. D2G+!AS. !he researchers deleted the 6nd o0ser%ation since it has the highest (oo*Bs D. After deletion, the outlier ith the highest (oo*Bs D is"
Dependent +redi(ted Std "rror Std "rror Student 0ooE' O' Variale Value Mean +redi(t $e'idual $e'idual $e'idual 21 1 2 D 28.51 .-668 5.8434 2.541 2.2-- .128 32 22.267
After deletion of o0ser%ation 3" 15
21.5354 27.44
1.75 5.46-
2.426 2.255
.146
2.386 2.551
.144
.167
After deletion of o0ser%ation1" 54 21.788 27.1658
.877 6.86-
After deletion of o0ser%ation7" 34 35.833 2-.5-6
.831-
6.2343
2.277
2.738
16
After deletion of o0ser%ation 37" 46 17.-2-2 22.6487
1.173- 4.71-5
1.-68 2.3-8
.341
After deleting o0ser%ation 76, no other o0ser%ations as deleted since no other %alue of (oo*Bs D is significant.
2igure 11. SAS :utput for !ests !ests of Normality after outliers ha%e 0een remo%ed.
e't' for #or)ali t& e't
Stati'ti(
p Value
Shapiro;il ; .-84211 +r / ; .5656 ol)ogoro=S)irno= ol)ogoro=S)irno= D .-2826 +r , D ,.15 0ra)er=on Mi'e' ;S* .626- +r , ;S* ,.25 Ander'onDarling AS* .38518- +r , AS* ,.25
:etero'(eda'ti(it& e't Stati'ti( DF +r , 0hiS*
"*uation
e't
"#$O%
;hiteE' e't
17.66
2
.61
Variale' 0ro'' of all =ar'
?ith this, the researchers concluded that this ne data set still generates error terms that are normally distri0uted and ha%e constant %ariances. Also, the residuals are spread randomly in a hori'ontal 0and.
17
AUTOCORRELATION
!he last pro0lem to 0e diagnosed is autocorrelation. !his is of minimum priority since e are only dealing ith --4 data. ;oe%er, it ill still help %alidate the assumption that the error terms are uncorrelated. 2igure 1. SAS :utput for !est !est of Autocorrelation
Dependent Variale! "#$O% "#$O% Durin;at'on D 2.23 #u)er of O'er=ation' 66 1't Order Auto(orrelation .33
Gased on the Dur0in5?atson Dur0in5?atson !est first :rder Autocorrelation Autocorrelation is Eust 5-.-
he A$MA +ro(edure #a)e of Variale G re'id Mean of ;oring Serie' 85-"17 Standard De=iation 2.-67-5 #u)er of O'er=ation' 66
Auto(orrelation'
%ag 1 2 3 4 5 6 7 8 1 11 12 13 14 15 16
0o=arian(e
0orrelation
4.3-6547 .1468 .436768 .225-- .3444.87--6.685755 .1137 .648- .535145 .31876 .133435 .84637 .6456 .112-81 .13-338 .41377
1. .3321 .--34 .514 .6-25 .215 .155-8 .251 .1476 .12172 .7235 .335 .1-25 .14558 .257 .316.-41
1 - 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 - 1
Std "rror
. . .123-1 . . .123227 . . .124435 . . .124756 . . .125337 . . .13- . . .1328-3 . . .1328-4 . . .132-1. . .1345-7 . . .135185 . . .135288 . . .13532. . .137682 . . .137754 . . .137865
H.H )ar' t?o 'tandard error' n=er'e Auto(orrelation' %ag
0orrelation
1 2 3
.13727 .1-128 .13227
1 - 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 - 1
. . . . . .
18
4 5 6 7 8 1 11 12 13
.125.1-13 .17183 .1574 .2744 .117-1 .8636 .655 .3-68 .16357
. . . . . . . . . . . . . . . . . . . .
Gased on the output, autocorrelation is not significant e%en up to the first order. # did not change and the corrected parameter parameter estimates ha%e %ery small difference difference ith the pre%ious pre%ious estimates. All the %aria0les are still significant. VI. CONCLUSION
^
ENROL 6.6<8<8 J 18.-73!+A(; J !he estimated regression function ill 0e ENROL 3.767-IM$ K -.1674(:;:#! J.--17-2IN#+S J.-7377(A#. # is %ery high at .477 this indicates that the independent %aria0les can e/plain 4.77= of the %aria0ility of percentage of enrolment. Among all the independent %aria0les considered at the start of the study, fi%e of them ere found to 0e significantPercentage of !eachers, !otal 2inancial #esource, Percentage of 2ully Immuni'ed (hildren from - to 4 months, (ohort Sur%i%al #ate and Percentage of Pri%ate Motor Motor )ehicles hicles.. !he percent percentage age of teache teachers rs has the highes highestt positi positi%e %e relati relations onship hip ith ith the percentage, a unit in increase in the percentage of teachers may result to 18.-73 increase in percentage of enrolment. !his result shos that the higher percentage of teachers present in a pro%ince ill 0e a0le to accommodate more students thus increasing the percentage of enrolment. !he uality of education and participation rate of students can increase as the teacher5student ratio increases. If the num0er of teachers is relati%ely small compared to the num0er of students, the teachersB attention and focus ill 0e di%ided greatly leading to lo uality of education and decrease in studentsB interest. !he higher percentage of fully immuni'ed children ill impro%e the physical capa0ilities of child to go to school thus increasing the percentage of enrolment. !he (ohort sur%i%al rate has a negati%e effect on the percentage of enrolment since it indicates the rate of
1-
students students ho finished finished elementary and secondary secondary le%el meaning those students students ill not enrol in the ne/t school year. !he higher total financial resource can gi%e higher 0udget for education and 0etter material resources that can impro%e the percentage of enrolment. !hose people ho ons a pri%ate motor %ehicles indicates that they ha%e the financial capa0ility of sending their child to school. :ning a pri%ate motor %ehicles can also resol%e pro/imity 0arriers caused 0y a0sence of near0y pu0lic schools. Also, more support from the go%ernment is essential in impro%ing the percentage of enrolment since the total financial resource is a significant factor. It is also recommended for the go%ernment to increase the num0er of health care ser%ices offered to children and gi%e more support to the teachers 0y pro%iding 0enefits such as increasing their salary.
2
VII. REFERENCES ing, +.M. and Cillard C. @Determinants of schooling attainment and enrolment rates in the Philippines. April 1483. The Rand Publication Series. PD2 2ile. !ullao, !ullao, !. and #i%era O.P. @Demographic, @Demographic, and other factors affecting school .participation among children in ur0an and rural households" the case of Pasay and +astern Samar. )o )ol. II, No. 6. PD2 2ile. (aHete, C. @#e%ieing the +ffects of Population 9roth on Gasic +ducation De%elopment. PD2 2ile National Statistics (oordination Goard. @-1 2irst Semester :fficial Pro%incial Po%erty Statistics of the Philippines. PD2 2ile. (apones, M. @#eport of the Philippine go%ernment on Millennium De%elopment 9oals. August --8. PD2 2ile $NI(+2. @+ducation statistics" Philippines. May --8 Di%ision of Policy and Practice, Statistics and Monitoring Section. PD2 2ile National +conomic and De%elopment Authority Authority.. @Philippine Midterm Progress #eport on the Millennium De%elopment 9oals. PD2 2ile Anonymous. -1-, 1-, Ap April ril 1< 1<. . Imp Impro% ro%ing ing Phi Philip lippin pinee edu educat cation ion.. http">>opinion.inuirer http">>opinion.inuirer.net. .net. #etrie%ed March 3-, -17, from http">>opinion.inuirer.net>inuireropinion>tal*oftheton>%ie>-1--71<5 6786<>Impro%ing5Philippine5education Fap, Ooseph -1, August 6. :PINI:N" Impro%ing !he &uality :f +ducation In !he Philippines. http">>.asianscientist.com.
#etrie%ed
March
3-,
-17,
f r om
http">>.asianscient http">>.asianscientist.com>academia>ph ist.com>academia>philippines5educatio ilippines5education5asia5pacific5Eosef n5asia5pacific5Eosef5yap5pids5-1> 5yap5pids5-1>
21
VIII. APPENDICES
22
23
