Open your copy of the State Demographics Starter File and click "Run".
Build a Model Computationally
1 Evaluate lr-plot(states-table, "state", "pct-college-or-higher", "median-income"). What is S?
2 On the line below, write the optimal linear model that was computed through linear regression:
optimal(x) = slope (m)x + y-intercept / vertical shift fun optimal(x): ( * x) + end
Interpret the al-ak Model
We started with a model based on Alabama and Alaska (fun al-ak(x): (5613.67 * x) + -83616.02 end),
and got an S-value of ~36164.68. We can interpret this as follows:
The Alabama-Alaskasensible name model predicts that a 1
percentx-axis units increase in
percent college degreesexplanatory variable (x) is associated with a
~5614 dollarrate of change in y-units
increaseincrease / decrease in
median household incomeresponse variable (y).
With median household incomeresponse variable (y) ranging from
$39,031lowest y-value to
$73,538highest y-value and an S-value of
~36,164.68S-value
dollarsy-axis units, I
strongly disagreestrongly agree, agree, disagree, strongly disagree that this model is a good fit.
3 What does the slope (m) of this linear model tell us?
4 How would we use this model predict to predict the median income for a state where 30% of the population has attended college?
Interpreting the Optimal Model
The linear-regressionsensible name model predicts that a 1
x-axis units increase in
explanatory variable (x) is associated with a
rate of change in y-units
increase / decrease in
response variable (y).
With response variable (y) ranging from
lowest y-value to
highest y-value and an S-value of
S-value
y-axis units, I
strongly agree, agree, disagree, strongly disagree that this model is a good fit.
5 What median income does this model predict when 30% of a state’s population has attended college?
6 Why doesn’t it make sense to use this model to predict median income for a state with no college attendees (0%)?
7 If a state’s college graduation increases from 10% to 11%, what change in median income does this model predict?
-
What if it goes from 50% to 51%?
-
What if it goes from 90% to 91%?
-
Does this model predict the same increase in income for every additional 1%
college-or-higher? 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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