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 / 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 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 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).
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