MATH200 Project 1
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Purdue University *
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Mathematics
Date
Feb 20, 2024
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docx
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MATH 200 - Project 1 Sameer Rai Singhal
2/5/2023
The purpose of this project was to analyze the data provided about the 2019 fertility rate and life expectancy in all the countries around the world. Table of Contents
Descriptive Statistics
2
Regression
4
Conclusions
5
D
ESCRIPTIVE
S
TATISTICS
Figure 1: Histogram for 2019 fertility Figure 1 shows the histogram for 2019 fertility rate. Analyzing the graph it is seen that it is skewed to the right.
Summary statistics:
Column
Mean
Median
Mode
Std. dev.
Variance
2019 Fertility
2.636267
2.2
1.7
1.2439831
1.547494
Table 1: Descriptive statistics for 2019 fertility Analyzing the descriptive statistics for the 2019 fertility rate, it is seen that on average the fertility rate in all the countries in the study is 2.6. Looking at the mode it was inferred that the most frequent observation of fertility rate was 1.7. The standard deviation and variance show that
the data is spread around the mean. Figure
2: Histogram for 2019 Life Expectancy
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Figure 2 shows the histogram for 2019 life expectancy. Analyzing the graph it is seen that it is skewed to the left. Summary statistics:
Column
Mean
Median
Mode
Std. dev.
Variance
2019 Life Expectancy
73.808325
75.01
Multiple modes
7.1194883
50.687113
Table 2: Descriptive statistics for 2019 life expectancy Analyzing the descriptive statistics for the 2019 life expectancy, it is seen that on average the life
expectancy in all the countries in the study is 73.8. Looking at the mode it was inferred that there
was more than one country that had the most frequent observation of different life expectancies. Having a high standard deviation and variance shows that the data is spread around the mean. R
EGRESSION
Fig
ure 3: Scatter plot
Fertility rate was the predictor variable and life expectancy was the response variable. Linear correlation coefficient = -0.8146
Coefficient of determination = 0.6636
This means that 66.36% of the variability in life expectancy is explained by the least square regression line. Having a negative linear correlation coefficient reflects that there is a negative relationship between the fertility rate and life expectancy.
Fertility Rate of US: 1.7
Countries with the fertility rate like that of the United States: Australia, Bahamas, Brazil, China, Costa Rica, Czech Rep., Denmark, Estonia, Ireland, Montenegro, New Zealand, Sweden, Trinidad and Tobago, Least square regression line equation: y = -4.662x + 86.099
y = -4.662(1.7) + 86.099
y = 78.0836
Actual Life Expectancy of US = 79.11
Expected Life Expectancy of US = 78.0836
Comparing the actual and expected life expectancy of the US, we can see that the actual life expectancy is greater than the expected life expectancy.
C
ONCLUSIONS
Lurking variables:
Wealth of the nation can be a lurking variable as richer countries have better healthcare and cleaner environment. Urbanization is another lurking variable. Population of the nation impacts the life expectancy directly. The difference between causation and correlation is that causation means one event causes another event. However, correlation just means that two events are related to each other, but are not caused by the other event. In the case of fertility and life expectancy, there is no cause and effect relationship as there are many factors that impact life expectancy. Life expectancy does not depend on the fertility rate of the country. We can not use the regression model in order to predict the life expectancy of one particular person as there are many variables such as physical exercise, diet, routine, etc. that impact one’s life expectancy.
From the Hans Rosling Ted talk it was seen that in 1962, the graph of fertility vs life expectancy was very different from what was recorded in 2019. In 1962 there were many countries that had a much larger fertility rate and much lower life expectancy as compared to 2019. There can be many reasons for this, poor healthcare and less technological advancements are a few. In 1970 there was a great number of people living in poverty and most of them were from Asia. That was
also a big reason for having lower life expectancy. In 2000 there were many people who grew out of poverty that helped in improving the life expectancy.
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