This document presents an econometric analysis of the population growth of India from 2005 to 2014. A linear regression model is used to test the relationship between population and life expectancy. The results show a positive correlation, with a high R-squared value of 0.938 indicating life expectancy explains 93% of the variation in population. Specifically, for every one year increase in life expectancy, the population increases by approximately 41,922 people on average. Therefore, the analysis finds support for the hypothesis that countries with higher life expectancies will have higher populations.
1. ~ 1 ~
SYMBIOSIS SCHOOL OF ECONOMICS
AN ECONOMETRIC ANALYSIS OF
POPULATION GROWTH OF INDIA (2005-2014)
Submitted to: Prof- Ishita Ghoshal
Name-TANVI AHUJA
PRN-16060242063
2. ~ 2 ~
ECONOMIC RATIONALE
The countries with a high average life expectancy will have a high
population.
We will test the reliability of this statement by examining the relationship
between the two fields and trying to establish a positive correlation through
a series of data presentation.
Life expectancy which is defined as the period that a person may expect to
live has been increased from less than 45 years in 1950 to more than 65
years today. These improvements are part of health awareness and
improved medical facilities around the globe.
And due to this increase in life expectancy it has lead to increase in
population of India which today proves to be one of the major hurdles for
any policy implementation and country’s economic development.
3. ~ 3 ~
LINEAR REGRESSION MODEL
Yi = β0hate + β1hat life expectancy + ei
Where,
Yi POPULATION
β0hat constant
β1hat Coefficient of LIFE EXPECTANCY
Ei Error
DATA SET STUDY
Years Population Life expectancy `
2005 11,44,326.29 65
2006 11,62,088.30 65
2007 11,79,685.63 65
2008 11,97,070.11 66
2009 12,14,182.18 66
2010 12,30,984.50 67
2011 12,47,446.01 67
2012 12,63,589.64 67
2013 12,79,498.87 68
2014 12,95,291.54 68
4. ~ 4 ~
ON RUNNING LRM ON EXCEL WE GET THE
FOLLOWING RESULTS
Regression Statistics
Multiple R 0.96861
R Square 0.938206
Adjusted R
Square 0.930481
Standard
Error 13394.79
Observati
ons 10
ANOVA
Df SS MS F
Significan
ce F
Regression 1
2.18E+1
0
2.18E+
10
121.46
14 4.09E-06
Residual 8
1.44E+0
9
1.79E+
08
Total 9
2.32E+1
0
Coefficie
nts
Standar
d Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -1562219
252612.
2
-
6.1842
6
0.0002
64 -2144744
-
979694
-
214474
4
-
979694
X Variable
1 41922.22
3803.86
5
11.020
95
4.09E-
06 33150.49
50693.
95
33150.
49
50693.
95
THE ESTIMATED MODEL
Yi = -1562219 + 41922.2X
5. ~ 5 ~
INTERPRETATION
As the regression results show,there is a positive relationship between
population and life expectancy i.e. β1hat is significant .Therefore,if
the life expectancy increases by 1 unit ,on average,population goes up
by 41922.2 units.
From the regression results we see that the intercept value is -
1562219.If the life expectancy is zero, the regression equation
predicts that population is -1562219. Clearly this constant seems
meaningless and you should not even try to give it meaning
The value of R^2 is 0.938206 which means it has positive correlation
which signifies more life expectancy=increase in population of a
country i.e. 93% of variation in independent variable signifies the
model.
Also for the Test of Good Fit (F Test) since, Calculated F > Critical
F, H0 is rejected at 5% level of significance and hence it is significant.
As we can see that value of T stat 11.02095 for β1hat doesn’t lies in
confidence interval which specifies that β1hat is statistically
significant. The greater the value of T the greater the evidence against
the null hypothesis.
A larger p value (>0.05) for predictor’s variable indicates that changes
in the X variable are not associated with changes in the dependent
variable.
