Part 3

**Please use R studio to answer the following questions and please provide the R script. Thanks**

Set up 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.

Set up a simulated dataset with the following characteristics:

• N = 100,000
• X1 = random_uniform
• X2 = random_uniform
• X3 = 0.2*X1 + random_normal(mean=1, sd=.2)
• Y = 0.2*X1 + 0.2*log(X2) + 0.1*X3 + random_normal(mean=1, sd=.2)

1. Use the population and report the following regression specifications
   1. Y ~ X2
   2. Y ~ log(X2)
   3. Comparing models: why does model fit (R2) change?

*** The following screenshots are the sample codes, please use them as reference/help***

simulated data # 1 - create the simulated data # total number of observations obs = mean(X2))] # dependent variable Y # Y is a function of X1 (b=.4) + X2 (b=.1) + random noise simdata[,Y := .4*X1 +.1*X2 + rnorm(obs, mean = 1, sd = .2 )] w