Question

WILL RATE HIGH! question 2.4.1, problem 6 The data set airquality is one of R’s included data sets. It shows daily measurements of ozone concentration (Ozone), solar radiation (Solar.R), wind speed (Wind), and temperature (Temp) for 5 summer months in 1977 in New York City. Some of the observations are missing and are recorded as NA, meaning not available. View an overall summary of the variables in airquality with the command > summary(airquality) Ignore the summaries for Month and Day since those variables should be factors, not numeric variables, and their summaries are meaningless. Attach airquality to your workspace Go to TOC CHAPTER 2. DESCRIPTIVE AND GRAPHICAL STATISTICS 33 > attach(airquality) and make boxplots of Ozone, Solar.R, Wind, and Temp. Comment on any noteworthy features

Answer 1

All the sentences beginning with # are comments

a)

# R-code

# View some records of the dataset airquality
head(airquality)

#--output--

We can see that the required fields are present and some observations have NA

b) View an overall summary of the variables in airquality

#R-Code

#View an overall summary of the variables in airquality
summary(airquality)

#--output

6 point summary of all the variables is in the putput. Ozone has 37 observations with missing values and Solar.R has 7.

We can look at if the mean is less than or greater than the median and comment on the skewness of each of the variable. We will do that in the box plot.

c) Attach airquality to your workspace & make boxplots

#R code

#Attach airquality to your workspace
attach(airquality)

#command to plot all the plots in one window -- comment this if you want to have separate plots
par(mfrow=c(2,2))

#make boxplots of Ozone, Solar.R, Wind, and Temp
boxplot(Ozone,main="Ozone Concentration",xlab="ozone concentration",horizontal=TRUE)
boxplot(Solar.R,main="Solar Radiation",xlab="Solar Radiation",horizontal=TRUE)
boxplot(Wind,main="Wind Speed",xlab="wind speed",horizontal=TRUE)
boxplot(Temp,main="Temperature",xlab="Temperature",horizontal=TRUE)

#--output

Boxplots

• Presence of outliers. Outliers are the observations which are outside the fence. Let Q1 be the 1st quartile and Q3 is the 3rd quartile then Inter quartile raneg IQR = Q3-Q1 and the lower value of the fence is lci=Q1-1.5*IQR and the upper value of the fence is uci=Q3+1.5*IQR. Any observation which is less than lci or more than uci is considered an outlier.
  • Ozone concentration has 2 outliers and wind speed has 3 outliers indicated by the dots outside of the wiskers.
• skewness
  • Ozone: The median and the box are located to the left and hence the data is right skewed. This is also indicated by median (31.50) being less than the mean (42.13)
  • Solar radiation: The data is left skewed (as the median is located towards to right). This is also indicated by median (205.0) being larger than the mean (185.9)
  • Wind speed looks almost symmetric. Also indicated by similar values for mean and median.
  • Temperature: Almost symmetric. Also indicated by similar values for mean and median.
• Spread. It is not appropriate to compare the spreads as the variables have different units. But we can see that the solar radiation has the biggest spread among the variables (as indicated by the box width)