Open the Preview: State Demographics Starter File.
1 Record the pct-college-or-higher and median-income values for the alabama and alaska rows, as (𝑥,𝑦) pairs below:
(AL pct-college-or-higher, AL median-income) (AK pct-college-or-higher, AK median-income)
2 We want to understand how change (Δ) in the percent of the population that attended college relates to change (Δ) in the median income.
Compute Δ median-income = AK median-income - AL median-income =
Compute Δ pct-college-or-higher = AK pct-college-or-higher - AL pct-college-or-higher =
Compute the slope/rate of change between AL and AK: $$\displaystyle \frac{\Delta \mbox{median-income}}{\Delta \mbox{pct-college-or-higher}} =$$ $$\displaystyle \frac{\qquad\qquad\qquad}{\qquad \qquad \qquad \qquad } =$$
Based solely on data from Alabama and Alaska, we are seeing that a Δ pct-college-or-higher percent increase in college graduates among the population translates to a Δ median-income dollar increase in median income.
3 Now, let’s use the slope intercept form of the line to calculate the y-intercept of the line passing through AK and AL.
A) Replace 𝑚 with the slope we just calculated.
B) Replace 𝑥 and 𝑦 with the relevant values from the AK row: (x :: AK pct-college-or-higher, y :: AK median-income)
C) Solve for 𝑏. y = m × x + 𝑏
𝑏 =
4 Write the complete model below (in both Function and Pyret notation):
𝑎𝑙 - 𝑎𝑘(𝑥) = slopex + y-intercept fun al-ak(x): ( * x) + end
-
Type your function into the Definitions Area on the left, modifying the existing function
f(x). -
Then click "Run", and make sure you fix any errors or warnings.
-
In the Interactions Area, try plugging in the
pct-college-or-highervalue for Alabama by typingf(22.6)
5 How well does it predict the correct median income for Alabama? What about Alaska?
Consider: If it doesn’t predict it perfectly, why might that be?
Try different pct-college-or-higher values from other states, to see how well our Alabama-Alaska model fits the rest of the country.
6 Identify a state for which this model works well:
7 Identify a state for which this model works poorly:
8 What median income does this model expect a state with zero college graduates to earn?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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.