Open your copy of the Fuel Efficiency Starter File and click "Run".
Before we try to model our fuel-efficiency data, we need to learn a new Pyret function!
1 Can you predict what the output of the following expressions will be? Enter them into the Interactions Area, and record the result.
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2 What is the Contract for num-sqr?
3 What does num-sqr do?
Interpreting a Quadratic Model
In the Definitions Area of your Fuel Efficiency Starter File, you’ll find the definition of a quadratic model quad1.
4 In quad1, the value of 𝑎 is , the value of ℎ is , and the value of 𝑘 is
5 Fit this model to your dataset, using fit-model. What 𝑅2 value did you get?
Hint: If you forgot the contract for fit-model, look it up in the contracts pages!
6 In your own words, describe what needs to change about this model to fit the data.
Modeling Fuel Efficiency
Vertex Form: 𝑦=𝑎(𝑥 − ℎ)2 + 𝑘 |
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7 We’ve determined that peak fuel efficiency is around 45 mph. What variable in the equation should we replace with 45?
Update the definition of quad1, click "Run" and re-fit the model. What 𝑅2 value did you get?
8 What y-coordinate of the vertex would best match the shape of the curve?
Update the definition of quad1, click "Run" and re-fit the model. What 𝑅2 value did you get?
9 What value of 𝑎 best matches the shape of the curve?
Update the definition of quad1, click "Run" and re-fit the model. What 𝑅2 value did you get?
10 See any small changes you’d like to make to the definition, trying to get 𝑅2 as close to 1 as you can? Write your final definition below.
fun f(x) : end 𝑅2:
★ What does this model actually mean? Try completing the sentence below:
After experimenting, I came up with a quadratic model showing that speed explains R-squared * 100% of the variability in gas mileage for cars in this dataset. The vertex of the parabola drawn by this model is (x, y), which means that
★ How does the fact that the value of 𝑎 is negative impact this parabola?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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