1.6.3: Illustration- Ruritanian Crops

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As usual, His Majesty Rudolph II would like some input from his Council of Ministers on his next five-year plan. Currently, the primary crop in Ruritania is corn. To help optimize the profits made by farmers, Rudolph wants to know if that crop should be changed to summer wheat or to soybeans.

To help him, let us model the relationship between farmer profit and crop in Ruritania. The dependent variable is the profit per acre, and the independent variable is the crop. Using linear models, we see that it is more profitable at this point to grow wheat. The average profit per acre is $845.75. This is about $150 greater than that of corn and about $300 greater than soybeans.

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Linear models can also be applied to cases where the independent variable is categorical, as here. This method is actually termed "analysis of variance" (ANOVA). The difference between ANOVA and regression is only conceptual, in that each level of the categorical variable is treated as a separate variable.

Using statistics to inform policy decisions is an important use. However, we professionals need to be aware of the limitations of our research --- and let our clients know them as well. Here, we only looked at the current average profit per acre for each crop. Future prices may fluctuate enough to make soybeans more valuable. Furthermore, shifting all Ruritanian crops to wheat puts the entire economy at risk of a drop in wheat prices. Diversification may be the better strategy, with some of the profit shared among all farmers.

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