For this page you will be working with both the Countries of the World Starter File and the Desmos file Fitting Wealth-v-Health and Exploring Logarithmic Models.

Follow the directions below to find linear, quadratic and exponential models for the relationship between pc-gdp and median-lifespan. As you find each model:

  • update the corresponding definition in the Countries of the World Starter File

  • click "Run" to load your new definition

  • use fit-model to calculate the S-value Hint: If you forgot the contract for fit-model (to calculate š‘†), look it up in the contracts pages!

1 Find the optimized linear model for this data using lr-plot.

š‘™š‘–š‘›š‘’š‘Žš‘Ÿ(š‘„) = slope (m)x + y-intercept (b)

S-value

The optimized linear model for this dataset predicts that a x-units increase / decrease in per-capita gdpx-variable
will increase y-variable by y-units. The error in the model is described by an š‘† - š‘£š‘Žš‘™š‘¢š‘’ of about Sy-units, which is insignificant / reasonable / significant / extreme considering y-units in this dataset range from lowest y-value to highest y-value.

Students "best" quadratic and exponential models will vary, as they are generated by eye - Solutions below are provided as a reference only.

2 Find the best quadratic model you can, using the second slide (Wealth-v-Health Quadratic) in the Desmos activity.

š‘žš‘¢š‘Žš‘‘š‘Ÿš‘Žš‘”š‘–š‘(š‘„) = quadratic coefficient (a)(š‘„ āˆ’vertex (h))2 + vertical shift (k)

S-value

The vertex of the parabola drawn by my model is a minima or maxima? at about (x, y). Before this point, as š‘„ increases, . After this point, as š‘„ increases .

The error in the model is described by an š‘† - š‘£š‘Žš‘™š‘¢š‘’ of about Sy-units, which is insignificant / reasonable / significant / extreme considering y-units in this dataset range from lowest y-value to highest y-value.

3 Find the best exponential model you can, using the third slide (Wealth-v-Health Exponential) in the Desmos activity.

š‘’š‘„š‘š‘œš‘›š‘’š‘›š‘”š‘–š‘Žš‘™(š‘„) = initial value (a)(growth factor (b)š‘„ ) + vertical shift (k)

S-value

According to this exponential model, a country with a x-variable of zero x-unit would have a y-variable of a + k y-units, for a total of about a + k. This number grows exponentially, increasing by a factor of Growth Factor: b or Gš‘Ÿš‘œš‘¤š‘”š’½ š‘…š‘Žš‘”š‘’: (š‘ - 1) Ɨ 100 % with every x-unit increase in x-variable.

The error in the model is described by an š‘† - š‘£š‘Žš‘™š‘¢š‘’ of about S y-units, which is insignificant / reasonable / significant / extreme considering y-units in this dataset range from lowest y-value to highest y-value.

4 Are any of these models a good fit for this data? 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.