To identify the factors that have most influence on the performance of elementary Schools in California using SAS Regression Analysis.

1. PREDICTION OF ACADEMIC
PERFORMANCE OF ELEMENTARY SCHOOL
SAS CASE STUDY
Presented by
Vaibhav Jain(A13021)
Maruthi Nataraj K(A13009)
Sunil Kumar(A13020)
Punit Kishore(A13011)
Arbind Kumar(A13003)
Praxis Business School , Kolkata

2. AGENDA
 Introduction
 Business Objective
 Regression Equation
 Key Drivers
 Analysis and Inferences
 Recommendations
 Appendix

3. INTRODUCTION
 API : The Academic Performance Index (API) is a measurement
of academic performance and progress of individual schools in California,
United States.
 API scores ranges from a low of 200 to a high of 1000.
 The API is closely tied to monetary and incentive awards by setting
Annual Percent Growth Targets for each school and whether the school
met or exceeded this goal.
 Why API ? To benchmark a school’s performance against other peer
schools that are educating similar students to build upon a school’s
strengths by focus on indicative metrics and identify areas for
improvement.
 Allows teachers, parents, school administrators, students, and
taxpayers to analyze and compare the academic performance of
individual schools.

4. BUSINESS OBJECTIVE
“To identify the factors that have most influence on the
performance of elementary Schools in California”
 Probable Indicators
- Class Size
- Enrollment
- Poverty
- Parent Education
- Student Performance
- Teachers Credentials
 Tools used :SAS
 Techniques : Regression Analysis

5. REGRESSION EQUATION
y=
x1
x2
x3
 Dependent variable (y) is api00 (Academic Performance Index 2000)
 Independent variables :
 x1 is meals (Percentage free meals i.e. poverty)
 x2 is ln(grad_sch) where grad_sch (Parent grad school)
 x3 is emer (Percentage teacher emergency credentials)
 Intercept
 Coefficient
 Coefficient
 Coefficient
 Final Equation is y = 857.63-3.43x1+22.25x2-1.95x3

6. KEY DRIVERS
Based on Regression Model
Percentage
Free Meals
(Poverty)
Positive
Academic
Performance
Index
Parent
Graduation
School
(Parent
Education)
Percentage
Emergency
Credential
(Teacher
Credentials)

7. ANALYSIS AND INFERENCES
Indicator 1 - Poverty
 The percentage of children eligible for free school meals is thought
to be a fair measure of deprivation.
 School with most children eligible for free school meals could have
negative effect in its performance as it has been likely to be teaching
children with access to fewer resources and less home encouragement.
 Many of the students entitled to free meals do not take them
because of worry about bad quality food and insufficient quantity of
the meals, which affects their health and in turn worsens academic
performance.
 Comparing the students availing the free meals option vis-a-vis
others in the school, the API might also get affected due to
performance of other students who are not part of the scheme.

8. ANALYSIS AND INFERENCES
Indicator 2 – Parent Education
 A child exposed to parents who models achievement-oriented behaviour (e.g.,
obtaining advanced degrees; etc) and provide achievement-oriented opportunities
(e.g., library and museum trips etc) develops the guiding belief that achievement is to
be valued and this belief in turn improves his performance in school.
 Graduated parents are more likely to use complex language and a wider
vocabulary with their young children. Therefore, the children develop language skills,
vocabulary, and cognitive skills earlier and perform better.
 Better educated parents are familiar with how schools work and are more likely to
get involved in the school, thereby monitoring their child’s academic progress.
 The more education they have, the higher their income-earning potential. People
with more money can afford to live in more expensive neighbourhoods and facilitate
better learning environment for the children which is sure to have an impact on
his/her academic performance.

9. ANALYSIS AND INFERENCES
Indicator 3 – Teachers’ Credentials
 Schools hire emergency-credentialed teachers to fill posts when
they cannot find fully certified teachers.
 It depends on the large number of students and high demand for
teachers.
 Emergency-credentialed teachers may have bachelor's degrees
and/or professional experience in the subjects they teach, but lack the
required teacher training and experience.
 A high percentage of teachers with emergency teaching certificates
may indicate that the school has difficulty in attracting and retaining
qualified teachers.
 Teachers’ salaries and greater number of unqualified teachers
seeking jobs also contribute to the teacher credentials.

10. RECOMMENDATIONS
 Investment will be needed in the schools offering free meals to eligible
students in order to bring their facilities up to standard.
 New standards should be set for school meals to ensure that the meals
are prepared with fresh , healthy ingredients and give children the
nutrients they need.
 The best strategy for closing achievement gaps is to make sure that
schools serving poor and minority students have their fair share of
qualified teachers.
 States and Districts can explore value-added methods to make
informed decisions about where to assign teachers, how to staff schools,
and what supports and professional development are needed to maximize
the benefits of having good teachers.

11. RECOMMENDATIONS
 States and Districts can establish and maintain intensive, long-term
induction programs that focus on helping new teachers to meet
challenging professional performance standards.
 Parents with lower levels of education are less likely to have high
expectations for the children's academic careers. When parents do not
have high expectations for children's academic achievement, the children
are unlikely to have expectations for themselves. Such children should be
provided additional motivation and exposure to learning for improved
academic results.

12. APPENDIX
DATA SNAPSHOT

13. OUTLIER TREATMENT
APPENDIX

14. MISSING VALUES
APPENDIX
 In order to treat the missing values as a part of data sanity check ,we need to
understand the data.
 When we look at the data closely, all the variables related to parent education
form a group.
 Also, we can observe that some of the percentage full values are less than 1
though in real most of them are expressed in percentages.
 As we have seen from PROC UNIVARIATE, there were some negative values in
average class size k-3 but fall within the same range as others when taken as
absolute values.
 Percentage free meals depends on the meals category also to some extent and
when replacing the missing values of meals, this point should be taken care.

15. MISSING VALUES
APPENDIX

16. APPENDIX
Understanding variable dependency on API00

17. APPENDIX
TESTING THE OVERALL SIGNIFICANCE OF THE MODEL
 Null Hypothesis : All the unknown population coefficients are
simultaneously zero.
 Alternate Hypothesis : At least one of them is non-zero.
In this case ,since p < alpha (0.01) , we rejected the null
hypothesis. It means that some of the independent variables can
influence dependent variable(api00).

18. APPENDIX
 The extent of multicollinearity for any variable is captured by variation inflation
factor (VIF) . As higher VIF is not desirable, we needed to bring it down to the
range of 1.5 – 2.0 .

19. APPENDIX
 Using COLLIN option’s collinearity diagnostic table, we identified variables
which had highest collinearity with others having highest VIF among the two
and retained the one which has lower p-value for higher significance.

20. APPENDIX
 Then , Heteroscedasticity (SPEC) check was carried out and also the
residual plots were observed to work out on the transformation of the
variables to reduce its effect.

21. APPENDIX
CHECK FOR SIGNIFICANCE OF INDIVIDUAL PARAMETERS
 Null Hypothesis : j = 0
 Alternate Hypothesis j <> 0
If p < alpha , we reject null hypothesis to claim that j is significantly
different from zero and Xj is an important variable in model.

22. APPENDIX
Output file with predicted and residual variables
Residuals plots of significant variables of model

23. APPENDIX
 Null Hypothesis : Model is homescedastic.
 Alternate Hypothesis : Model is heteroscedastic.
As p > alpha,
we accept the
null hypothesis.
 Here, grad_sch was
transformed
to
log(grad_sch) to reduce
the
heteroscedasticity
effect.

24. APPENDIX
 Null Hypothesis : Residuals are normally distributed
 Alternate Hypothesis : Residuals are not normally distributed
As p>alpha(0.01)
in all cases, we
accept the null
hypothesis.

25. APPENDIX
Mean Absolute Percentage Error captures the error percentage in the
model and for our model it is 7.92% which is within 10% (ideal).

26. APPENDIX
Dashboard