• History and Overview of R
• RStudio
• Sample R usage
• Swirl Package in R
• Incorporation of R in Statistics and Probability Lessons

• 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 be 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 3.6.1
• 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:

• The logo or R

• 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/

• It is called Statistics with Interactive R Learning or SWIRL for short.
• Using swirl package in R illustrates some key concepts in using R.
• The swirl package turns the R console into an interactive learning environment.
• Using swirl will also give you the opportunity to be completely immersed in an authentic R programming environment.

• Install swirl: install.packages(“swirl”)
• Load swirl: library(“swirl”)

• install_from_swirl(“R Programming”)
• install_from_swirl(“Exploratory Data Analysis”)
• install_from_swirl(“Getting and Cleaning Data”)
• install_from_swirl(“Statistical Inference”)
• install_from_swirl(“Regression Models”)

library("swirl")

## 
## | Hi! Type swirl() when you are ready to begin.

• swirl()

*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

*Estimation and Hypothesis Testing

Using the mtcars dat as shown below

head(mtcars)

##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

Question: Is there a significant difference on the mpg between manual and automatic transmissions at 5% level of significance?

t.test(mpg~am, data=mtcars)

## 
##  Welch Two Sample t-test
## 
## data:  mpg by am
## t = -3.7671, df = 18.332, p-value = 0.001374
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -11.280194  -3.209684
## sample estimates:
## mean in group 0 mean in group 1 
##        17.14737        24.39231

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/
4. http://swirlstats.com