Open your copy of the Fuel Efficiency Starter File and click "Run".
num-sqr
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 num-sqr expressions below will be?
Test them out in the Interactions Area, and record the results. num-sqr(4) num-sqr(6 - 2)
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 𝑆-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 𝑆-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 𝑆-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 𝑆-value did you get?
10 Make any small changes you’d like, trying to get 𝑆 as low as you can. Write your final definition below.
fun f(x) : end 𝑆:
What does this model actually mean?
Numerical responses will vary!
After experimenting, I came up with a quadratic model for this dataset showing that x-variable is correlated to y-variable. The error in the model is described by an S-value of about Sunits, which is insignificant, moderate, significant, extreme considering that y-variable in this dataset range from lowest y-value to highest y-value. The vertex of the parabola drawn by this model is a minima or maxima? at about (x, y) which means that
Before this point, as speed increases, mpg . After this point, as speed increases mpg
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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