Open your copy of the Fitting a Model: State Demographics Starter File.
Build a Model Computationally
lr-plot computes the optimal linear model using all of the data points.
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) = slopex + y-intercept fun optimal(x): ( * x) + end
Interpret the Model
We started with a model based on Alabama and Alaska. We can interpret the slope and 𝑆-value below:
The Alabama-Alaskasensible name model predicts that a 1 percent[x-axis units] increase in percent college degrees[x-axis] is associated with a 5613 dollar[slope, y-units] increaseincrease / decrease in median household income[y-axis]. Based on the 𝑆 - 𝑣𝑎𝑙𝑢𝑒 of ~36,164.68S-value, this model fits really, really poorlyreally well, decently, poorly, etc..
3 Describe the optimal model YOU created via linear regression:
The linear-regressionsensible name model predicts that a 1 percent[x-axis units] increase in percent college degrees[x-axis] is associated with a [slope, y-units] increase / decrease in median household income[y-axis]. With an 𝑆-value of S-value, this model fits really well, decently, poorly, etc..
4 What does the slope of this linear model tell us?
5 What does the y-intercept of this linear model tell us?
6 Suppose a state goes from 10% to 11% college graduation. According to this model,
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What kind of change would we expect to see in the median household income?
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What if it goes from 50% to 51%?
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What if it goes from 90% to 91%?
7 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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