Rate

ContentsIntroduction:..........................................................................................................................................1

Statement of Task:.................................................................................................................................2

Plan of Investigation..............................................................................................................................2

Least Squares Regression:.................................................................................................................3

Time Series Trend Analysis:...............................................................................................................5

Limitation:.............................................................................................................................................6

Conclusion:............................................................................................................................................6

References:............................................................................................................................................7

1 | P a g e

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 post-independence 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 conditions suitable 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. 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.

II. 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.

III. 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.

2 | P a g e

Plan of InvestigationMathematical 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 Literacy Rate GDP1951 18.33 3.61961 28.3 2.81971 34.45 31981 43.57 5.11991 52.21 5.42001 64.84 5.22011 74.04 8.5

Table 1: Data Source GDP Data : Institute of Applied Manpower Research (*GDP growth rate is calculated at 1993-

94 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

10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

8

9

Literacy Rate

GDP

Grow

th R

ate

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 derived from the following formulae.

3 | P a g e

Year

Literacy GDP

y2 x2 xyx y

1951 18.33 3.6 12.96335.988

9 65.988

1961 28.3 2.8 7.84 800.89 79.24

1971 34.45 3 91186.80

3 103.35

1981 43.57 5.1 26.011898.34

5 222.207

1991 52.21 5.4 29.162725.88

4 281.934

2001 64.84 5.2 27.044204.22

6 337.168

2011 74.04 8.5 72.255481.92

2 629.34

SUM 315.74 33.6 184.2616634.0

61719.22

7

y= 0.959929 + 0.085135x is 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

4 | P a g e

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

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

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 GROWTH RATE FOR INDIA POST INDEPENDANCE

Year GDP1951 3.61961 2.81971 31981 5.11991 5.42001 5.22011 8.5

Table 2: Data Source GDP Data : Institute of Applied Manpower Research (*GDP growth rate is calculated at 1993-

94 price levels)

GRAPH 2: GDP VS. YEAR ON A SCATTER PLOT.

5 | P a g e

1940 1950 1960 1970 1980 1990 2000 2010 20200

1

2

3

4

5

6

7

8

9

Year

GDP

Grow

th R

ate

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.

Year GDPx2 xyy x

1951 3.6 3806401 7023.61961 2.8 3845521 5490.81971 3 3884841 59131981 5.1 3924361 10103.11991 5.4 3964081 10751.42001 5.2 4004001 10405.22011 8.5 4044121 17093.5

13867 33.62747332

7 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

6 | P a g e

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 conducted at intervals of 10 years. So it can be assumed that each data point is 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.

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

7 | P a g e