Age = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
HeartRate= c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
plot(Age,HeartRate)
abline(lm(HeartRate~Age))

Result = lm(HeartRate~Age)
summary(Result)
coef(Result)

n=15
es = resid(Result) 
b1 =(coef(Result))[["Age"]]
s = sqrt( sum( es^2 ) / (n-2) )
SE = s/sqrt(sum((Age-mean(Age))^2))
t=(b1+1)/SE 
pt(t,13,lower.tail=F)


x = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178) 
plot(x,y) # make a plot
abline(lm(y ~ x)) # plot the regression line
lm.result=lm(y~x)
summary(lm.result)
coef(lm.result)
lm.res = resid(lm.result) 
summary(lm.res)
plot(lm.result)
es = resid(lm.result)
b1 =(coef(lm.result))[["x"]]
s = sqrt( sum( es^2 ) / (n-2) )
SE = s/sqrt(sum((x-mean(x))^2))
t=(b1-(-1))/SE
pt(t,13,lower.tail=FALSE)

SE = s * sqrt( sum(x^2)/( n*sum((x-mean(x))^2))) 
b0 = 210.04846
t = (b0 - 220)/SE
pt(t,13,lower.tail=TRUE) 


####
x = c(4,3,4,5,2,3,4,5)
y = c(4,4,5,5,4,5,4,4)
z = c(3,4,2,4,5,5,4,4)
scores = data.frame(x,y,z) 
boxplot(scores)
scores = stack(scores)
names(scores)
oneway.test(values ~ ind, data=scores, var.equal=T)
###
x = rnorm(5,40,10)
y = rnorm(5,60,10)
z = rnorm(5,60,10)
random= data.frame(x,y,z) 
boxplot(random)
df = stack(data.frame(x,y,z)) # prepare the data 
oneway.test(values ~ ind, data=df,var.equal=T)
anova(lm(values ~ ind, data=df))