Statistics 133 Midterm ExamMarch 2, 2011When I ask for an “R program”, I mean one or more R commands. Try your best to makeyour answers general, i.e. they shouldn’t depend on the specific values presented in theexamples.Total: 40 points1. Consider the following vector of values stored in a variable called x:> x[1] 7 12 9 15 NA 8 14 NA 2 9 NA 8(a) (2 points) Write an R program to return the positions of the missing values in x.Solution:which(is.na(x))(b) (2 points) Write an R program to count the number of non-missing values in x.Solution:sum(!is.na(x))(c) (2 points) Write an R program to replace the missing values in x with the mean ofthe non-missing values in x.Solution:x[is.na(x)] = mean(x,na.rm=TRUE)(d) (2 points) Write an R function that, when passed a vector, will return a vector withthe missing values in the vector replaced by the mean of the non-missing values ofthe vector.Solution:replacena = function(x){x[is.na(x)] = mean(x,na.rm=TRUE)x}12. Consider a data frame called cars:> summary(cars)Country Car MPG Weight HorsepowerFrance : 1 AMC Concord D/L : 1 Min. :15.50 Min. :1.915 Min. : 65.0Germany: 5 AMC Spirit : 1 1st Qu.:18.52 1st Qu.:2.208 1st Qu.: 78.5Italy : 1 Audi 5000 : 1 Median :24.25 Median :2.685 Median :100.0Japan : 7 BMW 320i : 1 Mean :24.76 Mean :2.863 Mean :101.7Sweden : 2 Buick Century Special: 1 3rd Qu.:30.38 3rd Qu.:3.410 3rd Qu.:123.8U.S. :22 Buick Estate Wagon : 1 Max. :37.30 Max. :4.360 Max. :155.0(Other) :32(a) (2 points) Write an R program to plot MPG on the y-axis and Horsepower on thex-axis, using a different color for each level of Country.Solution:library(lattice)xyplot(MPG~Horsepower,group=Country,data=cars)(b) (2 points) Write an R program that will rearrange the rows of the data frame sothat they are sorted by the value of Horsepower.Solution:cars[order(cars$Horsepower),](c) (2 points) Write an R program that will show the row number of the observationwith the with the highest ratio of MPG to weight.Solution:which.max(cars$MPG / cars$weight)23. Consider a vector called book, each element of which contains the text of one sentenceof a book. For the purposes of this question, consider a word as text separated fromother text by one or more blanks.(a) (2 points) Write an R program to find the average number of characters in eachsentence including the blanks, and another program to find the average number ofcharacters in each sentence not including the blanks.Solution:mean(nchar(book))mean(nchar(gsub(’ ’,’’,book)))(b) (2 points) Write an R program to find the average number of words in each line ofthe book.Solution:words = strsplit(book,’ +’)mean(sapply(words,length))(c) (2 points) Write an R program to find the line in the book with the most characters.Solution:book[which.max(nchar(book))]4. Consider a data frame called wine, which contains information about the chemical com-position of different types of wines. Here is some information about the data frame:Type Alcohol Malic.Acid ProlineA:36 Min. :11.03 Min. :0.740 Min. : 278.0B:46 1st Qu.:12.36 1st Qu.:1.597 1st Qu.: 500.5C:35 Median :13.05 Median :1.845 Median : 673.5D:31 Mean :13.00 Mean :2.298 Mean : 746.9E:30 3rd Qu.:13.68 3rd Qu.:3.030 3rd Qu.: 985.0Max. :14.83 Max. :5.510 Max. :1680.0NA’s :2.000(a) (2 points) Write an R program that willl calculate the median of Alcohol andMalic.Acid for each Type of wine.Solution:aggregate(wine[,c(’Alcohol’,’Malic.Acid’)],wine[’Type’],median,na.rm=TRUE)3(b) (2 points) Write an R program to count the number of observations with Alcoholgreater than 13 and Proline less than 650.Solution:sum(wine$Alcohol > 13 & wine$Proline < 650)(c) (2 points) If you were reading this data from a comma-separated file, what optionwould be passed to read.csv to insure that Type was read as a character variable,not a factor?Solution:stringsAsFactors=FALSE(d) (2 points) Write an R program to produce a barplot showing the number of winesof each type in the data frame.Solution:barplot(table(wine$Type))5. Consider the following vector:> text = c(’cat 122’,’dog 213’,’721 chicken’,’fish 42’,’893 duck’)Use regular expressions to answer the following questions:(a) (2 points) Write an R program to create a vector like text, with the number ineach element appearing before the animal name.Solution:sub(’([a-z]+) ([0-9]+)’,’\\2 \\1’,text)(b) (2 points) Write an R program to create a vector containing just the animal namesin text.Solution:gsub(’[0-9 ]’,’’,text)(c) (2 points) Write an R program to produce a vector containing the position of theblank in each element of text.Solution:unlist(gregexpr(’ ’,text))4(d) (2 points) Write an R program to remove the first three characters in each of theelements of textSolution:sub(’^...’,’’,text)6. Consider a data frame called stock. Here are the first few lines of the data frame:> head(stock,n=3)Date Price1 2011-02-25 1.442 2011-02-24 1.393 2011-02-23 1.44Suppose you tried to plot Price versus Date and saw the following:> plot(stock$Date,stock$Price)Error in plot.window(...) : need finite ’xlim’ valuesIn addition: Warning messages:1: In xy.coords(x, y, xlabel, ylabel, log) : NAs introduced by coercion2: In min(x) : no non-missing arguments to min; returning Inf3: In max(x) : no non-missing arguments to max; returning -Inf(a) (2 points) What would you do to fix the problem, and get a meaningful plot?Solution:stock$Date = as.Date(stock$Date)plot(stock$Date,stock$Price)(b) (2 points) What would the class of the stock$Date variable be in order to causethe error message regarding “no non-missing arguments” to min and max.Solution: It would have to be character, because a factor would produce a plotwith lots of little lines (and no error