Open the State Demographics Starter File.

The Alabama - Alaska Model

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 How does 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: $$\displaystyle \frac{\Delta \text{median-income}}{\Delta \text{pct-college-or-higher}} =$$ $$\displaystyle \frac{\qquad\qquad\qquad}{\qquad \qquad \qquad \qquad } =$$

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 Let’s use the slope-intercept form of the line to calculate the y-intercept / vertical shift of the line passing through AK and AL.

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

  • Find the x and y values from the AK row: (x :: AK pct-college-or-higher, y :: AK median-income)

  • Now, replace y, m, and x in the equation above with values from the AK row and the slope we just calculated in question 2.

  • Then solve the equation above for b =

4 Use the slope and y-intercept you calculated to write the complete model below (in both Function and Pyret notation):

al - ak(x) = slope (m)x + y-intercept / vertical shift fun al-ak​(​x​): (​  ​* x​) +   end

Return to your copy of the starter file and add the code you just wrote to line 44 of the Definitions Area. Then Click "Run".

5 In the Interactions Area, try plugging in the pct-college-or-higher value for Alabama by typing al-ak(22.6).

  • How well does it predict the correct median income for Alabama?

  • What expression would predict median income for Alaska? .

  • How well does it predict the correct median income for Alaska?

Try 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?

Another Model

9 Look at the scatter plot. Imagine you were going to define another model. Identify two other states that would likely generate a better fit.

and

Answers will vary. But West Virginia and Massachusetts could be a good option.

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.