Correlation between HIV mortality and GDP

Research question Is there a correlation between HIV mortality and GDP per capita?

Introduction HIV/AIDS was discovered in the United States in 1981, and since then, the condition has become one of the major global epidemics. It is estimated that in 2020 alone, at least 1 million people died from HIV-related complications, and 18% were young adults below 20. In 2020, it was estimated that 38 million people were living with HIV/AIDS (UNICEF). I first learned about HIV/AIDS when I was 14 years old, and since that time, I have been very interested to know more about this disease. While I was looking at 2020 HIV deaths, I realized that in the top 10 nations with the highest HIV deaths, 8 of them are African nations. It si through this grasp, that I decided to use my mathematical prowess to investigate if there is a relatiomship between HIV deaths and GDP per capita in 29 nations with the highest HIV mortality.

Mathematical exploration Correlation is an essential tool used in mathematics and statistics to indicate and describe the level of association/relationship between two variables. Correlation is based on strength (strong or weak) and direction (negative or positive). A correlation is described as a strong correlation when the correlation value is >0.5; on the other, a relationship is described as a weak correlation when R-value is less than 0.5 (0.5) (Schober et al., 1768). In terms of direction, a correlation can be described as a negative correlation (-) when one variable increases while the other is decreasing. On the other hand, as both variables move in a single direction (both are increasing or decreasing), the correlation is described as a positive (+) correlation.

In this exploration, I will use both the Pearson correlation method and scatter plot method to calculate the correlation between HIV mortality and GDP per capita in 29 countries and territories.

Pearson correlation The Pearson correlation method is also called Pearson product-moment (PPM). The formula to calculate the Pearson correlation is; Where; = Pearson product-moment (PPM) (R-value) = dependent-variable in the dataset = mean of x variable r=∑(x−x)(y −ȳ) ∑(x−x)2)(y−y2) r x x = independent-variable in the dataset = Average of y variable To calculate the average/mean, the following formula is used; Where; = sum of all the terms in the dataset = number of terms in the data set

Scatter plot A Scatter plot is a graphical representation of data used to show the trend and type of the association between variables. The dependent variables appear on the (x-axis), and the independent variable appears on the (y-axis). The figure below indicates various types of scatter plots;

The line of best fit in the 1st image indicates an upward trajectory and thus meaning that there is a positive association between the two variables. The gradient of the graph will be y ȳ Mean =xi n xi n positive, further confirming that there is a positive correlation. The trend line in the 2nd graph indicates a decline movement and thus confirming a negative correlation between the two variables. The gradient in this graph will have a negative gradient, indicating that there is negative relationship between the two variables. The 3rd graph shows no trend line. This means there is no correlation or the correlation coefficient between two variables is (0).

Aim This exploration aims to use mathematical tools (Pearson correlation and scatter plot) to find if there is a relationship between gross domestic product (GDP per capita) and HIV mortality/ deaths. In this exploration, I will provide GDP and HIV mortality data for 2020.

Hypothesis In this exploration, I hypothesize that there is no correlation between gross domestic product GDP per capita and HIV mortality. The correlation coefficient (R-value) will be close to (0), indicating no correlation. The trend line in the scatter plot will indicate no direction, confirming no correlation between the two variables.

Data The data for HIV deaths/mortality was obtained from: https://www.indexmundi.com/g/ r.aspx?t=100&v=37&l=en

The data for GDP per capita for 29 countries was obtained from: https://ourworldindata.org/grapher/gdp-per-capita-worldbank?tab=table&time=latest

Country

HIV deaths (000)

GDP

South Africa 12,666

India 6,166

Mozambique 1,230

Nigeria 4,917

Indonesia 11,445

Tanzania 2,625

Kenya 4,340

Uganda 2,175

Zimbabwe 3,353

Zambia 3,278

DRC 1,082

Ghana 5,446

Cameroon 3,666

Brazil 14,064

Thailand 17,285

Malawi 1,509

Angola 6,110

Ethiopia 2,297

South Sudan 9.1 3,114

Myanmar 7.7 4,875

Pakistan 6.8 4,563

Ukraine 5.9 12,376

Mali 5.8 2,226

Botswana 5.0 14,655

Vietnam 5.0 8,200

Lesotho 4.8 2,317

Congo 4.5 3,434

Colombia 4.1 13,449

Mexico 4.0 17,852

Pearson correlation To compute the Pearson correlation of the two variables (HIV mortality and GDP per capita), I used the following method; r= Where; R= Pearson correlation coefficient = HIV mortality = avergae of HIV mortality = GDP per capita = mean value of GDP per capita

The first method is to compute the average for HIV deaths (yi) and GDP per capita (yi), as shown below;

HIV deaths (000) (x)

GDP per capita (y) 12,666 6,166 1,230 4,917 11,445 2,625 4,340 2,175 3,353 3,278 1,082 5,446 3,666 14,064 17,285 1,509 6,110 2,297 9.1 3,114 7.7 4,875 6.8 4,563 5.9 12,376 5.8 2,226 14,655 8,200 4.8 2,317 4.5 3,434 I used the above formula to construct the Pearson correlation table 3 below;

HIV deaths (000) (x)

GDP per capita (y)

Dx =(xi-x) Dy=(yi-y) dx*dy dx*dx dy*dy 12,666 52.94138 6,089.621 322392.9 2802.79 37083483.9 6,166 49.94138 -410.379 -20494.9 2494.141 168410.924 1,230 31.94138 -5,346.379 -170771 1020.252 28583768.4 4,917 25.94138 -1,659.379 -43046.6 672.9552 2753538.67 11,445 18.94138 4,868.621 92218.4 358.7759 23703470.4 2,625 7.94138 -3,951.379 -31379.4 63.06552 15613396 4,340 1.94138 -2,236.379 -4341.66 3.768956 5001391.03 r= 2,175 1.94138 -4,401.379 -8544.75 3.768956 19372137.1 3,353 0.94138 -3,223.379 -3034.42 0.886196 10390172.2 3,278 -2.05862 -3,298.379 6790.109 4.237916 10879304 1,082 -4.05862 -5,494.379 22299.6 16.4724 30188200.6 5,446 -5.05862 -1,130.379 5718.158 25.58964 1277756.68 3,666 -5.05862 -2,910.379 14722.5 25.58964 8470305.92 14,064 -5.05862 7,487.621 -37877 25.58964 56064468.2 17,285 -5.05862 10,708.621 -54170.8 25.58964 114674564 1,509 -6.05862 -5,067.379 30701.32 36.70688 25678329.9 6,110 -6.05862 -466.379 2825.613 36.70688 217509.372 2,297 -7.05862 -4,279.379 30206.51 49.82412 18313084.6 9.1 3,114 -9.95862 -3,462.379 34480.52 99.17411 11988068.3 7.7 4,875 -11.3586 -1,701.379 19325.32 129.0182 2894690.5 6.8 4,563 -12.2586 -2,013.379 24681.25 150.2738 4053695 5.9 12,376 -13.1586 5,799.621 -76315 173.1493 33635603.7 5.8 2,226 -13.2586 -4,350.379 57680.02 175.791 18925797.4 14,655 -14.0586 8,078.621 -113574 197.6448 65264117.3 8,200 -14.0586 1,623.621 -22825.9 197.6448 2636145.15 4.8 2,317 -14.2586 -4,259.379 60732.87 203.3082 18142309.5 4.5 3,434 -14.5586 -3,142.379 45748.7 211.9534 9874545.78 4.1 13,449 -14.9586 6,872.621 -102805 223.7603 47232919.4 17,852 -15.0586 11,275.621 -169795 226.762 127139629 19.05862 6576.379 -88451.8 9655.19 750220813 ∑((x −x))((y −ȳ) [∑(x−x)2)(y−y)2)] r= r= -0.0329 The correlation coefficient based on the above calculation is -0.00329. This indicates that there is no relationship between HIV deaths and GDP per capita. This indicates that the GDP of the given nation does not affect HIV mortality.

Scatter plot method

Table 1 above can be represented by a graph (satter plot) below

Based on the graph above, the trend line indicates a slight negative movement. This indicates a less negative correlation between HIV mortality and GDP per capita. The GDP of a given nation/territory does not affect the mortality of HIV. The correlation coefficient of the above graph can be computed as follows; −88451.8 (9655.19)(750220813) R2= 0.0011 R= 0.0011

GDP vs HIV mortality (000)

GDP 4 500 9 000 13 500 18 000

HIV mortality (000) y = -9,1611x + 6751 R² = 0,0011 The correlation coefficient from thr image above is -0.0329. This clarifies that there is no correction between HIV mortality and GDP and thus confirms my hypothesis, which stated that "there is no association between HIV deaths and GDP per capita."

Conclusion The primary aim of this exploration was to investigate if there is a relation between GDP per capita and HIV mortality in 29 countries. Before the investigation, it was hypothesized that "there is no association between HIV deaths and GDP per capita." While using the Pearson correlation method, the R-value was (-0.0329), indicating that there is no assocation between gross domestic product (GDP) and HIV deaths. When using the scatter plot, the R-value was (-0.0239), further indicating that there is assoctaion between the two variables. Based on this exploration, it can be concluded that the GDP of a given nation does not affect the mortality rate of the same nation.

Evaluation The exploration was a big success as the aim and hypothesis were achieved. However, the data used in this exploration might be misleading and thus affect the final answer. The 2020 data (GDP and HIV mortality) was used in this exploration. This data might not be accurate due to COVID 19, declared a global pandemic in 2020. This might have impacted the GDP and HIV data and thus affected the final answer. In future investigations, it is imperative to use data for at least five years to increase data accuracy. R=−0.03