PLease use R and provide code with output and explanation

Simulation from the SLR Model

Use the rnorm function in R to generate 100 samples of X N(0,2) (for help use ?rnorm ) and for each draw, simulate Yi from the simple linear regression model Yi = 2.5 1.0Xi + i, where i N(0,3).

(i) Show the scatter plot of Y versus X along with the true regression line.

(ii) Split the sample into 2 subsets of size 25 and 75. For each subset, run the regression of Y on X. Add each fitted regression line (use color) to your plot from (i). Why are they not the same?

(iii) What is the marginal sample mean for Y ? What is the true marginal mean?

(iv) Add the bounds of the true 90% prediction interval to your plot (use ?qnorm for help with quantiles and and lty=2 in lines() to get a dashed line). What percentage of your observations are outside of this interval?