Political Correlation II

(10 pts)

In this problem, we're going to investigate the following question: How is the statewide proportion of Democratic votes for the US House related to the proportion of Democratic seats for that state?

In 2016, for example, $46.6%$ of the state votes for the US Congress went to Democrats statewide, but they received only $23.1%$ of the seats. I suppose that's a result of gerrymandering. How did things look nationwide in that election?

To address the question, open up this COLAB notebook. After perusing the notebook, generate a random sample from the data set with 8 rows. Then answer the following questions for your sample:

  • What states did you investigate?
  • What is the correlation between the two proportions for your sample?
  • What is an equation of the regression line for your proportions?
  • What proportion of seats does your regression predict for a statewide Democratic vote proportion of $40\%$?

Comments

  • edited November 2020

    The States that were randomly generated for me were: Arkansas, Hawaii, Indiana, Kentucky, Michigan, New Jersey, New Mexico, and Wisconsin.

    The Correlation between two proportions: rvalue = 0.981

    My equation of the regression line: 2.71*0.4-0.91

    My proportion of seats: 0.17400000000000004

    mark
  • My states are Delaware, Hawaii, Iowa, Kentucky, Michigan, North Carolina, South Dakota, Vermont

    The Correlation: R = 0.89

    The equation is: y = 2.32x - 0.73

    The proportion is: .19799999

    mark
  • .States being used-California, Delaware, Hawaii, Missouri, Nebraska, North Carolina, North Dakota, Vermont.

    .Correlation between the two proportions-0.88847

    .Y=2.09x-0.56

    .2.09*0.4-0.56=0.2759999999999999

    mark
  • edited November 2020

    What states did you investigate?

    • Alabama, Hawaii, Kentucky, Missouri, Nebraska, Pennsylvania, Texas, West Virginia

    What is the correlation between the two proportions for your sample?

    • %%r = 1.0%%

    What is an equation of the regression line for your proportions?

    • %%y = 0.82192x + 0.036%%

    What proportion of seats does your regression predict for a statewide Democratic vote proportion of 40%?

    • %%0.364768%%
    mark
  • States Investigated:

    state   dem_vote_proportion dem_district_proportion
    4   California  0.585   0.736
    9   Georgia 0.527   0.286
    10  Hawaii  0.723   1.000
    11  Idaho   0.307   0.000
    24  Missouri    0.379   0.250
    25  Montana 0.405   0.000
    32  North Carolina  0.466   0.231
    37  Pennsylvania    0.504   0.278
    

    Correlation (R-Value) between two proportions:

    0.9218293486125065
    

    Proportion of seats the line of regression predicts:

    y = 2.46x-0.85
    2.46*0.4-0.85=0.134
    

    Proportion of seats my regression line predicted:

    .134 or 13.4%
    
    mark
  • edited November 2020

    The States that were given to me were Connecticut, Kentucky, Massachusetts, Montana, New Jersey, New Mexico, Rhode Island, and Wisconsin

    The Correlation between the two proportions:

    rvalue=0.9390788375196548
    

    My equation of the regression line is

    3.681*0.4-0.939
    

    My proportion of seats is

    0.5335476000000002
    
    mark
    1. My states were Arizona, Arkansas, Maine, Massachusetts, Missouri, New Jersey, South Dakota and Utah.
    2. 0.981would be my correlation between the points.
    3. 2.83*0.4-0.94 This is my equation.
    4. 0.192 This is my vote proportion and prediction.
    mark
  • edited November 2020

    I investigated the following states: Colorado, Delaware, Kansas, Montana, Nevada, Ohio, Oregon, and West Virginia.

    The correlation between two proportions: rvalue = 0.9401541680298139

    My equation of the regression line: y = 4.6052712179874815x−1.6244213126212377

    My proportion of seats: 0.21768717457375475

    mark
  • edited November 2020

    My states:

    4   California  0.585   0.736
    6   Connecticut 0.582   1.000
    22  Minnesota   0.561   0.625
    25  Montana 0.405   0.000
    35  Oklahoma    0.269   0.000
    38  Rhode Island    0.611   1.000
    41  Tennessee   0.341   0.222
    44  Vermont 0.825   1.000
    

    My Correlation: 0.8817722888924145

    My Equation: 𝑦=2.19(0.4)-0.57y.

    The proportion of Seats: 0.30600000000000005

    mark
  • edited November 2020

    Alabama
    Delaware
    Hawaii
    Indiana
    Mississippi
    Nebraska
    Tennessee
    Wyoming

    The correlation is r= .891809

    The equation of the regression line is y= 2.65*0.4-0.8124

    The 40% proportion is .24760

    mark
  • edited November 2020

    Connecticut, Illinois, Maryland, Minnesota, North Dakota, Oregon, Rhode Island, and Vermont

    My correlation is 0.85781

    My equation is 𝑦=1.81*.4−0.28

    Which gives me a proportion of 0.44400000000000006

    mark
  • The states I investigated are
    Florida
    Hawaii
    Indiana
    Iowa
    Missouri
    Oregon
    South Dakota
    West Virginia

    The correlation between the two proportions:
    0.952

    Regression Line equation
    𝑦=2.67𝑥−0.85.

    Prediction
    0.218

    mark
  • edited November 2020

    I investigated Georgia, Massachusetts, Illinois, Vermont, Nebraska, Nevada, Rhode Island, Tennessee

    Correlation between the two proportions= 0.81537

    Regression Line Equation= 2.038*0.4-0.5276

    Prediction= 0.2876 or 28.76%

    mark
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