answer3

# Challenge 1

set.seed(456789)

fake_data2<-data.frame(x1 = rpois(50,5), x2 = rpois(50,2))
fake_data2$y <- fake_data2$x1 *2 + rnorm(50, sd = 2) + fake_data2$x2 *-4 + rnorm(50, sd = 2)

start.val1<- -4
max.val1 <- 6
  
start.val2<- -8
max.val2<- 0

poss.vals.x1 <- seq(start.val1,max.val1, by = 0.05)
poss.vals.x2 <- seq(start.val2,max.val2, by = 0.05)

SS_stor2 <- expand.grid(x1 =poss.vals.x1, x2 = poss.vals.x2, SS = NA )

for(i in 1:nrow(SS_stor2)){
  pred.vals2 <- fake_data2$x1 *SS_stor2$x1[i] +  fake_data2$x2 *SS_stor2$x2[i]
  
  SS_stor2$SS[i] <- sum((fake_data2$y - pred.vals2)^2)
}

beta_vals2<- SS_stor2[which(SS_stor2$SS==min(SS_stor2$SS)),]

beta_vals2

##        x1    x2       SS
## 15600 2.1 -4.15 487.7254