1. This exercise relates to the College data set, which can be found in the file College.csv. It contains a number of variables for 777 different universities and colleges in the US. The variables are

• Private : Public/private indicator • Apps : Number of applications received • Accept : Number of applicants accepted • Enroll : Number of new students enrolled • Top10perc : New students from top 10 % of high school class • Top25perc : New students from top 25 % of high school class • F.Undergrad : Number of full-time undergraduates • P.Undergrad : Number of part-time undergraduates • Outstate : Out-of-state tuition • Room.Board : Room and board costs • Books : Estimated book costs • Personal : Estimated personal spending • PhD : Percent of faculty with Ph.D.’s • Terminal : Percent of faculty with terminal degree • S.F.Ratio : Student/faculty ratio • perc.alumni : Percent of alumni who donate • Expend : Instructional expenditure per student • Grad.Rate : Graduation rate

  1. Use the read.csv() function to read the data into R. Call the loaded data college. Make sure that you have the directory set to the correct location for the data.
install.packages("ISLR")
## 
## The downloaded binary packages are in
##  /var/folders/71/vnhmr1ts6w354s54vd5n1xw80000gn/T//RtmpvTz9R3/downloaded_packages
library(ISLR)
data("College")
summary(College)
##  Private        Apps           Accept          Enroll       Top10perc    
##  No :212   Min.   :   81   Min.   :   72   Min.   :  35   Min.   : 1.00  
##  Yes:565   1st Qu.:  776   1st Qu.:  604   1st Qu.: 242   1st Qu.:15.00  
##            Median : 1558   Median : 1110   Median : 434   Median :23.00  
##            Mean   : 3002   Mean   : 2019   Mean   : 780   Mean   :27.56  
##            3rd Qu.: 3624   3rd Qu.: 2424   3rd Qu.: 902   3rd Qu.:35.00  
##            Max.   :48094   Max.   :26330   Max.   :6392   Max.   :96.00  
##    Top25perc      F.Undergrad     P.Undergrad         Outstate    
##  Min.   :  9.0   Min.   :  139   Min.   :    1.0   Min.   : 2340  
##  1st Qu.: 41.0   1st Qu.:  992   1st Qu.:   95.0   1st Qu.: 7320  
##  Median : 54.0   Median : 1707   Median :  353.0   Median : 9990  
##  Mean   : 55.8   Mean   : 3700   Mean   :  855.3   Mean   :10441  
##  3rd Qu.: 69.0   3rd Qu.: 4005   3rd Qu.:  967.0   3rd Qu.:12925  
##  Max.   :100.0   Max.   :31643   Max.   :21836.0   Max.   :21700  
##    Room.Board       Books           Personal         PhD        
##  Min.   :1780   Min.   :  96.0   Min.   : 250   Min.   :  8.00  
##  1st Qu.:3597   1st Qu.: 470.0   1st Qu.: 850   1st Qu.: 62.00  
##  Median :4200   Median : 500.0   Median :1200   Median : 75.00  
##  Mean   :4358   Mean   : 549.4   Mean   :1341   Mean   : 72.66  
##  3rd Qu.:5050   3rd Qu.: 600.0   3rd Qu.:1700   3rd Qu.: 85.00  
##  Max.   :8124   Max.   :2340.0   Max.   :6800   Max.   :103.00  
##     Terminal       S.F.Ratio      perc.alumni        Expend     
##  Min.   : 24.0   Min.   : 2.50   Min.   : 0.00   Min.   : 3186  
##  1st Qu.: 71.0   1st Qu.:11.50   1st Qu.:13.00   1st Qu.: 6751  
##  Median : 82.0   Median :13.60   Median :21.00   Median : 8377  
##  Mean   : 79.7   Mean   :14.09   Mean   :22.74   Mean   : 9660  
##  3rd Qu.: 92.0   3rd Qu.:16.50   3rd Qu.:31.00   3rd Qu.:10830  
##  Max.   :100.0   Max.   :39.80   Max.   :64.00   Max.   :56233  
##    Grad.Rate     
##  Min.   : 10.00  
##  1st Qu.: 53.00  
##  Median : 65.00  
##  Mean   : 65.46  
##  3rd Qu.: 78.00  
##  Max.   :118.00
  1. Look at the data using the fix() function. You should notice that the first column is just the name of each university. We don’t really want R to treat this as data. However, it may be handy to have these names for later. Try the following commands:
college = read.csv("/Users/gopakumargeetha/Google\ Drive/Predictive-Modelling-in-R/ISLR/College.csv",header = T) 
rownames(college)<-college[,1]
college<-college[,-1]
  1. Use the summary() function to produce a numerical summary of the variables in the data set.
  2. Use the pairs() function to produce a scatterplot matrix of the first ten columns or variables of the data. Recall that you can reference the first ten columns of a matrix A using A[,1:10].
  3. Use the plot() function to produce side-by-side boxplots of Outstate versus Private.
  4. Create a new qualitative variable, called Elite, by binning the Top10perc variable. We are going to divide universities into two groups based on whether or not the proportion of students coming from the top 10% of their high school classes exceeds 50 %.
summary(college)
##  Private        Apps           Accept          Enroll       Top10perc    
##  No :212   Min.   :   81   Min.   :   72   Min.   :  35   Min.   : 1.00  
##  Yes:565   1st Qu.:  776   1st Qu.:  604   1st Qu.: 242   1st Qu.:15.00  
##            Median : 1558   Median : 1110   Median : 434   Median :23.00  
##            Mean   : 3002   Mean   : 2019   Mean   : 780   Mean   :27.56  
##            3rd Qu.: 3624   3rd Qu.: 2424   3rd Qu.: 902   3rd Qu.:35.00  
##            Max.   :48094   Max.   :26330   Max.   :6392   Max.   :96.00  
##    Top25perc      F.Undergrad     P.Undergrad         Outstate    
##  Min.   :  9.0   Min.   :  139   Min.   :    1.0   Min.   : 2340  
##  1st Qu.: 41.0   1st Qu.:  992   1st Qu.:   95.0   1st Qu.: 7320  
##  Median : 54.0   Median : 1707   Median :  353.0   Median : 9990  
##  Mean   : 55.8   Mean   : 3700   Mean   :  855.3   Mean   :10441  
##  3rd Qu.: 69.0   3rd Qu.: 4005   3rd Qu.:  967.0   3rd Qu.:12925  
##  Max.   :100.0   Max.   :31643   Max.   :21836.0   Max.   :21700  
##    Room.Board       Books           Personal         PhD        
##  Min.   :1780   Min.   :  96.0   Min.   : 250   Min.   :  8.00  
##  1st Qu.:3597   1st Qu.: 470.0   1st Qu.: 850   1st Qu.: 62.00  
##  Median :4200   Median : 500.0   Median :1200   Median : 75.00  
##  Mean   :4358   Mean   : 549.4   Mean   :1341   Mean   : 72.66  
##  3rd Qu.:5050   3rd Qu.: 600.0   3rd Qu.:1700   3rd Qu.: 85.00  
##  Max.   :8124   Max.   :2340.0   Max.   :6800   Max.   :103.00  
##     Terminal       S.F.Ratio      perc.alumni        Expend     
##  Min.   : 24.0   Min.   : 2.50   Min.   : 0.00   Min.   : 3186  
##  1st Qu.: 71.0   1st Qu.:11.50   1st Qu.:13.00   1st Qu.: 6751  
##  Median : 82.0   Median :13.60   Median :21.00   Median : 8377  
##  Mean   : 79.7   Mean   :14.09   Mean   :22.74   Mean   : 9660  
##  3rd Qu.: 92.0   3rd Qu.:16.50   3rd Qu.:31.00   3rd Qu.:10830  
##  Max.   :100.0   Max.   :39.80   Max.   :64.00   Max.   :56233  
##    Grad.Rate     
##  Min.   : 10.00  
##  1st Qu.: 53.00  
##  Median : 65.00  
##  Mean   : 65.46  
##  3rd Qu.: 78.00  
##  Max.   :118.00
pairs(college[,1:10])

plot(college$Private,college$Outstate,col = c("red","green")) # for box plots the first argument should be a factor

Elite=rep("No",nrow(college))  # creates a vector with name Elite repeating No for all entries
Elite[college$Top10perc >50]="Yes"  # for the vector Elite make "yes" for all entries for which the condition is satisfied.
Elite=as.factor(Elite)  #store this as a factor variable
college=data.frame(college ,Elite)  # add this to the data frame making it the 19th variable

Use the summary() function to see how many elite univer- sities there are. Now use the plot() function to produce side-by-side boxplots of Outstate versus Elite.

summary(college$Elite)
##  No Yes 
## 699  78
plot(college$Elite,college$Outstate,col=c("brown","red"))

v. Use the hist() function to produce some histograms with differing numbers of bins for a few of the quantitative vari- ables. You may find the command par(mfrow=c(2,2)) useful: it will divide the print window into four regions so that four plots can be made simultaneously. Modifying the arguments to this function will divide the screen in other ways. vi. Continue exploring the data, and provide a brief summary of what you discover.

par(mfrow=c(2,2))
hist(college$Accept,main="Number of applications accepted",col="red",breaks=50)
hist(college$Enroll,main="Number of new students enrolled",col="green",bin=100)
## Warning in plot.window(xlim, ylim, "", ...): "bin" is not a graphical
## parameter
## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## "bin" is not a graphical parameter
## Warning in axis(1, ...): "bin" is not a graphical parameter
## Warning in axis(2, ...): "bin" is not a graphical parameter
hist(college$PhD,main="Percent of faculties with PhD",col="red",breaks=20)
hist(college$perc.alumni,main="Percent of alumini donate",col="green")

summary(college$Apps)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##      81     776    1558    3002    3624   48090
  1. This exercise involves the Auto data set studied in the lab. Make sure that the missing values have been removed from the data.

  1. Which of the predictors are quantitative, and which are qualitative? quantitative variables : mpg, cylinders, displacement, horsepower, weight, accelearation qualitative variables : year, origin, name

  2. What is the range of each quantitative predictor? You can an- swer this using the range() function. range()

  3. What is the mean and standard deviation of each quantitative predictor?

data("Auto")
summary(Auto)
##       mpg          cylinders      displacement     horsepower   
##  Min.   : 9.00   Min.   :3.000   Min.   : 68.0   Min.   : 46.0  
##  1st Qu.:17.00   1st Qu.:4.000   1st Qu.:105.0   1st Qu.: 75.0  
##  Median :22.75   Median :4.000   Median :151.0   Median : 93.5  
##  Mean   :23.45   Mean   :5.472   Mean   :194.4   Mean   :104.5  
##  3rd Qu.:29.00   3rd Qu.:8.000   3rd Qu.:275.8   3rd Qu.:126.0  
##  Max.   :46.60   Max.   :8.000   Max.   :455.0   Max.   :230.0  
##                                                                 
##      weight      acceleration        year           origin     
##  Min.   :1613   Min.   : 8.00   Min.   :70.00   Min.   :1.000  
##  1st Qu.:2225   1st Qu.:13.78   1st Qu.:73.00   1st Qu.:1.000  
##  Median :2804   Median :15.50   Median :76.00   Median :1.000  
##  Mean   :2978   Mean   :15.54   Mean   :75.98   Mean   :1.577  
##  3rd Qu.:3615   3rd Qu.:17.02   3rd Qu.:79.00   3rd Qu.:2.000  
##  Max.   :5140   Max.   :24.80   Max.   :82.00   Max.   :3.000  
##                                                                
##                  name    
##  amc matador       :  5  
##  ford pinto        :  5  
##  toyota corolla    :  5  
##  amc gremlin       :  4  
##  amc hornet        :  4  
##  chevrolet chevette:  4  
##  (Other)           :365
range(Auto$mpg)
## [1]  9.0 46.6
range(Auto$cylinders)
## [1] 3 8
summary(Auto[,c(7:9),])  # summary of qualitative variables
##       year           origin                      name    
##  Min.   :70.00   Min.   :1.000   amc matador       :  5  
##  1st Qu.:73.00   1st Qu.:1.000   ford pinto        :  5  
##  Median :76.00   Median :1.000   toyota corolla    :  5  
##  Mean   :75.98   Mean   :1.577   amc gremlin       :  4  
##  3rd Qu.:79.00   3rd Qu.:2.000   amc hornet        :  4  
##  Max.   :82.00   Max.   :3.000   chevrolet chevette:  4  
##                                  (Other)           :365
summary(Auto[,c(1:6),]) # summary of quantitative variables
##       mpg          cylinders      displacement     horsepower   
##  Min.   : 9.00   Min.   :3.000   Min.   : 68.0   Min.   : 46.0  
##  1st Qu.:17.00   1st Qu.:4.000   1st Qu.:105.0   1st Qu.: 75.0  
##  Median :22.75   Median :4.000   Median :151.0   Median : 93.5  
##  Mean   :23.45   Mean   :5.472   Mean   :194.4   Mean   :104.5  
##  3rd Qu.:29.00   3rd Qu.:8.000   3rd Qu.:275.8   3rd Qu.:126.0  
##  Max.   :46.60   Max.   :8.000   Max.   :455.0   Max.   :230.0  
##      weight      acceleration  
##  Min.   :1613   Min.   : 8.00  
##  1st Qu.:2225   1st Qu.:13.78  
##  Median :2804   Median :15.50  
##  Mean   :2978   Mean   :15.54  
##  3rd Qu.:3615   3rd Qu.:17.02  
##  Max.   :5140   Max.   :24.80
# range
sapply(Auto[,c(1:6),],range)
##       mpg cylinders displacement horsepower weight acceleration
## [1,]  9.0         3           68         46   1613          8.0
## [2,] 46.6         8          455        230   5140         24.8
#mean and standard deviation of quantitative predictors
sapply(Auto[,c(1:6),],mean)
##          mpg    cylinders displacement   horsepower       weight 
##    23.445918     5.471939   194.411990   104.469388  2977.584184 
## acceleration 
##    15.541327
sapply(Auto[,c(1:6),],sd)
##          mpg    cylinders displacement   horsepower       weight 
##     7.805007     1.705783   104.644004    38.491160   849.402560 
## acceleration 
##     2.758864
  1. Now remove the 10th through 85th observations. What is the range, mean, and standard deviation of each predictor in the subset of the data that remains?
  2. Using the full data set, investigate the predictors graphically, using scatterplots or other tools of your choice. Create some plots highlighting the relationships among the predictors. Comment on your findings.
  3. Suppose that we wish to predict gas mileage (mpg) on the basis of the other variables. Do your plots suggest that any of the other variables might be useful in predicting mpg? Justify your answer.
new.auto = subset(Auto[-c(10:85),])
sapply(new.auto[,-c(9)],range)
##       mpg cylinders displacement horsepower weight acceleration year
## [1,] 11.0         3           68         46   1649          8.5   70
## [2,] 46.6         8          455        230   4997         24.8   82
##      origin
## [1,]      1
## [2,]      3
sapply(new.auto[,-c(9)],mean)
##          mpg    cylinders displacement   horsepower       weight 
##    24.404430     5.373418   187.240506   100.721519  2935.971519 
## acceleration         year       origin 
##    15.726899    77.145570     1.601266
sapply(new.auto[,-c(9)],sd)
##          mpg    cylinders displacement   horsepower       weight 
##     7.867283     1.654179    99.678367    35.708853   811.300208 
## acceleration         year       origin 
##     2.693721     3.106217     0.819910
pairs(Auto,panel=panel.smooth,main="scatter plots of all pairs of variables")

#Seems mpg is incerasing till number of cylinders = 4 and then drops down. So large number of cylinders in a car does not mean fuel efficiency.

mpg Vz. cylinders

To draw a box plot the first variable should be a factor

plot(as.factor(Auto$cylinders),Auto$mpg) # this can be seen clearly in this boxplot.

#mpg Vz weight of the car

plot(Auto$mpg,Auto$weight)

#this shows the inverse proportinality which we expect between mpg and weight of the car.

#To understand about the performance of the car (mpg) with respect to the important parameters, we do plot the pairs plot again
pairs(~ mpg + horsepower + weight + displacement, data = Auto, panel = panel.smooth)

# We can see mpg is inversely proportional to horsepower, weight and displacement # hosrsepower, weight and displacement are directly proportional to each other.

# Now lets see the manufacturer and the mpg of the car
#Here 1 is American, 2 is European and 3 is Japanese
plot(factor(Auto$origin),Auto$mpg,names=(c("American","European","Japanese"))) 

# Japanese cars have larger miles per gallon as expected in comparison with the US gas guzzlers.

From the above plots and discussions thereon, we can understand that mpg(miles per gallon) is proportional to variables like number of cylinders, horsepower, weight, displacement etc..

  1. This exercise involves the Boston housing data set.
  1. To begin, load in the Boston data set. The Boston data set is part of the MASS library in R. library(MASS) Now the data set is contained in the object Boston. > Boston Read about the data set: ?Boston How many rows are in this data set? How many columns? What do the rows and columns represent?
library(MASS)
data(Boston)
summary(Boston)
##       crim                zn             indus            chas        
##  Min.   : 0.00632   Min.   :  0.00   Min.   : 0.46   Min.   :0.00000  
##  1st Qu.: 0.08204   1st Qu.:  0.00   1st Qu.: 5.19   1st Qu.:0.00000  
##  Median : 0.25651   Median :  0.00   Median : 9.69   Median :0.00000  
##  Mean   : 3.61352   Mean   : 11.36   Mean   :11.14   Mean   :0.06917  
##  3rd Qu.: 3.67708   3rd Qu.: 12.50   3rd Qu.:18.10   3rd Qu.:0.00000  
##  Max.   :88.97620   Max.   :100.00   Max.   :27.74   Max.   :1.00000  
##       nox               rm             age              dis        
##  Min.   :0.3850   Min.   :3.561   Min.   :  2.90   Min.   : 1.130  
##  1st Qu.:0.4490   1st Qu.:5.886   1st Qu.: 45.02   1st Qu.: 2.100  
##  Median :0.5380   Median :6.208   Median : 77.50   Median : 3.207  
##  Mean   :0.5547   Mean   :6.285   Mean   : 68.57   Mean   : 3.795  
##  3rd Qu.:0.6240   3rd Qu.:6.623   3rd Qu.: 94.08   3rd Qu.: 5.188  
##  Max.   :0.8710   Max.   :8.780   Max.   :100.00   Max.   :12.127  
##       rad              tax           ptratio          black       
##  Min.   : 1.000   Min.   :187.0   Min.   :12.60   Min.   :  0.32  
##  1st Qu.: 4.000   1st Qu.:279.0   1st Qu.:17.40   1st Qu.:375.38  
##  Median : 5.000   Median :330.0   Median :19.05   Median :391.44  
##  Mean   : 9.549   Mean   :408.2   Mean   :18.46   Mean   :356.67  
##  3rd Qu.:24.000   3rd Qu.:666.0   3rd Qu.:20.20   3rd Qu.:396.23  
##  Max.   :24.000   Max.   :711.0   Max.   :22.00   Max.   :396.90  
##      lstat            medv      
##  Min.   : 1.73   Min.   : 5.00  
##  1st Qu.: 6.95   1st Qu.:17.02  
##  Median :11.36   Median :21.20  
##  Mean   :12.65   Mean   :22.53  
##  3rd Qu.:16.95   3rd Qu.:25.00  
##  Max.   :37.97   Max.   :50.00
str(Boston) # rows:506 and columns = 14
## 'data.frame':    506 obs. of  14 variables:
##  $ crim   : num  0.00632 0.02731 0.02729 0.03237 0.06905 ...
##  $ zn     : num  18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
##  $ indus  : num  2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
##  $ chas   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ nox    : num  0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
##  $ rm     : num  6.58 6.42 7.18 7 7.15 ...
##  $ age    : num  65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
##  $ dis    : num  4.09 4.97 4.97 6.06 6.06 ...
##  $ rad    : int  1 2 2 3 3 3 5 5 5 5 ...
##  $ tax    : num  296 242 242 222 222 222 311 311 311 311 ...
##  $ ptratio: num  15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
##  $ black  : num  397 397 393 395 397 ...
##  $ lstat  : num  4.98 9.14 4.03 2.94 5.33 ...
##  $ medv   : num  24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
  1. Make some pairwise scatterplots of the predictors (columns) in this data set. Describe your findings.
pairs(Boston) #this is very difficult to undestand? Lets consider few and do pairwise graphs

pairs(~ crim + lstat + black, data = Boston, panel = panel.smooth)

pairs(~ black + medv + dis + age , data = Boston, panel = panel.smooth)

plot(as.factor(Boston$chas),Boston$age)  # older buildings near the river

plot(as.factor(Boston$chas),Boston$lstat)  # lower status population less near river

plot(as.factor(Boston$chas),Boston$medv)  # homes expensive near the river - but outliers with expensive houses far from river too...

(c) Are any of the predictors associated with per capita crime rate? If so, explain the relationship. From the above plots we can roughtly say that the crime rate is more on the lower status populated places.

plot(as.factor(Boston$chas),Boston$crim)  # crime is more far from river area

plot(Boston$dis,Boston$crim)  # crime is large close to five Boston employment centres

(d) Do any of the suburbs of Boston appear to have particularly high crime rates? Tax rates? Pupil-teacher ratios? Comment on the range of each predictor.

plot(as.factor(Boston$chas),Boston$tax) # surprisingly the tax is less near the river area..

range(Boston$crim)
## [1]  0.00632 88.97620
hist(Boston$tax)

hist(Boston$crim,breaks=50)

(e) How many of the suburbs in this data set bound the Charles river?

table(Boston$chas)  # 35 near the Charles river
## 
##   0   1 
## 471  35
  1. What is the median pupil-teacher ratio among the towns in this data set?
median(Boston$ptratio)
## [1] 19.05
  1. Which suburb of Boston has lowest median value of owner- occupied homes? What are the values of the other predictors for that suburb, and how do those values compare to the overall ranges for those predictors? Comment on your findings.
plot(as.factor(Boston$chas),Boston$medv) #median value of owner occupied homes more in Charles river area

which.min(Boston$medv)
## [1] 399
Boston[which.min(Boston$medv),]  # it is far from Charles river area; far from radial highways, 
##        crim zn indus chas   nox    rm age    dis rad tax ptratio black
## 399 38.3518  0  18.1    0 0.693 5.453 100 1.4896  24 666    20.2 396.9
##     lstat medv
## 399 30.59    5
summary(Boston$crim) # max is 88.98 and the median is 0.25; for the median value of owner occupied homes the crime is around 38.3518 and we can see that the crime is larger in this area.
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
##  0.00632  0.08204  0.25650  3.61400  3.67700 88.98000
  1. In this data set, how many of the suburbs average more than seven rooms per dwelling? More than eight rooms per dwelling? Comment on the suburbs that average more than eight rooms per dwelling.
summary(Boston$rm)  # Average is around 6.285 rooms
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.561   5.886   6.208   6.285   6.624   8.780
table(Boston$rm > 7)  # 64 houses with more than 7 rooms
## 
## FALSE  TRUE 
##   442    64
table(Boston$rm >8)   # 13 houses with more than 8 rooms
## 
## FALSE  TRUE 
##   493    13
rooms8 = Boston[Boston$rm > 8, ]
summary(rooms8)
##       crim               zn            indus             chas       
##  Min.   :0.02009   Min.   : 0.00   Min.   : 2.680   Min.   :0.0000  
##  1st Qu.:0.33147   1st Qu.: 0.00   1st Qu.: 3.970   1st Qu.:0.0000  
##  Median :0.52014   Median : 0.00   Median : 6.200   Median :0.0000  
##  Mean   :0.71879   Mean   :13.62   Mean   : 7.078   Mean   :0.1538  
##  3rd Qu.:0.57834   3rd Qu.:20.00   3rd Qu.: 6.200   3rd Qu.:0.0000  
##  Max.   :3.47428   Max.   :95.00   Max.   :19.580   Max.   :1.0000  
##       nox               rm             age             dis       
##  Min.   :0.4161   Min.   :8.034   Min.   : 8.40   Min.   :1.801  
##  1st Qu.:0.5040   1st Qu.:8.247   1st Qu.:70.40   1st Qu.:2.288  
##  Median :0.5070   Median :8.297   Median :78.30   Median :2.894  
##  Mean   :0.5392   Mean   :8.349   Mean   :71.54   Mean   :3.430  
##  3rd Qu.:0.6050   3rd Qu.:8.398   3rd Qu.:86.50   3rd Qu.:3.652  
##  Max.   :0.7180   Max.   :8.780   Max.   :93.90   Max.   :8.907  
##       rad              tax           ptratio          black      
##  Min.   : 2.000   Min.   :224.0   Min.   :13.00   Min.   :354.6  
##  1st Qu.: 5.000   1st Qu.:264.0   1st Qu.:14.70   1st Qu.:384.5  
##  Median : 7.000   Median :307.0   Median :17.40   Median :386.9  
##  Mean   : 7.462   Mean   :325.1   Mean   :16.36   Mean   :385.2  
##  3rd Qu.: 8.000   3rd Qu.:307.0   3rd Qu.:17.40   3rd Qu.:389.7  
##  Max.   :24.000   Max.   :666.0   Max.   :20.20   Max.   :396.9  
##      lstat           medv     
##  Min.   :2.47   Min.   :21.9  
##  1st Qu.:3.32   1st Qu.:41.7  
##  Median :4.14   Median :48.3  
##  Mean   :4.31   Mean   :44.2  
##  3rd Qu.:5.12   3rd Qu.:50.0  
##  Max.   :7.44   Max.   :50.0
#Crime seems to be less in the houses which have 8 rooms
table(rooms8$chas)
## 
##  0  1 
## 11  2
# 11 of the houses with 8 rooms are not near Charles river (only 2 are near Charles river)
summary(rooms8$black)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   354.6   384.5   386.9   385.2   389.7   396.9
summary(Boston$black)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.32  375.40  391.40  356.70  396.20  396.90
# All the rooms8 houses blacks population