# 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 $40\%$?

• 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

• 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

• .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

• 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
• 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%
``````
• 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
``````
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.
• 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

• 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

• edited November 2020

Alabama
Delaware
Hawaii
Indiana
Mississippi
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

• 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

• 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

• edited November 2020