# STAT_515_Lec_18

load(url("https://people.stat.sc.edu/gregorkb/data/beryllium.Rdata"))

Y <- beryllium$logN_Be
x <- beryllium$Teff
plot(Y~x)

# correlation
rxY <- cor(x,Y)

sY <- sd(Y)
sx <- sd(x)

Ybar <- mean(Y)
xbar <- mean(x)

b1hat <- rxY * sY / sx
b0hat <- Ybar - b1hat * xbar

abline(b0hat,b1hat)

# how to fit the simple linear regression model in R

lm_out <- lm(Y ~ x) # lm() is for "linear model"

lm_out
confint(lm_out,level=.99)

summary(lm_out)

# check normality of responses around the line:


plot(lm_out, which = 2)

# for linearity / constant variance

plot(lm_out, which = 1)