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) = slope (m)x + y-intercept / vertical shift fun optimal(x): ( * x) + end
Interpret the Model
We started with a model based on Alabama and Alaska fun al-ak(x): (5613.67 * x) + -83616.02 end S: ~36164.68
which we can interpret as follows:
The Alabama-Alaskasensible name model predicts that a 1 percentx-axis units increase in percent college degreesx-axis is associated with a 5613 dollarslope, y-units increaseincrease / decrease in median household incomey-axis. With an S - value of ~36,164.68S-value dollarsy-units and median household incomey-axis ranging from $39,031lowest y-value to $73,538highest y-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 x-axis units increase in x-axis is associated with a slope, y-units increase / decrease in y-axis. With an S-value of S-value dollarsy-units and y-axis ranging from lowest y-value to highest y-value, this model fits really well, decently, poorly, etc..
4 What does the slope (m) of this linear model tell us?
5 What does the y-intercept / vertical shift 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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