• Story Name: Billionaires 1992
  • Story Topics: Economics,
  • Datafile Name: Billionaires 92
  • Methods: ANCOVA, Distribution, Interaction, Transformation,
  • Abstract:

    Fortune magazine publishes a list of the world's billionaires each year. The 1992 list includes 233 individuals. Their wealth, age, and geographic location (Asia, Europe, Middle East, United States, and Other) are reported.

    The variable 'wealth' is right skewed, so the mean exceeds the median. There is a question of how we might look at the wealth distribution. We have here the upper tail of the distribution of the wealth of all humans. It is rare to know the extreme values of any distribution based on so many individuals. A common assumption about the distribution of wealth is that its logarithm is roughly Normal. If so, then the logarithm of these wealth values will still be skewed. Experiment shows that '1/wealth' is more nearly symmetric, but other transformations may be more appropriate.

    A Pie chart or bar chart can indicate how the billionares are distributed around the world.

    A scatterplot of '1/wealth' vs 'age' shows very little trend. Fitting lines individually by part of the world, shows a negative trend in '1/wealth' vs. 'age' for the Mideast that stands out from the other parts of the world. This makes sense because a negative association between '1/wealth' and 'age' implies a positive relationship between 'wealth' and 'age'.

    Fitting a model with the continuous explanatory variable 'age' and the discrete explanatory variable 'region' is an analysis of covariance (ANCOVA) with parallel regression lines for each region, each with a different intercept but the same slope of 'age'. Adding an 'age*region' interaction allows the slope for each regression line to be different.

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