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.

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 S), look it up in the contracts pages!

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

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

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 S - value 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.

quadratic(x) = quadratic coefficient (a)(x − horizontal shift (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 x-variable increases, y-variable increases or decreases?.

  • After this point, as x-variable increases, y-variable increases or decreases?.

The error in the model is described by an S - value 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.

exponential(x) = initial value (a) ( growth factor (b) x ) + 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 Growth Rate: (b - 1) × 100 % with every x-unit increase in x-variable.

The error in the model is described by an S - value 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?

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