loading the challenger dataset

getwd()

launch <- read.csv("challenger.csv")

b <- cov(launch$temperature, launch$distress_ct) / var(launch$temperature)
b

a <- mean(launch$distress_ct) - b * mean(launch$temperature)
a

r <- cov(launch$temperature, launch$distress_ct) /
       (sd(launch$temperature) * sd(launch$distress_ct))
r

cor(launch$temperature, launch$distress_ct)

r * (sd(launch$distress_ct) / sd(launch$temperature))

model <- lm(distress_ct ~ temperature, data = launch)
model

summary(model)

creating a simple multiple regression function

reg <- function(y, x) {
  x <- as.matrix(x)
  x <- cbind(Intercept = 1, x)
  b <- solve(t(x) %*% x) %*% t(x) %*% y
  colnames(b) <- "estimate"
  print(b)
}

str(launch)

testing regression model

reg(y = launch$distress_ct, x = launch[2])

regression model with multiple regression

reg(y = launch$distress_ct, x = launch[2:4])

model <- lm(distress_ct ~ temperature + field_check_pressure + flight_num, data = launch)
model

summary(model)