For this page, you’ll need to have Slide 6: Wealth-v-Health (Transformed) of Fitting Wealth-v-Health and Exploring Logarithmic Models (Desmos) open on your computer.

  • 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 second folder, called Log(Wealth) vs. Health, by clicking on the triangle ()

1 Compare the two tables. (Here is a side by side comparison of how they each begin.)

Wealth vs. Health Log(Wealth) vs. Health Compare the 2 tables. What do you notice? What do you wonder?

a table of x-y values including the points (1.99, 52.1), (11.77, 78.6), (15.19, 77.2)

a table of x-y values including the points (0.29, 52.1), (1.07, 78.6), 1.18, 77.2)

2 Read the comments in rows 3 to 6 of the Desmos file. Where do the x-values in the second table come from?

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

  • 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!

  • Rescale the graph () to see the cloud.

4 What is the shape of this point cloud? linear☐ quadratic ☐ exponential ☐

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

6 Through trial and error, 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)
Let’s compare the coefficients from your models.

Linear (From above)

slope (m)

vertical shift (b)

Logarithmic (From Changing the Scale)

log coefficient (a)

vertical shift (c)

7 How are they similar?

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.