Open your copy of Hybrid CO2 Models Starter File and click "Run".
Building a hybrid model for the entire co2-table
1 How well would you expect our hybrid-modern model to fit the data in the full co2-table, with data covering a span of 50 years?
2 Let’s test it out. What S-value do you get?
At the bottom of the Definitions Area, find the section titled "HYBRID MODEL for the full co2-table".
3 Define hybrid-all as a model that fits the full dataset, referring back to hybrid-modern to help you think through which functions you will need to define in order to be able to compose your function definition.
the line of best fit for the full co2-table data is y = 1.83453x - 3296.8
4 Use fit-model to fit your new hybrid-all model to the co2-table. What is the S-value of hybrid-all with this data?
5 Compute the change in S-values between hybrid-all and hybrid-modern, when used with the co2-table:
Percent Change = $$\displaystyle \frac{ \text{Difference} \text{between} \text{the} \text{S-values} } {\text{S-value} \text{for} \text{linear} \text{model}} \times 100 = $$ $$\displaystyle \frac{\qquad\qquad}{\qquad\qquad}$$
"For co2-table, we expect
percent
more / less
error from predictions made with hybrid-all than with hybrid-modern."
Comparing S-values doesn’t always make sense
You’ve had a lot of practice comparing the S-values of two different models on the same dataset (including what you just did on this page!), to quantify the error between them. But can we compare the S-values for one model fit to two different datasets?
6 In the first row of the table below, we’ve fit the periodic-cos model to all three datasets.
recent-table |
modern-table |
co2-table |
|
|---|---|---|---|
S-value of |
~1.2ppm |
~17.76ppm |
~55.89ppm |
lowest y-value (CO2 in ppm) |
415.74ppm |
387.03ppm |
327.28ppm |
highest y-value (CO2 in ppm) |
424ppm |
424ppm |
424ppm |
The periodic-cos model was built from recent-table, so there’s no surprise it was a good fit for recent-table! But for datasets that reach farther and farther back in time, that model fits worse and worse.
7 It’s tempting to compare the S-values in this table, to quantify how much more error we’d expect from the periodic-sin model for the co2-table. Why shouldn’t we?
★ Just as there’s nothing to say that midlines have to be horizontal, there’s also nothing to say that midlines need to be straight! If you look closely, the co2-table’s midline almost looks quadratic… can you come up with a hybrid-curve model for the co2-table that can beat the S-value you just found?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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