The Hydra

The Hydra 2020. The world watches as the celebrated biologist Brian Matterosi goes on trial for his life before the International Criminal Court under draconian new powers granted by the Abuja Treaty. His crime? To engineer a virus which has swept the globe and sterilised entire populations. Is Matterosi a genius or a madman with a God complex? Only one thing is certain: he is a complicated man with a difficult past.

Nobody would acknowledge that more than Matterosi’s defence attorney, Art Blume, who is spearheading the campaign to save thescientist’s life. Prosecutor Leeton Kgabu has no such difficulty: to him Matterosi is a vicious murderer who deserves to die for his crimes against the human race. The world craves justice, and Leeton is determined it will get it. At all costs.

To Art Blume’s dismay, Brian Matterosi appears to be intent on helping Kgabu achieve his goal. What dark secrets are driving the scientist to seek his own annihilation? Is he truly the worst mass murderer of mankind or its saviour? As the trial progresses, Art discovers he is running out of time to find the truth.

virus
Graham at Amazon.co.uk

Graham at Amazon.com

As with birth rates, we use data for 4 categories of countries from 1990 to 2015 (100 observations total). We have two explanatory variables, AGE and Y, where AGE is defined as the percentage of the population aged over 65 and Y is per capita GDP.

After eyeballing the scattergrams, we test the following functional form:

d = (minY^a)/Y^a * (1/AGE^g)

Where minY is the constant equal to the smallest value of Y in the series.

Logarithmic transformation gives:

ln(d) = ln(minY^a) – a*ln(Y) – g*ln(AGE)

which we test on the data using OLS. Here are the results:

Adjusted R square: 75.191

Intercept coefficient: 7.37384
t-Stat: 20.4011

Y coefficient: -1.01444
t-Stat: -13.1059

AGE coefficient: 2.0097
t-Stat: 11.5208

The estimated intercept is a good, but not perfect, approximation of ln(minY^a)

Here are the fitted against actual values of the scattergram for death rate against per capita GDP:

While the results are not as good as with the birth rates calculations, it is nevertheless a good enough fit and the explanatory variables have a strong enough confidence factor to be usable in our estimations.

We begin by examining the scatter of data for 100 observations of per capita GDP and per capita emissions for 4 categories of countries, over 25 years (1990 – 2015).

The scatter suggests a cubic functional form, so we test:

GHG = a + b*Y + c*Y^2 + d*Y^3

where GHG are per capita emissions of GHG, and Y is per capita GDP.

The results from OLS regression are:

Adjusted R square: 0.980438073

coefficient a: 1090
t-stat a: 3.06

coefficient b: 0.709310153
t-Stat b: 8.241453

coefficient c: -0.0000047025
t-Stat c: -1.01233

coefficient d: -0.000000000105314
t-Stat d: -1.47005

While the t-scores on the squared and cubed terms are low, the number of observations are also limited.

Here is the plot of the fitted against actual values: