This document analyzes the relationship between literacy rate and GDP growth rate in India post-independence. It uses least squares regression and time series trend analysis on data from 1951 to 2011 to develop models. The regression model estimates that India will achieve 100% literacy at a GDP growth rate of 9.48%. Extrapolating from the time series trend line estimates that India will reach this GDP growth rate, and thus universal literacy, in the year 2026. However, the analysis is limited by the small sample size of only 7 data points taken from census data every 10 years.

1. Literacy vs. GDP Rate
Argha Ray (15)
Chakradhar Kundu (22)
Abhijeet Tomar (03)
QTM Assignment

2. Contents
Introduction: ........................................................................................................................................... 2
Statement of Task: .................................................................................................................................. 2
Plan of Investigation ............................................................................................................................... 3
Least Squares Regression:................................................................................................................... 3
Time Series Trend Analysis: ................................................................................................................ 5
Limitation: ............................................................................................................................................... 6
Conclusion: .............................................................................................................................................. 7
References: ............................................................................................................................................. 7
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3. Introduction:
Illiteracy is one of the major problems faced by the developing world, specially Africa and South-East
Asia and has been identified as the major cause of socio-economic and ethnic conflicts that
frequently surface in the region. Literacy in India is the key to socio-economic progress.
Literacy, as defined in Census operations, is the ability to read and write with understanding in any
language. A person who can merely read but cannot write is not classified as literate. Any formal
education or minimum educational standard is not necessary to be considered literate.
Indian literacy rate grew to 74.04% in 2011 from 12% at the end of British rule in 1947. Although this
was a greater than six fold improvement, the level is well below the world average literacy rate of
84%, and of all nations. India currently has the largest illiterate population. Despite government
programmes, India's literacy rate increased marginally and a 1990 study estimated that it would take
until 2060 for India to achieve universal literacy at then-current rate of progress.The 2011 census,
however, indicated a 2001–2011 decadal literacy growth of 9.2%, which is the slower than the
growth seen during the previous decade.
Post liberalization India was able to shrug of the ignominy of Hindu Rate of growth and signaled itself
on the world stage as the balance of economic power shifted to Asia. It clocked phenomenal growth
and lifted millions out of poverty and gave voice and identity to its subaltern. Literacy, an important
indicator of the human and economic development also rose as educational infrastructure was being
created and endowment programmes like National literacy Mission, Sarva Siksha Abhiyaan, Mid-Day
Meal,Ladli Scheme and Anganwadi Project were launched. These were all linked to an expanding
economy and its rapid growth measured in GDP.
The Gross Domestic Product (GDP) is the total value of all goods and services produced in a country,
in one year. GDP per capita is an important indicator of the standard of living in a nation.
This study tries to identify the relationship between GDP Growth rate and Literacy rate in the postindependence era and how it affected the socio economic and cultural fabric of the country.
Apparently, these seem interconnected as a growing economy is fueled through technological
advances and a productive workforce which are both functions of educational accomplishments of a
country’s populace. On the other hand a robust economy allows creating social and economic
conditionssuitable for increasing the general standards of living of which Literacy is only one aspect.
Our study tries to statistically establish that relationship.
Statement of Task:
The main purpose of this investigation is explored in this section.
I.
II.
III.
To establish correlation between GDP Growth Rate and literacy rate of India:A statistical
regression model has been developed to establish the correlation between GDP Growth
Rate and Literacy Rate. The statistical fit of the model has been calculated to establish a
moderately positive correlation.
To estimate the GDP for which Indian can achieve 100% literacy rate: The statistical model
developed above has been extrapolated to arrive at the GDP Growth rate figure when India
will achieve 100% Literacy.
Forecast the year in which India will achieve the GDP when the literacy rate is 100%:A
Time Series forecasting model has been developed to arrive at the Trend Line to project into
the year when India will have the estimated GDP which corresponds to 100% Literacy Rate.
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4. Plan of Investigation
Mathematical processes used to analyse the data are Least Square Regression and Time Series Trend
Analysis. The Regression model is tested for statistical significance using the Coefficient of
Determination.
TABLE 1: GDP AND LITERACY RATE FOR INDIA POST-INDEPENDENCE
Year
1951
1961
1971
1981
1991
2001
2011
Literacy Rate
18.33
28.3
34.45
43.57
52.21
64.84
74.04
GDP
3.6
2.8
3
5.1
5.4
5.2
8.5
Table 1: Data Source
GDP Data: Institute of Applied Manpower Research (*GDP growth rate is calculated at 199394 price levels)
Literacy rate: Economic Survey, 2011-12; Office of the Registrar General : 2011, India;
M/Home Affairs
GRAPH 1: GDP VS. LITERACY RATE ON A SCATTER PLOT
9
8
GDP Growth Rate
7
6
5
4
3
2
1
0
0
10
20
30
40
50
60
70
80
Literacy Rate
Graph 1 shows the GDP vs. Literacy rate on a scatter plot. It can be assumed to have a moderate
positive correlation.
Least Squares Regression:
Least Square Regression calculation identifies the relationship between the independent variable x,
and the dependent variable y. The least square regression is derivedfrom the following formulae.
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5. Literacy
Year
GDP
x
y
y2
1951
18.33
3.6
1961
28.3
2.8
1971
34.45
1981
x2
12.96 335.9889
65.988
800.89
79.24
3
9 1186.803
103.35
43.57
5.1
26.01 1898.345
222.207
1991
52.21
5.4
29.16 2725.884
281.934
2001
64.84
5.2
27.04 4204.226
337.168
2011
74.04
8.5
72.25 5481.922
629.34
315.74
33.6
SUM
7.84
xy
184.26 16634.06 1719.227
SSXY= Σ xy - (Σx) (Σy)/ n = 1719.277 - 315.74*33.6 / 7 = 203.675
SSXX = Σ x2 - (Σx)2 / n = 16634.06 - 315.142 / 7 = 2392.379
b1 = SSXY / SSXX = 203.675 / 2392.379 = 0.085135
b0= Σy/n - b1Σx / n = 33.6 / 7 - .085135 x 315.74 / 7 = 0.959929
y= 0.959929 + 0.085135xis the least squares regression model that defines the correlation
between the dependant variable (GDP Growth Rate) and the independent variable (Literacy Rate).
Using this model we can extrapolate the GDP value for which India will achieve universal literacy
rate.
The regressing model is now tested using the Coefficient of Determination to explain the variability
of the independent variable that is accounted for or explained by the variability of the dependant
variable. The r-square test is given below.
r2 = b12* SSXX/ SSYY
r2 = 0.754563
The r-square test suggests that there is a moderately good fit between the GDP Growth Rate and the
Literacy rate. We can thus project the estimated GDP value for which India can achieve universal
literacy. If we assign 100 for independent variable x which corresponds to 100% Literacy rate we get
the value of the dependant variable y which corresponds to the estimated GDP Growth Rate.
y= 0.959929 + 0.085135*100
y=9.48
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6. Thus the Regression model suggests that India will achieve 100% Literacy rate for a GDP Growth rate
of 9.48.
Time Series Trend Analysis:
From the above Regression model and its derivations we can now apply a Time Series analysis on the
GDP Growth rate data points to plot a Trend Line which will enable us to estimate the exact year
when the GDP Growth Rate will be 9.48 which in turn correspond to the year when India will achieve
universal Literacy Rate.
TABLE 2: GDP GROWTHRATE FOR INDIAPOSTINDEPENDANCE
Year
1951
1961
1971
1981
1991
2001
2011
GDP
3.6
2.8
3
5.1
5.4
5.2
8.5
Table 2: Data Source
GDP Data: Institute of Applied Manpower Research (*GDP growth rate is calculated at 199394 price levels)
GRAPH 2: GDP VS. YEAR ON A SCATTER PLOT.
9
8
GDP Growth Rate
7
6
5
4
3
2
1
0
1940
1950
1960
1970
1980
1990
2000
2010
2020
Year
The Trend Line equation can be derived using the following formulae.This Time Series model allows
us to project the year when GDP will be 9.48.
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7. Year
y
1951
1961
GDP
x
3.6
2.8
x2
3806401
3845521
xy
7023.6
5490.8
1971
1981
1991
2001
2011
3
5.1
5.4
5.2
8.5
3884841
3924361
3964081
4004001
4044121
5913
10103.1
10751.4
10405.2
17093.5
13867
33.6
27473327
66780.6
b1= (Σ xy - (Σx) (Σy)/ n /) / (Σ x2 - (Σx)2/n)= (66780.6 – 33.6 x 13867 / 7) / (184.26 – 33.62
/7)= 9.53002
b0= Σy/n - b1Σx / n = 13867/7 – 9.53002 x 33.6/7 = 1935.25
y= 1935.25 + 9.53002x is the trend line that we derive from the above analysis.
Using this model we can extrapolate the year when India will achieve GDP growth rate of 9.48. If we
assign 9.8 for the independent variable, GDP Growth rate, we can project the dependant variable
Year to estimate as to when India will achieve universal Literacy.
y= 1935.25 + 9.53002*9.48
y= 2026
Thus year 2026 is tentatively the year when India will achieve universal literacy rate.
Limitation:
The study is based on data points derived from the Census data published by the Government of
India agencies. Since Census is conducted every ten years the data used in the investigation is only
from 1951 to 2011 and is limited. Since data sources other than the Government approved ones are
often unreliable we have restricted our study to the small number of data points available to us. This
tends to introduce bias in the statistical analysis and may result in over or under estimation.
However, since we have been able to establish a working model for the correlation of GDP Growth
Rate and Literacy we can assume to make robust analysis with more precision had the data points
been more than the sample size of 7.
Another limitation of the data is that Census is conductedat intervals of 10 years. So it can be
assumed that each data pointis a Central Tendency of all data during that period.So each data point
for GDP Growth Rate or Literacy Rate is a representative figure for a 10 year period recorded during
any particular Census.
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8. Conclusion:
Literacy matters immensely when it comes to the health of an economy. We infer from the study
that there is a positive correlation between Literacy Rate and the GDP per capita. If we project GDP
Growth Rate and Literacy Rate figures from post-independence era we conclude via our Regression
Model that literacy will be 100% at GDP growth rate of 9.48. This GDP Rate will be achieved in the
year 2026 which enables us to infer that India will achieve universal Literacy rate in that year. Since
our analysis is based on Census data collected over 10 years it discounts the fact that India has
shortly grown over 9% GDP Growth rate during 2008-2009. But since this was only a spike and not
sustained over a period it does not substantially affect our Regression model. Also since the model is
a representative of 10 year intervals we infer that sustained GDP growth over 9.5 for a decade can
lead India to achieve universal Literacy rate in the near term.
References:
‘Literacy in the Context of the Constitution of India’ by Shri K. Ramamoorthy, IAS (Retd.)
http://lawmin.nic.in/ncrwc/finalreport/v2b1-5.htm
Wikipedia
http://en.wikipedia.org/wiki/Literacy_in_India
Indiastat.com
http://www.indiastat.com/default.aspx
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