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# MS-C1620
# Statistical inference
# Lecture 1




####################################################################################
# Examples of data sets

iris
help(iris)
str(iris)


# A data set that is the whole population
Titanic
help(Titanic)





####################################################################################
# Examples of data from different types of studies

randu
help(randu)

chickwts 
help(chickwts)

occupationalStatus
help(occupationalStatus)

presidents
help(presidents)


# More data sets can be found using the command data()
data()





####################################################################################
# Visualization

library(rgl)
# Opens in a new window
open3d()
plot3d(randu)


boxplot(weight ~ feed, data = chickwts)


heatmap(occupationalStatus, Colv = NA, Rowv = NA, revC = TRUE)
# Or something fancier
heatmap(occupationalStatus)


plot.ts(presidents)






####################################################################################
# Descriptive statistics and robustness

# Three data sets
x <- iris$Sepal.Width
hist(x)
y <- c(x[1:149], 100)
hist(y)
z <- c(x[1:145], rnorm(5, 100, 10))
hist(z)

# Location
mean(x)
mean(y)
mean(z)

mean(x, trim = 0.2)
mean(y, trim = 0.2)
mean(z, trim = 0.2)

median(x)
median(y)
median(z)

(quantile(x, 0.25) + quantile(x, 0.75))/2
(quantile(y, 0.25) + quantile(y, 0.75))/2
(quantile(z, 0.25) + quantile(z, 0.75))/2


# Scatter
sd(x)
sd(y)
sd(z)

mad(x)
mad(y)
mad(z)

max(x) - min(x)
max(y) - min(y)
max(z) - min(z)

IQR(x)
IQR(y)
IQR(z)


# Skewness
library(moments)

skewness(x)
skewness(y)
skewness(z)

(mean(x) - median(x))/sd(x)
(mean(y) - median(y))/sd(y)
(mean(z) - median(z))/sd(z)


# Kurtosis

kurtosis(x) - 3
kurtosis(y) - 3
kurtosis(z) - 3


# Correlation

x1 <- iris$Sepal.Length
x2 <- iris$Petal.Length
plot(x1, x2)

cor(x1, x2)
abline(lm(x2 ~ x1))