For this page, you’ll need to load Fitting Wealth-v-Health, Part 2 (Desmos) open on your computer.

Transforming the Data

  • Find the Wealth vs. Health folder, which is open at the top of the expression list

  • This is the same table we’ve seen before, and the "points" circle () shows us that these dots are "on" and visible.

  • Underneath the Wealth vs. Health folder, you’ll see a function 𝑔(𝑥) and a list 𝑦2 defined to be the same as 𝑦1.

  • Open the Log(Wealth) vs. Health folder by clicking on the triangle ()

1 Compare the two tables. What do you Notice?

2 What do you Wonder?

3 Why is the second column of both tables the same?

4 How is the first column of this new table different from the original?

Turn the points for the first table OFF, then turn the points for our new table ON. Our log transformation is so drastic that it looks like all the black datapoints are smashed against the y-axis!

5 Rescale the graph () to see the cloud. What is the shape of this point cloud? Is it linear? Quadratic? Exponential?

6 Move the sliders for 𝑚 and 𝑏 to create the best-fitting linear model you can find, and write it below.

𝑓(𝑥) =slope (m)𝑥 +y-intercept / vertical shift (b)

7 Why do you think transforming the x-values make our data look linear?

Transforming Axes vs. Transforming Data

8 From your linear model above, copy your values for slope (𝑚) and vertical shift (𝑐):

slope (m)

vertical shift (c)

9 Look back at the values you wrote for log coefficient (𝑎) and vertical shift (𝑐) on question 8 of Changing the Scale and copy them here:

log coefficient (a)

vertical shift (c)

10 Are they similar? Why or why not?

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). CCbadge Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.