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Exercise

Exponential growth

The simple data frame Oil_production gives the annual worldwide production of crude oil in millions of barrels (mbbl) from 1880 to 1970. As you can see from the graph, production increased at a faster and faster rate through the years. This pattern of growth is often called exponential growth.

In this exercise, you'll see that a linear model can capture exponential growth only after the effect of log-scaling the y-variable, or in this case, mbbl. You'll also calculate the annual growth using the effect size obtained from this linear model.

Instructions
100 XP
  • Train model_1, a linear model of mbbl explained by year in the Oil_production data frame.
  • Plot the model. You can add the training data with the statement geom_point(data = Oil_production). Note how the linear model fails to capture the exponential growth.
  • Find the effect size of year on mbbl. At this rate, how many years would it take production to increase by 3800 mbbl (i.e. to double from its 1950 level)? (Hint: 3800 mbbl divided by the effect size in mbbl per year gives years.)
  • Train model_2 which, instead of modeling mbbl, uses logmbbl as the response variable.
  • For this model, find the effect size of year on logmbbl.
  • Calculate the annual growth rate based on model_2 by exponentiating the effect size, subtracting 1 from it, then multiplying the result by 100 for easy interpretability.