# Problem 1.
dielectric <- read.csv("Dielectric.csv", header=TRUE)
summary(dielectric)
# y x
# Min. :4.260 Min. :4.350
# 1st Qu.:4.355 1st Qu.:5.412
# Median :4.425 Median :5.845
# Mean :4.413 Mean :5.964
# 3rd Qu.:4.465 3rd Qu.:6.490
# Max. :4.550 Max. :7.880

# a)
# THe outcome/response variable is y = diaelectric constant
# and the independent/predictor variable is x = air void (%).

# b)
# Scatter plot
plot(y~x, data=dielectric)
# Box plot
boxplot(dielectric)
# Density plot
par(mfrow=c(1,2))
apply(dielectric, 2, hist, freq=FALSE)

# The scatter plot appears to show that both y and x have
# a strong linear relationship following the downward straight
# line.
# Two boxplots for y and x show that both are distributed evenly
# around the mean with no outliers.
# Density plots for y and x show that both appear to be close
# to the normal distribution.

# c)
cor(dielectric)
# y x
# y 1.0000000 -0.8830173
# x -0.8830173 1.0000000

# 0.88 (or -0.88) is a pretty high linear correlation number.
# Clearly they are linearly correlated from this result.

7. Given tan 2n+1 evaluate the integral Sx2 tan- 7. (7pts.)