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 forfit-model
(to calculate š), look it up in the contracts pages!
1 Find the optimized linear model for this data using lr-plot
.
šššššš(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£ššš¢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.
šš¢ššššš”šš(š„) = quadratic coefficient (a)(š„ āvertex (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£ššš¢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.
šš„šššššš”ššš(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 Gššš¤š”š½ š šš”š: (š - 1) Ć 100 % with every x-unit increase in x-variable.
The error in the model is described by an š - š£ššš¢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).
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