계량 경제학 레포트

On Relationship Between Private Tutoring Expense and Quality of Public School

Team Golf

김수정 20071925

이우진 20091384

이창화 20090703

김웅희 20090604E-mail : godoftheman@naver.com

Index

A. IntroductionB. Question and HistoryC. Variable Definition and DataD. RegressionE. Result and InterpretationF. Policy ImplicationsG. ConclusionH. ReferenceI. Appendix – Full regression report

AbstractWe questioned whether the notion, commonly shared among policy makers,

that disbelief in public education is the prime cause of private education demand, and policies devised under the notion are valid. Specifically, we questioned the relationship between quality of school and private education

demand. The relationship is found out to be irrelevant. Hence, the notion is not valid and the policy is ineffective. Further, interesting picture of Korean family’s support on children’s education from 8th grade to 12th grade are captured. Higher wage and father’s education level persistently had a significant impact on higher private education demand. It is likely that the time distance from the Korean Scholastic Aptitude Test do work as a major determinant of private education demand

A. Introduction

Education fever has been an unavoidable word explaining phenomenon in Korea for decades. Recognized as a key for climbing socioeconomic ladder, this word attracts attention of every class in Korea - from young students to the parents and from the poor to the rich, so much that even polices and corporation cooperates on Korean Scholastic Aptitude Test day, and location of good schools and academies are one of major factors of house prices(Lee(2010)). Education policy is now in Korea more than mere description of methods to teach the young and raise them as good persons and citizens ; is about overall fairness and important determinant of life long decisions of students and their parents.

Given this, it is not surprising that excessive pressures on education is made in this country, so much that even UNHRC warned possibility of infringing students' human rights. As one result, private tutoring is prevalent that size of the industry is estimated to be 24-42 trillion won, possibly more than the money spent by Korean government on education, 38 trilion won. Average Korean family spends about 16% percent of monthly income, and, in aggregation, 20 trillion won are spent on private educational services.

In order to relax ever increasing private tutoring expenses, the government has been trying various policies including introduction of EBSi, pubilc after-school programs, admission officer system, and so on. Policy makers have been believed that demand on private tutoring is from unsatisfactory public education, and hence, increasing qualities of private education will ease burdens on private tutoring. However, we questioned whether these policies were effective, and if the policy makers' common notion on relation between public and private education is right. In more specific, we examined the relation between qualities

of school and expenses on private tutoring. From this, implication on the notion and policies will be derived.

B. Question and HistoryWe questioned whether government’s policy devised under the notion that

disbelief in public education is the prime cause of private education demand is working well. In specific, we questioned the relationship between quality of school and private education demand, represented by monthly expense on this category in average population. Since education has always been one of the hottest issues in Korea for decades, a number of researchers have been studying on similar topics, despite that only very few attempted to question on the direct relationship between the variables above.

Recent research has found relationship participation process of private tutoring and public education. Han, Lee and Park (2012) recently found Students’ Self-Determination is important thing. They said three conclusions. First, the percentage of females in students who participate in private tutoring with their own self-determination is higher than that of males, and the parents of the students who participate in private tutoring with their own self-determination have more income than those under pressure of their parents and others around them. Females have strong self-determination, but it is opposition about social common idea. Second, students who participate in private tutoring with their own self-determination are higher in academic self-efficacy, school satisfaction, and academic achievement than in those of students under pressure of their parents and others around them, and all of those three factors are statistically significant. Third, the correlations are positively significant among academic self-efficacy, school satisfaction, and academic achievement. We think this thesis show important fact. That is self-determination is most important thing to student. It gives them motivation, patience and interest on studying. Spontaneous makes good grade.

So, what kind of policy needs to intensify public education. People have been speaking of many solutions. Kim(2012) said some policy and solution. It said private tutoring is not substitute goods of public education but complementary goods of public education. We need to intensify public education by after school class. Education environment be better than now and teacher's right must be

assured. Public education needs more inquiry instruction. But this thesis research on middle school students. It can't reflect our high school education environment and hard to match for our reality. He said demand for private tutoring has increased due to students’ dissatisfaction and distrust to public education. This thesis said public education regain trust by society. Our social awareness must be change to public education is more important than private education or the private tutoring can’t be suppressed.

Some people want to know How much effect rise when the public education is stronger than today. Kim(2012) had researched on those topic. He found high rank student improve their grade by after school class and private tutoring in high school. Especially, 11~30% rank student have more effective by private tutoring than after school class. However, If the student which is middle rank student without private tutoring, it have huge effect to those student. Priavte tutoring and after school class are considerably improve student's grade in the low rank student. Also, He found when Students spend more time in the private tutoring Students can't do self-determination study it makes their grades down. This conclusion connects Shinill Han, Sukyeol Lee and Jineun Park (2012). Self-directed learning is important thing for whoever studying students.Some people think student’s evaluation about the high school will be effect on

private tutoring. Kyoungoh Song, Sungsu Jeong (2010), researched on this topic. The purpose of this study is to examine the policy argument that demand for private tutoring has increased due to student’s dissatisfaction to public education. Although these arguments have been accepted pervasively, there exits little evidence explored by empirical studies. This study found statistically significant relationships between participation in private tutoring and student’s satisfaction to school education, but the effects of these are marginal. In addition, it did not show the significant effects of student’s perception of teacher quality on demand for private tutoring. These finding from this study suggest that policy strategies for decreasing demand for private tutoring is hard. This study against Nam e Kim(2012). Public education regains trust isn’t solution about private tutoring.Our research purpose like this thesis, Kyungah Sang(2010) found there is insignificant effects of student and school level factors on students' participation in private tutoring. It was found that student level factors such as household income, gender, self-efficacy and school level factors like community size, mean of household income affected the odds participating in private tutoring. But

school level factors representing school's efforts to enhance quality of education such as remedial class, after-school program, grouping by ability didn't show significant effect on the odds participating in private tutoring. Similarly, student level factors such as father's educational background, household income, gender, self-efficacy and school level factor like community size, mean of household income increased the time spent for private tutoring. But school level factors representing school's efforts to enhance quality of education such as remedial class, after-school program, grouping by ability didn't show significant effect on the time spent for private tutoring.

C. Variable Definition and DataWe wanted to know the relationship between quality of public school’s

educational services and level of private tutoring expenses. Using argument of Gahng(2009) that level of satisfaction a student feels from public schools’ educational services collected in KYPS is positively correlated with actual quality of school in average, we use the level of students’ satisfaction from public school’s educational services as an instrumental variable for the quality.

To find a clearer relationship, we needed to control other variables possibly affecting the level of expenditures. We suspected that there are mainly 4 conditions of private tutoring demand – public school condition, student’s personal condition, family condition, policy condition and number of years left from the students’ National Scholastic Aptitude Test. Policy condition is omitted based on Baek, Kil and Yoon’s analysis(2010) that major policy changes during the years(2003~2007) did not have a significant impact. Other variables such as parents’ jobs in family condition are omitted either because of multi-collinearity problem, irrelevance or to follow principle of frugality in choosing variable(for example, according to Gahng(2009), how a child designs his career is found out to be significant, but the model is too complicated to incorporate in this analysis). Hence, only 3 main variables are left. Using KYPS data helped us to numerated definition of each variable in detail.

We used data from 'Korean Youth Panel Search (KYPS)' done by National Youth Policy Institute. KYPS analyzed middle school second grade's cohort data. Middle school second grade's cohort data research started in 2003 until high school longitudinally. We analyzed data from 2003(8th grade), 2005(10th grade) and

2007(12th grade).The KYPS cohort is done with 'stratified multi-stage cluster sampling' and made

to represent nation-wide population data. In the first year, it is made up with 3,449 students from 104 schools. And after that, longitudinal data's student number is 3,106, 3,081, 3,077, 2,925 each year.

This KYPS's data is useful for this research at least with these two points. First, this data have a continuous data of same individuals over 5 years so that we can examine the impact of grade change in determining private tutoring expenses without disturbance from further considering differences among different individuals. Second, KYPS data have substantial amount variables which have effects on private education, allowing us to fully control other possible factors affecting the level of expenditure.

Using the data, we could define the 3 main independent variables numerically – public school condition, student’s personal condition, family condition

1) Public school condition① School quality : This data is gathered by asking students the question : "My

school is not helpful for going university", and grading the answers from Exceptionally Bad(0) to Exceptionally Good(6). This variable represents students' satisfaction from public school's educational services. Following the interpretation argued by Kahng(2009), we assume that this variable in average approximates actual quality of school. It is believed widely among policy makers that disbelief to the school create the demand of private education.

2) Student’s personal condition ① Gender : Dummy variable representing sex(male = 1, female = 0)② Score : This is a student's achievement with percentage record. If there is no

whole school grade percentage, we used class grade percentage. Higher the value, lower the students’ scores.

3) Family condition① Father's level of education : This is ranged from none(1 point) to Doctor's

degree(8 points). ② Mother's level of education : Same with father's scholarship.③ Income per month : Average monthly income of parents

For dependent variable, since our object is to find the relationship between school quality and private tutoring expenditure, we define this as monthly average private education expenses in each year extracted also from KYPS. We take a logarithm on this.

We believed that, despite the fact that so many variables are involving in determining the private expenditure, these are sufficient to show the essence mechanics behind it.

D. RegressionWith the notions above, we could define following variables

Name of Variables

Explanation

ln(P) Q Score S PS F M ln(N) u

log of monthly private tutoring expense satisfaction from educational service and quality of public schoolstudents’ score ; lower the score, better the performancesex(male = 1, female = 0)personal study hours(Korean, English, Math)father’s education levelmother’s education levellog of monthly incomeError term

Table 1. Variable list

The aim of this paper is to clarify the relationship between quality of public school’s educational services and level of private tutoring expenses. To do this, we are going to control other variables that may significantly influence on private expenditure and then examine the impact of the variable we would like to focus on, the quality.

This can be achieved by putting variables into following regression equation1 : 1 Professor Choi pointed out that it would be recommendable to use panel data method. However, we wanted to include changes in coefficients and statistics over time, as they turn out to be very important in interpreting the reality, while keeping the model as simple as possible. Yet, the model should reveal essential mechanics behind phenomenon. Final alternative model devised satisfying the criteria stated above is as follow :

ln(P) = b0 + b1*Q + b2*S + b3*Score + b4*PS + b5*F + b6*M + b7*ln(N)+ b12*y2*Q + b22*y2*S + b22*y2*Score + b42*y2*PS + b52*y2*F + b62*y2*M + b72*y2*ln(N)+ b13*y3*Q + b23*y3*S + b23*y3*Score + b43*y3*PS + b53*y3*F + b63*y3*M + b73*y3*ln(N)

ln(P) = b0 + b1*Q + b2*S + b3*Score + b4*PS + b5*F + b6*M + b7*ln(N) + u

where each variable represents what’re stated in Table 1.

E. Result and interpretationWe applied the equation onto 5 sample groups : from 8th grade to 12th grade.

However, we present summary statistics of 8th grade, 10th grade, and 12th grade only, since 9th and 11th are not qualitatively different from the above.2 Since KYPS is panel data, it is expected that differences between significant coefficients will reveal information about how private expenditure is constituted in each age group.

Following table(Table2) is the summary of statistics.

8th grade 10th grade 12th gradecoefficien

t t-stat p-valuecoefficien

t t-stat p-value coefficient t-stat p-valueConstant .296 2.284 .022 -.138 -.610 .542 -.435 -1.348 .178Q .011 .650 .516 -.007 -.291 .771 -.027 -.987 .324Score -.056 -3.037 .002 -.064 -2.783 .005 -.043 -1.527 .127S .033 1.902 .057 .047 2.083 .037 -.002 -.076 .940PS .063 3.490 .000 .085 3.695 .000 .019 .681 .496F .095 3.776 .000 .086 2.802 .005 .108 2.906 .004M .115 4.623 .000 .069 2.245 .025 .041 1.121 .262ln(N) .351 17.60

7.000 .319 12.73

7.000 .304 10.51

5.000

R2 .258 .197 .151F 75.598 56.572 29.599

+ b14*y4*Q + b24*y4*S + b24*y4*Score + b44*y4*PS + b54*y4*F + b64*y4*M + b74*y4*ln(N)+ b15*y5*Q + b25*y5*S + b25*y5*Score + b45*y5*PS + b55*y5*F + b65*y5*M + b75*y5*ln(N) + b8*t + b9*t2 + u

where y represents year dummies designed to catch changes in partial impact of variables in each year. Variables t and t2 represent quadratic effect of years distanced from the National Scholastic Aptitude Test day for each student in each grade. This model, however, is complicates operation and interpretation of data, while the simple formula,

ln(P) = b0 + b1*Q + b2*S + b3*Score + b4*PS + b5*F + b6*M + b7*ln(N) + ugives sufficient information for our primary purpose, the relationship between quality of school and private education demand. We judged that it is better to use simpler model that fits to our purpose, rather complicating it, and hence, used the simple formula.2 Full regression result is reported in the appendix

p-value(F) .000 .000 .000Table2. Regression Analysis

Firstly, school satisfaction or quality is found out to be insignificant. It constantly has a very high p-value throughout all the years. This simply means the variable and private tutoring expenses are uncorrelated whatsoever. Its full implication will be explored in Policy Implication section.

The table shows quite an interesting result. From 8th-11th grades(see Appendix to check out full 5 regression reports), all coefficients but quality of school and sex – from score, personal study hours, parents’ educational level and income level – are significant at 5% level in the same direction. Throughout the years, students’ academic performance, personal study hours, parents’ education levels and family’s income level has positive linear relationship with private tutoring expenses. This matches with our common sense. Its likeliness and the consistency throughout the years are evidences that the regression equation listed above is showing essential mechanics among variables.

The dummy variable for sex is ambiguous. Despite relatively high p-value in 8 th

(.057) and 12th (.940) grade which would be a base to reject its significance, it has one of the lowest p-value in grade 9 (.005). Its significance is inconsistent over time. Probably the reason of inconsistency results from effects of omitted variables. Only after removing further mechanisms, whether it is really significant or not would be illuminated.

F statistics in all models are very high, and its p-value is effectively zero, which means these variables are jointly significant and the model is appropriate in a sense. This is another evidence, along with the consistency mentioned above, that the model is capturing a facet of the truth and may serve as a basis for further researches.

Movements of statistics over time are interesting to watch. R2 is observed to be dropping as grade goes up : 0.258, 0.197 and 0.151 in each grade. This suggests that as grades get higher, variables other than specified is influencing their decision making on private tutoring higher. Perhaps the missing variable is the time itself. As the National Scholarly Test day gets nearer, students and parents gets panic, spending tremendous money in a hope of getting one point higher in the National Test and enter a better university, as its expected return both in social and financial sense is perceived to be high.

Sudden changes in significance of variables at 12th grade also support this

theory. Until 11th grades, all variables but quality component and sex are significantly influencing private tutoring expense in the same direction, even though exact credibility and values may vary over time. However, out of the blue, all coefficients but father’s educational level and monthly income become insignificant. Whether you are high or low on score, male or female, study personally hours or not - all do not matter. This is very likely because of the reason mentioned above – upcoming of National Scholastic Aptitude Test. Although this theory is very interesting, this is beyond the purpose of this paper, and should be studied by different papers. Here, we focus on the quality of school only.

It is worth to note that fathers’ education level and monthly income has a very strong, positive correlation with the level of private education. With the observation that R2 is dropping and coefficients are becoming less significant over years, statistics are may be suggesting that as grade goes up, parents put their children in private academy at their best level possible, no matter what the student’s status and family backgrounds are. They will support as much as their monthly income allows, resulting highly significant income variable. Between families with the same income, a family with highly educated father, who is likely to be more interested in giving higher education to their children, may put more allowances for educating expenses than lowly educated father, resulting significant coefficient. Another observation that significance of mother’s education level is decreasing may reflect in-family power distribution between husband and wife. This interpretation gives a very interesting picture of how Korean family works with respect to education over years.

Full regression reports over all 5 years are included in the Appendix.

F. Policy ImplicationOur primary focus is Q, variable representing students’ satisfaction from and

quality of public education. If coefficient of Q is negatively significant, then dissatisfaction about the public educational service leads to higher private tutoring demand. This is a common belief shared among policy makers, making them to devise policies to enhance public school’s quality.

If coefficient of Q is positively significant, then higher quality is associated with higher private education demand. This is suspected to be the result of survival effort in an intense competition in good schools leads to the higher education. If

it is the case, then increasing the quality of school leads to rather higher demand for private education, given others are the same. This means current belief and direction of educational policy is rather generating adverse effects.

If the coefficient is insignificant in either way, i.e. effectively zero, then it means school quality and private education demand are not correlated. This means all the money spent to increase public schools’ educational service are simply a waste of money, time and effort, as it does not have a significant impact.

As long as Q is not negatively significant, private education demand is not a result of problematic public education, but other social factors such as intense inner competition or prevalent educational heats. This means that the phenomenon’s solvency, if that’s a problem, is not individual educational policy such as enhancement of public school, but must be found from socioeconomic structures, which is far out of range of a single department of education.

In the analysis, the coefficients are consistently found to be insignificant through all the years. This means quality is not meaningfully related to private education demand over all grades of school : from 8 to 12. As explained above, enhancing public educational service does have nothing to do with increasing private education demand. The policy is a waste of energy if its sole purpose is to settle the demand down. The policy makers’ beliefs must be changed now!

G. ConclusionAre our educational policy and governors’ shared notions on private educations

are valid? Are private tutorship demand and school qualities are correlated? Can a single educational policy address current private education demand? Not that we found of.

We found that there does not exist any meaningful relationship between private education and school satisfaction. Taking the argument of Gahng(2009) that school satisfaction can be regarded as a measure of school quality in average, we can extend the result to imply that there does not exist a stable relationship between the demand and the quality of public schooling services. Hence, the commonly shared beliefs among policy makers that dissatisfactory public education is prime cause of private education demand are invalid. The policies devised under this notion is ineffective for this purpose, and hence, a waste of great money and social effort. Since the uncorrelation, current boom on

private education is a phenomenon resulting rather from socioeconomic dynamics, rather than micro phenomenon that can be handled with a single educational policy. The policy packages dealing with the whole society rather than educational level is needed to settle the private education demand.

As a by-product, an interesting picture of current Korean families with respect to educational support is captured. Among all other significant variables, father’s educational level and family’s monthly income are found out to be the most impactful. Sudden upheavals in significances of coefficients except those two when students become 12th grade suggest two implications on Korean families. Frist, they tend to spend on education as much as their income allows, especially when their children are in 12th grades. Second, relative power distribution between husband and wife seems to be skewed in favor of the husband, hence, allowing more voices for husbands when it comes to a family decision. Further, as suggested by the sudden upheavals and decreasing R2 over time, it is likely that the time distance from the Korean Scholastic Aptitude Test do work as a major determinant of private education demand.

Although the model has limitations in that it greatly simplified and omitted few possibly important variables and mechanics for either absence of data or for the sake of simplicity, it still serves well enough to clarify the relationship between private tutoring demand and public school’s quality, capturing the essence mechanics behind the variables. This itself provided interesting pictures on policy and Korean family issues with respect to education. Further research with more delicate design and rich data based from this model will provide clearer picture.

H. ReferenceGhwangHyun Lee, 2010, Effects of School District Reputation, Educational Input and Outcome Variables on Apartment Price, Resident Study, Vol.18, No.1, pp69-88Shinill Han, Sukyeol Lee, Jineun Park, 2012, Relationship Analysis of Academic Self-Efficacy, School Satisfaction, and Academic Achievement with Students’ Self-Determination on Their Participation Process of Private Tutoring, Korea Holistic Education Academy, Vol.16, No.2, pp.67 ~ 90

Nam E Kim, 2012, Through a comparison of public and private education, public education efforts to private education for reducing. Konkuk University Journal Jinyoung Kim, 2012, Comparing the Efficiency of the After-School Program and the Private Tutoring through a Value-Added Educational Production Function,

Finance Analysis, Vol.5, No.3, pp.1 ~ 32

Kyungah Sang, 2010, Effects of Student and School Level Factors on Students' Participation in Private Tutoring. Eduation Evaluation Analysis, Vol.23, No.2, pp.265-280

Kyoungoh Song, Sungsu Jeong, 2010, An analysis of Influences of students' perception of school education on demands for private tutoring, Education Public Administration Analysis, Vol.28, No.3, pp.275 ~ 299

Gahng Tae Joong, 2009, The gender difference in spending for private tutoring, Asian Journal of Education, Vol.10, No.2, pp.348-381

Changhui Kang and Bohun Hyun, 2012, Effects of Family Size on Private Tutoring Expenditures in Korea, Korean Economic Journal of Labor, Vol.35, No.1, pp.111-132

SunGeun Baek, HyeJi Kil, JiYoon Yoon, 2010, The Effects of EBS Lecture Watching Hours on Private Tutoring Expenses, Asian Journal of Education, Vol.11,

HyeonJin Kim, GyunDal Park, 2011, The Structure of Private Tutoring Expenditure by the General High School Students and the Foreign Language High School Students in Korea, Journal of Education and Administration, Vol.29, No.1, pp.131~151

I. Appendix8th grade

Coefficientsa

Model Non-std coeffi. Std. Coeffi.t p-value

95% CI to B MulticollinearityB S.D. Beta Lower Upper Tolerance VIF

1 Constant .296 .129 2.284 .022 .042 .550Q .006 .009 .011 .650 .516 -.012 .024 .992 1.008Score -.001 .000 -.056 -3.037 .002 -.002 .000 .903 1.107F .049 .013 .095 3.776 .000 .023 .074 .481 2.078M .069 .015 .115 4.623 .000 .040 .099 .494 2.024S .043 .023 .033 1.902 .057 -.001 .088 .996 1.004ln(N) .428 .024 .351 17.607 .000 .380 .475 .769 1.301PS .008 .002 .063 3.490 .000 .003 .012 .951 1.052

a. Dependent Variable : ln(P)

Model Summary

ModelR R2 Adjusted R2

S.D. of estimator

1 .508a .258 .256 .56126

Variance Analysisb

ModelSS D.F.

Mean Sqrd F p-value

1 Explained 266.068 7 38.010 120.660 .000a

Residual 765.801 2431 .315 Sum 1031.869 2438

9th gradeCoefficientsa

Model Non-std coeffi. Std. Coeffi.t p-value

95% CI to B MulticollinearityB S.D. Beta Lower Upper Tolerance VIF

1 Constant .407 .171 2.377 .018 .071 .743Q -.009 .013 -.013 -.676 .499 -.034 .017 .991 1.010Score -.003 .001 -.099 -4.702 .000 -.004 -.002 .884 1.131F .046 .015 .083 3.003 .003 .016 .077 .518 1.929M .064 .018 .096 3.521 .000 .028 .099 .531 1.883S .034 .028 .024 1.227 .220 -.021 .089 .991 1.009ln(N) .432 .032 .304 13.685 .000 .370 .494 .796 1.256PS .007 .002 .056 2.718 .007 .002 .012 .929 1.076

a. Dependent Variable : ln(P)

Model Summary

ModelR R2 Adjusted R2

S.D. of estimator

1 .455a .207 .205 .62825

Variance Analysisb

ModelSS D.F.

Mean Sqrd F p-value

1 Explained 208.869 7 29.838 75.598 .000a

Residual 798.082 2022 .395 Sum 1006.951 2029

10th gradeCoefficientsa

Model Non-std coeffi. Std. Coeffi.t p-value

95% CI to B MulticollinearityB S.D. Beta Lower Upper Tolerance VIF

1 Constant -.138 .227 -.610 .542 -.583 .307Q -.004 .015 -.007 -.291 .771 -.034 .025 .996 1.004Score -.002 .001 -.064 -2.783 .005 -.003 -.001 .932 1.073F .051 .018 .086 2.802 .005 .015 .087 .522 1.916M .049 .022 .069 2.245 .025 .006 .091 .521 1.919S .540 .042 .319 12.737 .000 .457 .623 .794 1.260ln(N) .069 .033 .047 2.083 .037 .004 .135 .991 1.009PS .008 .002 .085 3.695 .000 .004 .012 .936 1.069

a. Dependent Variable : ln(P)

Model Summary

ModelR R2 Adjusted R2

S.D. of estimator

1 .444a .197 .193 .66894

Variance Analysisb

ModelSS D.F.

Mean Sqrd F p-value

1 Explained 177.203 7 25.315 56.572 .000a

Residual 722.681 1615 .447 Sum 899.884 1622

11th gradeCoefficientsa

Model Non-std coeffi. Std. Coeffi.

t p-value

95% CI to B Multicollinearity

B S.D. Beta Lower UpperToleranc

e VIF1 Constant .291 .214 1.362 .173 -.128 .711

Q -.002 .014 -.003 -.144 .886 -.030 .026 .997 1.003Score -.003 .001 -.084 -3.578 .000 -.004 -.001 .929 1.077F .059 .018 .104 3.330 .001 .024 .094 .533 1.875M .069 .021 .103 3.308 .001 .028 .110 .532 1.881S .049 .032 .034 1.508 .132 -.015 .112 .994 1.006ln(N) .457 .039 .295 11.703 .000 .380 .534 .817 1.225PS .004 .002 .051 2.162 .031 .000 .008 .923 1.083

a. Dependent Variable : ln(P)

Model Summary

ModelR R2 Adjusted R2

S.D. of estimator

1 .448a .200 .197 .63542Variance Analysisb

ModelSS D.F.

Mean Sqrd F p-value

1 Explained 156.352 7 22.336 55.321 .000a

Residual 623.803 1545 .404 Sum 780.155 1552

12th grade계수 a

Model Non-std coeffi. Std. Coeffi.t p-value

95% CI to B MulticollinearityB S.D. Beta Lower Upper Tolerance VIF

1 Constant -.435 .323 -1.348 .178 -1.069 .198Q -.020 .020 -.027 -.987 .324 -.059 .019 .995 1.005Score -.002 .001 -.043 -1.527 .127 -.004 .000 .907 1.103F .075 .026 .108 2.906 .004 .025 .126 .526 1.901M .034 .030 .041 1.121 .262 -.025 .092 .535 1.868S -.004 .047 -.002 -.076 .940 -.095 .088 .995 1.005ln(N) .594 .057 .304 10.515 .000 .483 .705 .871 1.148PS .001 .002 .019 .681 .496 -.003 .005 .898 1.113

a. Dependent Variable : ln(P)

Model Summary

ModelR R2 Adjusted R2

S.D. of estimator

1 .389a .151 .146 .794537

Variance Analysisb

ModelSS D.F.

Mean Sqrd F p-value

1 Explained 130.798 7 18.685 29.599 .000a

Residual 733.558 1162 .631 Sum 864.356 1169