For this page, you’ll need to open the Fuel Efficiency Starter File on your computer. If you haven’t already, select Save a Copy from the "File" menu to make a copy of the file that’s just for you. Read the comments at the top of the file, which describe what each column in the dataset means.
Fitting Linear Models
1 Evaluate A15, A45 and A75 in the Interactions Area. What model of car is used in all three rows?
2 At what three speeds is this model being tested in these rows?
3 Does there appear to be a relationship between speed and miles-per-gallon? .
4 Looking at the numbers in the mpg-table, describe its form (e.g. - linear, non-linear, or none) and strength (strong, moderate, or weak).
If it appears to be linear, what is the direction? If it does not appear to be linear, describe its shape.
5 Use lr-plot(mpg-table, "model", "speed", "mpg") to find the optimal linear model. What is S for this model?
Write the model below, in both math and Pyret notation.
y = slopex + y-intercept / vertical shift fun y(x): ( * x) + end
6 Is the best-possible linear model a good fit? . Why or why not?
Fitting Curves
7 Sketch your lr-plot in the space below, showing the relationship between
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8 What do you Notice?
9 What do you Wonder?
10 Do you think a curve would fit better? |
11 Draw a curve on your scatter-plot, which shows the overall shape in the data. At what speed is the "peak"?
12 Based on your best-guess curve, what do you predict mpg would be for a new test run at 25mph ? 60mph ? 90mph ?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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