Statistical Analysis: Life Expectancy and Literacy Rates Study

This assignment analyzes the relationship between life expectancy and literacy rates across different countries using data gathered from Wolfram Alpha. It identifies countries with the highest and lowest life expectancies, and then uses linear regression to model the relationship between life expectancy and literacy rates. The analysis includes creating scatter plots, determining the equation of the line, and interpreting the slope to understand the correlation. The assignment also involves predicting the literacy rate of Nigeria based on its life expectancy, comparing the predicted value with the actual rate, and discussing potential reasons for discrepancies. Furthermore, it investigates the relationship between a country's population and GDP using a similar analytical approach, including calculating the inverse of the slope and interpreting its significance. The study uses references for linear regression analysis.

1. In what year{s}was the data gathered? 2000, 2002, 2005, 2009, 2010, 2012, 2013 and 2016
2. Which county had the highest life expectancy? San Marino, How many years 85.4 years.
3. Which county had the lowest life expectancy? Sierra Leone, How many years? 51.8 years
4. The United States has a life expectancy of 78.1 years
5. Japan life expectancy? is 84 years
6. Switzerland life expectancy is 82.9 years
7.
Country
Life Expectancy (x-
axis)
Literacy rate (y-
axis)
USA 78.1 99
Swaziland 57.7 87.5
Macau 84.8 96.54
Switzerland 82.9 99
Japan 84 99
8. With the data above, we can draw a scatter diagram using software like Excel, SPSS, R or Python. I used
Excel to draw below Scatterplot. To Sketch Scatter diagram, select both x and y variables, go to insert then
select Scatter plot under Recommended Charts. You will obtain the below chart. To obtain the line of plot,
go to design. Select Add Chart Element, select Trendline, then select linear then click ok. Format your plot
by clicking on the equation part. You will obtain the equation of the line.
55 60 65 70 75 80 85 90
80
82
84
86
88
90
92
94
96
98
100
f(x) = 0.405612067298395 x + 64.7730647843744
Linear Life Expectancy vs Literacy Rate
Life Expectancy
Literacy rate
9. From the plot, the equation of the line is y = 64.773 + 0.4056x where 64.773 is the intercept while 0.4056 is
the slope of the plot.
10. From the equation of the plot, we have a positive slope i.e. 0.4056. This implies that the independent
variable (Life Rate) has a positive effect on the dependent variable (Life Expectancy). This means that Life
Expectancy is directly proportional to the Literacy rate. In other words, when the is a higher life expectancy
in a country, then the literacy rate of that country also increases.
11. We are asked to determine whether the scatter plot from Wolfram Alpha (life expectancy vs. literacy)
indicates that people who live in countries with a higher literacy rate also have a higher life expectancy.
Below is the diagram from Wolfram Alpha.

We can see that there is a positive slope between Life Expectancy and Literacy rate, therefore, we can deduce that
people who live in countries with the higher rate of literacy also have a higher life expectancy rate.
12. We will select Nigeria as the country to conduct the study below.
a) Nigeria
b) Life Expectancy of Nigeria is 53.4 years.
c) We will use our previous equation y = 64.773 + 0.4056x, where y is the Literacy rate and x is the Life
expectancy rate, to predict the Literacy rate of Nigeria
Literacy rate = 64. 773 + 0.4056* 53.4
= 86.43204
From our solution, the literacy rate in Nigeria is 86.4%.
d) The actual literacy rate from Wolfram Alpha is 51.08%. There's a big gap between the Literacy rate of
Nigeria and Actual rate from Wolfram Alpha. The reason why there is a big error is that we selected a
smaller number to conduct the experiment.
13. The aim of the equation is to select two characters of the above-mentioned countries and check if there is a
linear relationship between those two characteristics. We will choose the population and GDP and check if
there's a relationship between them. Below the extract of the information.
County Population in Millions
GDP(trillion $ per
year)

USA 324 19.39
Swaziland 1.37 4.872
Macau 0.4628 0.05036
Switzerland 8.48 0.6708
Japan 127 4.383
We will now try to investigate whether they are a linear relationship between the population of a country
and the GDP of the similar country. We will draw a linear scatter plot to investigate this hypothesis. Below
is the scatter diagram of the above information.
0 50 100 150 200 250 300 350
0
5
10
15
20
25
f(x) = 0.0526856135319295 x + 1.01232242037354
Population vs GDP)
Population
GDP
From the plot, we can see that we have a positive slope. This means that there is a linear relationship
between the population of a county and its GDP.
The next objective is to obtain the inverse of the slope, define it and give its insights.
Our equation is y = 1.10123 + 0.0527x
The inverse of this equation is y1 = 0.987849 – 18.975x
The inverse function implies that when there is a higher GDP in a country, then the population of them is
lower.

Reference
Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to linear regression analysis (Vol. 821). John
Wiley & Sons.
Bates, D., Mächler, M., Bolker, B., & Walker, S. (2014). Fitting linear mixed-effects models using lme4. arXiv preprint
arXiv:1406.5823.