Regression Project

SMBA-Project Report 1

Relationship between Literacy and Population exposed to Primary Schools

In Uttar Pradesh

Statistical Modeling for Business Analytics PROJECT REPORT

Submitted By:

Nishu Navneet (12125032) Sushil Panigrahi (12125048) Mangesh Dharwad(12125026)


INDEX

Introduction3

Data Collection and References.4

Variables 5

Tools and Methods.....7

Analysis .....8

Observation and Conclusion .....10

Result .11

Annexures...12


Introduction

Uttar Pradesh is the most populous state in India. Its population accounts for 16.4

per cent of the countrys population. It is also the fourth largest state in

geographical area covering 9.0 per cent of the countrys geographical area. It has

83 districts, 901 development blocks and 112,804 inhabited villages. The density

of population in the state is 473 persons per square kilometers while of the country

it is 274. The literacy rate in Uttar Pradesh stood at 56.27% overall with 67% male

and 43% female literate.

Indian constitution defines literacy for people aged seven years and above with

ability to read and write with understanding in any language. In India we

denominate its poor literacy rate with following reasons-

1. Absence of adequate school infrastructure

2. Improper facility

3. Inefficient teaching staff

4. Existence of Caste-Religion disparity

5. Poverty

The purpose of this report is to find the relationship between literacy of a district

in Uttar-Pradesh with number of person exposed to primary schools in their

villages. We have tried to measure its significance while putting many other factors

in account.


Data Collection

The relevant data to do the analysis has been collected from the government census

website.

It can be found here-

http://censusindia.gov.in/Tables_Published/Basic_Data_Sheet.aspx

Through the website data for each district can be collected. The tabling of data into

the excel sheet has been done manually. Utmost sincerity and precaution has been

taken care while putting data in excel columns.

The data collected is from the source of 2001 census data.

Other references have been taken from here-

http://lawmin.nic.in/ncrwc/finalreport/v2b1-5.htm

http://upgov.nic.in/upecon.aspx


Variables

Data collected has been assigned under various variables listed below.

Primary Variables - Collected in raw form

1. District (String) Name of the district

2. Literacy (Scale) Number of population literate in the district, according to

government standards.

3. Population (Scale) Population of the district

4. Males (Scale) Male population in the district

5. Hindu (Scale) Hindu population in the district

6. Muslim (Scale) Muslim population in the district

7. NoOfHouseholds (Scale) Number of Household present in the district

8. TotalVillages (Scale) Total number of villages present in the district

9. PrimarySchoolsAvail (Scale) Total number of villages with the facility of

primary schools

10. BusServiceAvail (Scale) Total number of villages with bus service

availability.

Secondary Variables Variables with operations on primary variables to do further

analysis

11. PrimarySchoolExposure (Scale) Average population exposed to primary

schools

12. BusServiceExposure (Scale) Average population exposed to Bus service

13. PctHindu (Scale) Percentage of hindu population in the district

14. PctMuslim (Scale) Percentage of Muslim Population in the district


15. PrimarySchoolExposureSquared (Scale) Square of Average population

exposed to primary schools

16. PrimarySchoolExposureCube (Scale) Cube of Average population


17. NormalLofOfPrimarySchoolExposure (Scale) Normal logarithm of

Average population exposed to primary schools

18. NormalLofOfPrimarySchoolExposureSqaured (Scale) Square of Normal

logarithm of Average population exposed to primary schools

19. NormalLofOfPrimarySchoolExposureCube (Scale) Cube of Normal

logarithm of Average population exposed to primary schools

20. HighPercentageOfMuslimPopulation (Binomial) Value 1 assigned to

variable if the Percentage Muslim Population is above the mean of the

percentage Muslim population

21. InteractionBetweenMuslimPopulationAndPopulationExposureToSchool

(Numeric) Multiplication of the variables

HighPercentageOfMuslimPopulation and PrimarySchoolExposure, to study

interaction effect

22. HouseholdSize (Numeric) Average number of person staying in a

household for the district.

23. HighPercentHouseHoldSize (Binary) - Value 1 assigned to variable if the

Household size of the district is above the mean of the Household sizes

24. InteractionBetweenHighHouseholdSizeAndPSExpsoure (Numeric) -

Multiplication of the variables

InteractionBetweenHighHouseholdSizeAndPSExpsoure and

PrimarySchoolExposure, to study its interaction effect


Tools and Methods

IBM SPSS Statistics software has been used to do regression and other statistical

analysis.

The analysis includes

1. Scatter Plot

2. Curve Estimation

3. Linear Regression

4. Multiple Linear Regression

5. Polynomial Non-linear Regression

6. Linear-Log Modeling

7. Linear-Log Model with Higher Powers

8. Interaction Between Continuous and Binary Variable


Analysis

The relationship between Literacy and population exposed to primary schools can

be shown by the scatter plot. The scatter plot is suggesting a linear relationship.

1. Model 1 The equation 1 in Result (Page Number - 11) is depicting a linear

relationship of literacy with population exposed to primary schools. The

coefficient is statistically significant at 5% significance level and is giving a

model with Adjusted 2 as high as 71.7%

2. Model 2 The equation 2 in Result (Page Number - 11) is depicting a multiple

relationship of literacy with population exposed to primary schools, population


exposed to bus services and percentage of Hindu population. The coefficients

are statistically significant at 5% significance level for two regressors but not

for the population exposed to bus service. The Adjusted 2

for the model is

72.90%.

3. Model 3 - The equation 3 in Result (Page Number - 11) is depicting a non-

linear relationship of literacy with population exposed to primary schools, to its

square and cube. The coefficient is statistically significant at 5% significance

level for the population exposed to primary schools only but not for its square

and cube. The Adjusted 2 for the model is 72.20%.

4. Model 4 - The equation 4 in Result (Page Number - 11) is depicting a Linear-

Log model of literacy with population exposed to primary schools. The

coefficient is statistically significant at 5% significance level for the natural log

of population exposed to primary schools. The Adjusted 2

for the model is

66.5%.

5. Model 5 - The equation 5 in Result (Page Number - 11) is depicting a Linear-

Log model of literacy with population exposed to primary schools, to its square

and cube. The coefficient is statistically significant at 5% significance level for

the natural log of population exposed to primary schools and to its cube but not

for its square. The Adjusted 2 for the model is 71.30%.


relationship of literacy with population exposed to primary schools, High

percentage of Muslim population and their interaction term. The coefficients are

statistically significant at 5% significance level for population exposed to

primary schools but not for others. The Adjusted 2 for the model is 74.5%.


relationship of literacy with population exposed to primary schools, High

percentage of Household size and their interaction term. The coefficients are

statistically significant at 5% significance level for population exposed to

primary schools and for high percentage of household size but not for their

interaction. The Adjusted 2 for the model is 72.7%.


Observation

1. There is a significant relationship between Literacy and population exposed to

primary schools.

2. There is no association between Literacy and population exposed to bus service.

3. Percentage of Hindu population is associated with literacy.

4. Relationship between Literacy and population exposed to primary schools is

linear in nature.

5. High percentage of Muslim population is negatively related with the Literacy

but it is not statistically significant.

6. High percentage of Household Size is negatively related with the Literacy but

there is no interaction between household size and population exposed to

primary schools.

Conclusion

1. From the above analysis we can conclude that more the population is exposed

to primary schools more will be the literacy in Uttar-Pradesh.

2. 1% increase in population exposed to primary school will lead to an increase of

[.01 * 998974.215 = 9989.74215] ~ 10000 literates in Uttar Pradesh

3. Decreasing the Household Size (number of people per household) will increase

the literacy in Uttar Pradesh

Result

Regressor 1 2 3 4 5 6 7

Unstandarised Intercept Coeffecients 96260.478 -599561.359 -207629.731 -13046171.64 70834486.19 73238.91 -80423.001

Population Exposed To Primary Schools 0.849 0.659 1.85 0.931 0.946(Sig.) 0.001 0.001 0.105 0.001 0.001

Sqaure Population Exposed To Primary Schools -1.105(Sig.) 0.273

Cube of Population Exposed To Primary Schools 1.706(Sig.) 0.206

Natural Log Of Population Exposde To Primary Schools 0.813 -0.6402(Sig.) 0.001 0.001

Square Of Natural Log Of Population Exposde To Primary Schools **(Sig.)

7.219Cube of Natural Log Of Population Exposde To Primary Schools 0.001

(Sig.)

Population Exposed To Bus Service 0.073(Sig.) 0.701

Percentage of Hindu Population 0.151(Sig.) 0.033

High Percentage Of Muslim Population -0.063(Sig.) 0.694

High Percentage Of Muslim Population * Population Exposed To Primary Schools -0.147(Sig.) 0.411

High Percentage Of HouseholdSize 0.32(Sig.) 0.05

High Percentage Of HouseholdSize* Population Exposed To Primary Schools -0.272(Sig.) 0.118

R Sqaure 0.721 0.741 0.734 0.661 0.721 0.757 0.739 Adjusted R Square 0.717 0.729 0.722 0.665 0.713 0.745 0.727

Regression Model of Literacy in Uttar PradeshDependent Variable : Literacy; 68 Observations, Significance Level = 10% , RED = Insignificant

(Sig.) p-Value


Annexures

Curve Estimation

Model Summary and Parameter Estimates

Dependent Variable:Literacy

Equation

Model Summary Parameter Estimates

R Square F df1 df2 Sig. Constant b1 b2 b3

Linear .721 170.983 1 66 .000 96260.478 .638

Logarithmic .661 128.472 1 66 .000 -

13046171.63

6

998974.215

Quadratic .727 86.753 2 65 .000 323034.544 .354 7.442E-8

Cubic .734 58.944 3 64 .000 -207629.731 1.390 -5.096E-7 9.829E-14

The independent variable is Population Exposed to Primary Schools.


Means

Descriptive Statistics

N Minimum Maximum Mean Std. Deviation

Percentage Muslim Population 68 2.95 49.14 18.0329 10.63096

Percentage Hindu Population 68 47.05 96.21 81.3617 11.00021

HouseholdSize 68 5.66 8.36 6.4465 .46777

Valid N (listwise) 68

Regression Results Linear Regressions

1. Linear Relation b/w Literacy and Primary School Exposure to the Population

Literacy = 0 + 1PopulationExposedToPrimarySchool

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .849a .721 .717 305639.51070

a. Predictors: (Constant), Population Exposed to Primary Schools

Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients

t Sig.

95.0% Confidence Interval

for B

B Std. Error Beta

Lower

Bound

Upper

Bound

1 (Constant) 96260.478 92742.929 1.038 .303 -88906.754 281427.710

Population Exposed to

Primary Schools

.638 .049 .849 13.076 .000 .541 .735

a. Dependent Variable: Literacy

2. Multiple Regressions with linear Regressor

Literacy = 0 + 1PopulationExposedToPrimarySchool + 2 PopulationExposedToBusService + 3PercentageHinduPopulation

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .861a .741 .729 299389.95576

a. Predictors: (Constant), Population Exposed to Primary Schools,

Percentage Hindu Population, Population Exposed to Bus Service

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) -599561.359 332102.285 -1.805 .076

Population Exposed to Bus

Service

.073 .190 .030 .386 .701

Percentage Hindu

Population

7875.853 3622.053 .151 2.174 .033


Primary Schools

.659 .057 .877 11.526 .000


Non-Linear Regression

1. PolynomialRegression Model

Literacy = 0 + 1PopulationExposedToPrimarySchool + 2 PopulationExposedToPrimarySchool

2 + 3 PopulationExposedToPrimarySchool

3

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .857a .734 .722 303187.19985

a. Predictors: (Constant), Cube of population exposed to primary

school, Population Exposed to Primary Schools, Square of Population


Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients

t Sig.

95.0% Confidence Interval for

B

B Std. Error Beta Lower Bound Upper Bound

1 (Constant) -207629.731 465363.453 -.446 .657 -1137300.100 722040.638


Primary Schools

1.390 .846 1.850 1.643 .105 -.300 3.079

Square of Population

exposed to primary

schools

-5.096E-7 .000 -2.647 -1.105 .273 .000 .000

Cube of population

exposed to primary

school

9.829E-14 .000 1.706 1.278 .206 .000 .000


2. Linear-Log Model

Literacy = 0 + 1ln(Population Exposed To Primary School)

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .813a .661 .655 337395.93911

a. Predictors: (Constant), Normal Log of Population Exposed to Primary

School

Coefficientsa

Model


Standardized

Coefficients

t Sig.

95.0% Confidence Interval for B


1 (Constant) -13046171.636 1258245.056 -10.369 .000 -15558338.945 -10534004.327

Normal Log of

Population Exposed

to Primary School

998974.215 88135.391 .813 11.335 .000 823006.230 1174942.201

3. Linear Log Model with powers

Literacy = 0 + 1ln(PopulationExposedToPrimarySchool)+ 2[ln(PopulationExposedToPrimarySchool)]

2+ 3[ln(PopulationExposedToPrimarySchool)]3

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .849a .721 .713 308180.18029

a. Predictors: (Constant), Cube of Normal Log of Population Exposed to

Primary School, Normal Log of Population Exposed to Primary School

Coefficientsa

Model


Standardized

Coefficients

t Sig.

95.0% Confidence Interval

for B


1 (Constant) 70834486.18

5

22362519.46

9

3.168 .002 26173450.82

6

1.155E8

Normal Log of


Primary School

-

7868268.095

2362248.104 -6.402 -3.331 .001 -

12586003.33

3

-

3150532.856

Cube of Normal Log of


Primary School

14632.725 3895.918 7.219 3.756 .000 6852.039 22413.410


Interaction between Independent Variables

1. Continuous and Binary Variable

Literacy = 0 + 1PopulationExposedToPrimarySchool + 2HighPercentageOfMuslimPopulation+ 3(HighPercentageOfMuslimPopulation * PopulationExposedToPrimarySchool )

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .870a .757 .745 290132.86319

a. Predictors: (Constant),

InteractionBetweenMuslimPopulationAndPopulationExposureToSchool,

Population Exposed to Primary Schools, Binary Variable of High

Muslim Population

Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients

t Sig.


B


1 (Constant) 73238.912 110327.732 .664 .509 -147166.071 293643.894


Primary Schools

.700 .062 .931 11.247 .000 .575 .824

Binary Variable of High

Muslim Population

-74442.482 188655.158 -.063 -.395 .694 -451324.484 302439.521

InteractionBetweenMusli

mPopulationAndPopulati

onExposureToSchool

-.079 .096 -.147 -.828 .411 -.271 .112


1. Continuous and Binary Variable

Literacy = 0 + 1PopulationExposedToPrimarySchool + 2 HighPercentageOfHouseholdSize+ 3 (HighPercentageOfHouseholdSize* PopulationExposedToPrimarySchool )

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .860a .739 .727 300233.86148

a. Predictors: (Constant), Interaction Between HighHousehold Size and

Exposure to Primary Schools, Population Exposed to Primary Schools,

Binary Variable of High Household size

Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients

t Sig.


B


1 (Constant) -80423.001 126561.439 -.635 .527 -333258.541 172412.539


Primary Schools

.711 .066 .946 10.705 .000 .578 .844

Binary Variable of High

Household size

365077.504 182345.455 .320 2.002 .050 800.582 729354.427

Interaction Between

HighHousehold Size and

Exposure to Primary

Schools

-.152 .096 -.272 -1.586 .118 -.344 .039


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