heteroskedasticity.Rmd

---
title: "How Endogenous Caused Heteroskedasticity?"
subtitle: A Simulation Study
author: "Zheyi Shen"
date: "21/12/2020"
framework   : io2012        # {io2012, html5slides, shower, dzslides, ...}
highlighter : highlight.js # {highlight.js, prettify, highlight}
hitheme     : tomorrow       # zenburn 
widgets     : [bootstrap, quiz] # {mathjax, quiz, bootstrap}
mode        : selfcontained # {standalone, draft}
knit        : slidify::knit2slides
---

## Heteroskedasticity
The heteroskedasticity problem would be in presence when variances of error terms are not constant.
This would increase the variance of coefficient estimate, reducing the liability of our estimate.

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## Endogenous variable
Regressors correlated with the error term are endogenous, and will caused heteroskedasticity.

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## Example: Y = beta0 + beta1*X + u, u ~ N(0, f(x))
- f(x) = x^2  
- f(x) = sqrt(x) 
- f(x) = exp(x)  
- f(x) = x^(-1)  

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## Simulation illustration
See how the error term variance changes when specified different functional form and number of observations:

[Shiny Example](https://zoey1102.shinyapps.io/heteroskedasticity/)