x = c(1, 1, 2, 2, 3, 3.5, 4, 4.5, 5.2, 6, 6.5, 7, 7, 8, 8.5, 9, 9.5)
y1 = rnorm(17, 2, 0.5)
y = x * y1
plot(x, y)
abline(lm(y ~ x))

lm( y ~ x)
summary( lm( y ~ x ))

install.packages("UsingR")
library("UsingR")

lm.result = simple.lm(x,y)

install.packages("UsingR")
library("UsingR")

## library("UsingR", lib.loc="C:/Users/jacobson/Documents/R/win-library/2.15")

summary(lm.result)

lm.result$coefficients

coef(lm.result)

plot(lm.result)
b1 = (coef(lm.result))[['x']]
b1
z <- fitted(lm.result)
b0 = (coef(lm.result))[[1]]
b0

z <- fitted(lm.result)
xy <- data.frame(x, y, z)
xy

plot(x, y)
predict(lm.result, data.frame(x = c(4, 12)))

simple.lm(x, y, show.ci=TRUE,conf.level=0.90)
simple.lm(x, y, show.ci=TRUE,conf.level=0.95)

lm.result = lm(y ~ x)
lm.result

summary(lm.result)
plot(x,y)
abline(lm.result)

resid(lm.result)
coef(lm.result)

fitted(lm.result)

coefficients(summary(lm.result))['x','Std. Error']

coefficients(summary(lm.result))[2,2]

predict(lm.result,data.frame(x=c(11, 12, 14)))

predict(lm.result,data.frame(x=sort(x)), level = .05, 
        interval="confidence")

pre22 <- predict(lm.result,data.frame(x=sort(x)), level = .05, 
        interval="confidence")
pre22

plot(x,y)
abline(lm.result)

ci.lwr = predict(lm.result,data.frame(x=sort(x)),
                   level=.9,interval="confidence")[,2]

points(sort(x), ci.lwr,type="l") 

ci.upr = predict(lm.result,data.frame(x=sort(x)),
                 level=.9,interval="confidence")[,3]

points(sort(x), ci.upr,type="l")