Instructions:

In this assignment, we will create a simulated dataset to explore: A$)$ how sample size influences coefficient precision, B$)$ how collinearity influences point estimates, and C$)$ how variable functional form influences model fit.

Create a simulated dataset with the following characteristics:

$N=100,000$

X$1=$ random$\_$uniform

$x2=$ random$\_$uniform

$x3={0\mathrm{.}2}^{**}x1+$ random$\_$normal$($mean$=1,$ sd$=\mathrm{.}2)$

$Y={0\mathrm{.}2}^{**}x1+{0\mathrm{.}2}^{**}log(x2)+{0\mathrm{.}1}^{**}x3+$ random$\_$normal$($mean$=1,($:$sd=\mathrm{.}2\}$

Perform and report on the following analysis:

Draw random samples of varying sizes $(N=50,100,200,1000,$ etc.$)$ and run regression models

What happens to estimate precision across models? Why?

Using the population run and report the following regression specifications:

$Yx1$

$Yx1+x2$

$Yx1+x2+x3$

Comparing models: Why does the coefficient on X$1$ change? Why does the coefficient on $x2$ not change?

Using the population and report the following regression specifications

$Yx1+x2+x3$

$Yx1+log(x2)+x3$

Comparing models: why does model fit $($R$2)$ change?

Submission Format Guidelines:

Treat this assignment as if you are writing a professional memo. The report must consist of prose $($PDF or MS Word format$)$ and contain neatly formatted tables and figures. You may use bullet points to summarize facts and findings but must fully explain those points. You may not exceed one page of prose and one page of tables or figures. Submit your code as a separate appendix.