x <- c( 1.0,   1.5,  1.5,  1.5, 2.5,   4.0,  5.0,  5.0,  7.0,
        8.0,   8.5,  9.0,  9.5, 9.5,  10.0, 12.0, 12.0, 13.0,
        13.0, 14.5, 15.5, 15.5, 16.5, 17.0, 22.5, 29.0, 31.5)
Y <- c(1.80, 1.85, 1.87, 1.77, 2.02, 2.27, 2.15, 2.26, 2.47,
       2.19, 2.26, 2.40, 2.39, 2.41, 2.50, 2.32, 2.32, 2.43,
       2.47, 2.56, 2.65, 2.47, 2.64, 2.56, 2.70, 2.72, 2.57)
lgage <- log(x)
plot(lgage, Y, xlab="log(age)", ylab="length", pch=20)

reg.out <- summary(lm(Y ~ lgage))
beta1hat <- reg.out$coefficients[2,1]
beta1.se <- reg.out$coefficients[2,2]

n <- 27
beta1.CI <- c(beta1hat+qt(0.025, df=n-2)*beta1.se ,
              beta1hat+qt(0.975, df=n-2)*beta1.se)
cat("95% classical CI for beta_1 is:",beta1.CI,"\n")