** You must use R (e.g., RStudio) to complete this problem **

#1 - Assume y = 5 + 0.9x₁+ 3x₂+ . Generate data with x₁ norm(2, 0.52), x₂ norm(1, 0.12), and x₃=_x1*x2,and norm(0, = 1). Use sample size n = 200.

Run the following R code:

set.seed(123) n <- 200 s <- 1 x1 <- rnorm(n, 2, 0.52) x2 <- rnorm(n, -1, 0.12) x3 <- x1*x2 e <- rnorm(n, 0, s) y <- 5 + 0.9*x1 + 3*x2 + e#true model summary(y) 

Summary(y) must produce the following, if it does not, run it again until it does:

## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 0.8576 3.0472 3.9772 3.8429 4.5566 7.1697

Run model 1 which is y ~ x₁+ x₂+x₃. What is the R²for this model? Enter your answer to 4 decimal places.

Run model 2 which is y ~ x₁+ x₂. What is the R²for this model? Enter your answer to 4 decimal places.

Run model 3 which is y ~ x₁+ x₃. What is the R²for this model? Enter your answer to 4 decimal places.