Coincidence on Linear Regression Analysis with president election data

by fungarwai, Feb 16, 2021, 12:58 AM

The Linear Regression model with president election data indicates that a candidate has stolen other candidates averagely 120 votes on each ward in Milwaukee
Here are data sources from Milwaukee
11-3-20 General and Presidential Election - Unofficial Results
My Regression Model is
Candidate's vote = Candidate's voting rate × Total votes
which is no constant term expected

Form data at Nov. 4, 2020
Biden's vote = 5.3191 + 0.5821 × Total votes
R^2=0.9087
Trump's vote = -6.6928 + 0.4002 × Total votes
R^2=0.8255
No constant term is expected.
This constant term is possibly caused by Biden stealing other candidate's vote.
However, the constant term lies on the convincible interval involving 0.

Without constant term, my Linear Regression model at Nov. 4, 2020 becomes:
Biden's vote = 0.5877 × Total votes
R^2=0.9085
Trump's vote = 0.3931 × Total votes
R^2=0.8262
which is Candidate's vote = Candidate's voting rate × Total votes

Guess what?

Form data at Nov. 5, 2020
Biden's vote = 121.6115 + 0.5629 × Total votes
R^2=0.8128
Trump's vote = -120.573 + 0.4171 × Total votes
R^2=0.7051
The constant term lies on the convincible interval far from 0.
My Linear Regression model indicates that Biden has stolen other candidates averagely 120 votes on each ward.

What a Coincidence!

That's all.
Here is my video concerning this Linear Regression Analysis if you're interested.

Possible leakage of this Linear Regression model
Suppose there are two different groups of votes (mail-in ballots and in-person ballots) with different voting rate
$\begin{cases}y_A=\hat{\beta_A} x_A,~\hat{\alpha_A}=\bar{y_A}-\bar{x_A}\hat{\beta_A}=0\\
y_B=\hat{\beta_B} x_B,~\hat{\alpha_B}=\bar{y_B}-\bar{x_B}\hat{\beta_B}=0\end{cases}$
$\hat{\alpha}=\frac{p_A p_B \bar{x_A}\bar{x_B}(\hat{\beta_B}-\hat{\beta_A})}
{p_A D(x_A)+p_B D(x_B)}
(\bar{x_A}-\bar{x_B}+\frac{D(x_A)}{\bar{x_A}}-\frac{D(x_B)}{\bar{x_B}})$
$\hat{\alpha}=y-x\hat{\beta}=0$ holds when $E(x_A)=E(x_B)~\text{and}~D(x_A)=D(x_B)$
The nature of mail-in ballots and in-person ballots possibly fluctrates the constant term.

Proof
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This post has been edited 3 times. Last edited by fungarwai, Feb 18, 2021, 12:40 AM

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