• Provide History and Overview of R
• Introduce basic commands in R
• Introduce R Script and R Markdown
  
• Install some R packages
  
• Illustrate: generate R data, data in R, and Export Excel Data in R

• R is an independent open source implementation of a statistical analysis system developed by Ross Ihaka and Robert Gentleman at the University of Auckland in 1995.
• R can be used both as a programming language, and as a piece of software. It can be used for data manipulation, calculation and graphical display.
• One of the biggest advantage of R is that it can be distributed for free.
• R is freely downloaded in the internet

• Obtain a copy of an R language installer from a dependable source or directly from the Internet. The URL is http://cran.r-project.org/
• The latest version of R is 4.0.5
• Once the installation is done, start R by clicking the Desktop icon for R

• Along the top of the window is a limited set of menus, which can be used for various tasks including opening, loading and saving script windows, loading and saving your workspace, and installing packages.
• When you open an R session (i.e. start the R program), the R console opens and you are presented with a screen like this:

• RStudio is an integrated development environment (IDE) for R. It includes a console, syntax-highlighting editor that supports direct code execution, as well as tools for plotting, history, debugging and workspace management.
• RStudio is available in open source and commercial editions and runs on the desktop (Windows, Mac, and Linux).
• You can download the latest version of RStudio at https://www.rstudio.com/products/rstudio/

*Lesson: Mean and Variance of a Random Variable

Question: What is the expected number of heads in tossing a coin twice?

x<-c(0, 1, 2)
p<-c(.25, .5, .25)
coin<-rbind(x, p)
xbar<-sum(x*p)
xbar

## [1] 1

*Lesson: Mean and Variance of a Random Variable

Question: What is variance number of headsin tossing a coin twice?

x<-c(0, 1, 2)
p<-c(.25, .5, .25)
coin<-rbind(x, p)
xbar<-sum(x*p)
xbarobs<-c(1, 1, 1)
variance<-sum(p*(x-xbarobs)^2)
variance

## [1] 0.5

*Lesson: Binomial Probability Distribution

Question: You flip a fair coin 5 times, what is the probability of getting 4 or 5 heads?

bn4<-dbinom(4, 5, 0.5)
bn5<-dbinom(5, 5, 0.5)
bntotal<-bn4+bn5
bntotal

## [1] 0.1875

*Lesson: Binomial Probability Distribution

Or using the pbinom function:

bntotalalt<-1-pbinom(3, 5, .5)
bntotalalt

## [1] 0.1875

*Lesson: Normal Distribution

Question: Suppose that diastolic blood pressures (DBPs) from men aged 30-44 are normally distributed with a mean of 85mmHg and a standard deviation of 10 mmHg. What is the probability that a random 30-44 year old has a DBP less than 80?

pnorm(80,mean=85,sd=10,lower.tail = TRUE)

## [1] 0.3085375

*Lesson: Normal Distribution

Question: Brain volume for adult men is normally distributed with a mean of about 1,100 cc with a standard deviation of 70 cc. What brain volume represents the 95th percentile ?

qnorm(0.95,mean=1100,sd=70, lower.tail = TRUE)

## [1] 1215.14

*Lesson: Normal Distribution

Refer to previous example: Brain volume for adult men is normally distributed with a mean of about 1,100 cc with a standard deviation of 70 cc. Consider the sample mean of 100 random adult men from this population. What is th 95th percentile of the distribution of the sample mean?

*Lesson: Normal Distribution

Note: As the number of people is large enough, we can consider that the sample mean follows a normal distribution where the population mean is 1100, population standard deviation is 70 and n=100.

qnorm(0.95,mean=1100,sd=70/10,lower.tail = TRUE)

## [1] 1111.514

*Estimation and Hypothesis Testing

Question: In a population of interest, a sample of 9 men yielded a sample average brain volume of 1,100cc and a standard deviation of 30cc. What is a 95% Student’s T confidence interval for the mean brain volume in this new population?

*Estimation and Hypothesis Testing

n<-9
mu<-1100
st.dev<-30
quantile = 0.975 # is 95% with 2.5% on both sides of the range
conf= mu + c(-1, 1) * qt(quantile, df=n-1) * st.dev/sqrt(n)
conf

## [1] 1076.94 1123.06

Can be used as an interactive calculator

Addition

5+7

## [1] 12

Subtraction

10-5

## [1] 5

Storing result to a variable

x<-5+7

Now,

x

## [1] 12

Working with data in R, generated data, and excel data

1. Deng, Roger D., R Probramming for Data Science, 2014, Lean Publishing.
2. http://cran.r-project.org/
3. https://www.rstudio.com/products/rstudio/