1.6.4: Illustration- Wealth in Ruritania

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The gross domestic product (GDP) per capita is one of many measures of average wealth in countries. If extant theory is correct, then the wealth in the country is directly affected by the level of corruption in the government — countries with higher levels of corruption should be poorer (on average) than those with low levels of corruption. Furthermore, if theory is correct, the level of democracy in a country should also influence the country's level of wealth — countries with higher levels of democracy should be wealthier than countries with lower levels of democracy.

His Majesty is curious to see how Ruritania fits in this model. If the actual GDP per capita is greater than what is expected from modeling the rest of the world, then Rudolph is doing a great job as king. Otherwise, he needs to improve the lot of his people.

And so, to help Rudolph, we predict that the GDP per capita for Ruritania, according to the model, is $26,795.64, with a 95% prediction interval from $5232 to $48,360. Since the actual GDP per capita is $55,000, King Rudolph is happy that he is better than average at guiding Ruritania forward towards prosperity.

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Frequently, we can use our models in novel ways. Usually, we would model the data and calculate predictions and confidence intervals. However, if we have confidence in our model, we can use it to determine which units are under- or over-performing expectations (the line of best fit). In this case, Ruritania's GDP per capita is significantly higher than what the model predicts.

This means either the model needs to take more covariates into consideration or that Ruritania is much more prosperous than one would expect... or both.

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