math <- c(78.93,58.20,67.47,37.47,45.65,32.92,29.97)
lsd <- c(1.17,2.97,3.26,4.69,5.83,6.00,6.41)


# Fit the simple linear regression model with Y = math (score) and X = lsd (concentration)
mathlsd.reg <- lm(math ~ lsd)
#png("mathlsd1.png")
# Plot the data and regression line (Note you enter X first, then Y in plot statement)
plot(lsd,math)
abline(mathlsd.reg)
#dev.off()

# Print out the estimates, standard errors and t-tests, R-Square, and F-test
summary(mathlsd.reg)

# Print out the ANOVA table (Sums of Squares and degrees of freedom)
anova(mathlsd.reg)

# Compute the correlation coefficient (r) and test if rho=0
cor(math,lsd)
cor.test(math,lsd)
#png("mathlsd2.png")
# Plot Residuals versus Fitted Values
plot(predict(mathlsd.reg),residuals(mathlsd.reg))
abline(h=0)
#dev.off()
# Print out standardized, studentized Residuals and Influence Measures
round(rstandard(mathlsd.reg),4)
round(rstudent(mathlsd.reg),4)
influence.measures(mathlsd.reg)