Chapter 2 Hmwk. STA-6543-91T-202630
Mark Hertzfeld (OPT121)
2026-06-25
#install.packages("ISLR2")
library(ISLR2)Chapter 2 Homework:
2a. Regression. Regression is used when the outcome is continuous/numerical. The CEO’s salary will be a numerical outcome.
We are interested in inference since we want to know which factors affect CEO Salary.
N = 500, P = 3
2b. Classification. Classification is used when the outcome is categorical. In this case, the only thing wanting to be known is if the product succeeds or fails (no numbers).
We are interested in prediction because we want to know if the product will succeed or fail. We’re not interested in the relationship between the predictors and the outcome variable.
N = 20, P = 14
2c. Both. Classification is used when the outcome is categorical. Regression is used when the outcome is continuous/numerical. In this case, either approach would work, depending on what was asked. We would use classification if all we wanted to know is if the percent change increases or decreases. We would use regression if we were actually wanting to determine the actual number the percent change increased or decreased by.
We are interested in prediction because we want to predict the % change in the USD/Euro exchange rate in relation to the weekly changes in the world stock markets. The weekly changes are not expressly stated; therefore, we can assume the problem expects us to view the factors as not as important as the desired outcome.
N = 52, P = 4
- The advantages of a very flexible approach for regression are that a more flexible model can yield a lower Training MSE, accurately predict all points in a training data set and have low bias.
The disadvantages are that a very flexible model will have high variance, can be harder to interpret and be less accurate in predicting future models because it can be overfitted.
A more flexible approach would be preferred over a less flexible approach when the outcome desired is more concerned with prediction, reducing bias and there are many observations/relationships to consider.
A less flexible approach would be preferred over a more flexible approach when the outcome desired is more concerned with inference, interpretability and linearity.
- The parametric statistical approach is when you make an assumption about the shape/form of f. The assumed shape determines how many parameters you will be attempting to find values for in the training data. You then fit the model to the training data to determine what parameter values yield the best fit.
The non-parametric statistical approach does not make assumptions about the shape of f. It does require a large amount of observations to fit the model correctly and avoid overfitting.
The advantages are it gives us a place to start, does not require a lot of observations to fit the model, and limits the level of variance.
The disadvantages of using a parametric approach are the resulting models have a higher risk of yielding incorrect results, can contain a high amounts of bias, and can struggle to handle complex relationships.
8a.
college=read.csv("~/Grad School/Prediction Statistics/Module 2/College.csv")8b.
View(college)
rownames(college) <- college[, 1]
View(college)
college_fixed_names <- college[, -1]
View(college_fixed_names)8ci.
summary(college_fixed_names)## Private Apps Accept Enroll
## Length:777 Min. : 81 Min. : 72 Min. : 35
## Class :character 1st Qu.: 776 1st Qu.: 604 1st Qu.: 242
## Mode :character Median : 1558 Median : 1110 Median : 434
## Mean : 3002 Mean : 2019 Mean : 780
## 3rd Qu.: 3624 3rd Qu.: 2424 3rd Qu.: 902
## Max. :48094 Max. :26330 Max. :6392
## Top10perc Top25perc F.Undergrad P.Undergrad
## Min. : 1.00 Min. : 9.0 Min. : 139 Min. : 1.0
## 1st Qu.:15.00 1st Qu.: 41.0 1st Qu.: 992 1st Qu.: 95.0
## Median :23.00 Median : 54.0 Median : 1707 Median : 353.0
## Mean :27.56 Mean : 55.8 Mean : 3700 Mean : 855.3
## 3rd Qu.:35.00 3rd Qu.: 69.0 3rd Qu.: 4005 3rd Qu.: 967.0
## Max. :96.00 Max. :100.0 Max. :31643 Max. :21836.0
## Outstate Room.Board Books Personal
## Min. : 2340 Min. :1780 Min. : 96.0 Min. : 250
## 1st Qu.: 7320 1st Qu.:3597 1st Qu.: 470.0 1st Qu.: 850
## Median : 9990 Median :4200 Median : 500.0 Median :1200
## Mean :10441 Mean :4358 Mean : 549.4 Mean :1341
## 3rd Qu.:12925 3rd Qu.:5050 3rd Qu.: 600.0 3rd Qu.:1700
## Max. :21700 Max. :8124 Max. :2340.0 Max. :6800
## PhD Terminal S.F.Ratio perc.alumni
## Min. : 8.00 Min. : 24.0 Min. : 2.50 Min. : 0.00
## 1st Qu.: 62.00 1st Qu.: 71.0 1st Qu.:11.50 1st Qu.:13.00
## Median : 75.00 Median : 82.0 Median :13.60 Median :21.00
## Mean : 72.66 Mean : 79.7 Mean :14.09 Mean :22.74
## 3rd Qu.: 85.00 3rd Qu.: 92.0 3rd Qu.:16.50 3rd Qu.:31.00
## Max. :103.00 Max. :100.0 Max. :39.80 Max. :64.00
## Expend Grad.Rate
## Min. : 3186 Min. : 10.00
## 1st Qu.: 6751 1st Qu.: 53.00
## Median : 8377 Median : 65.00
## Mean : 9660 Mean : 65.46
## 3rd Qu.:10830 3rd Qu.: 78.00
## Max. :56233 Max. :118.00I decided to change the ‘Private’ field to a factor type in order to avoid trying to execute the pairs() function against a character type value.
8cii.
college_fixed_names$Private = as.factor(college_fixed_names$Private)
firstTen = college_fixed_names[,1:10]
pairs(firstTen)
8ciii.
plot(Outstate ~ Private, data = college_fixed_names)
8civ.
Elite <- rep("No", nrow(college_fixed_names))
Elite[college_fixed_names$Top10perc > 50] <- "Yes"
Elite <- as.factor(Elite)
college_fixed_names <- data.frame(college_fixed_names, Elite)
summary(college_fixed_names)## Private Apps Accept Enroll Top10perc
## No :212 Min. : 81 Min. : 72 Min. : 35 Min. : 1.00
## Yes:565 1st Qu.: 776 1st Qu.: 604 1st Qu.: 242 1st Qu.:15.00
## Median : 1558 Median : 1110 Median : 434 Median :23.00
## Mean : 3002 Mean : 2019 Mean : 780 Mean :27.56
## 3rd Qu.: 3624 3rd Qu.: 2424 3rd Qu.: 902 3rd Qu.:35.00
## Max. :48094 Max. :26330 Max. :6392 Max. :96.00
## Top25perc F.Undergrad P.Undergrad Outstate
## Min. : 9.0 Min. : 139 Min. : 1.0 Min. : 2340
## 1st Qu.: 41.0 1st Qu.: 992 1st Qu.: 95.0 1st Qu.: 7320
## Median : 54.0 Median : 1707 Median : 353.0 Median : 9990
## Mean : 55.8 Mean : 3700 Mean : 855.3 Mean :10441
## 3rd Qu.: 69.0 3rd Qu.: 4005 3rd Qu.: 967.0 3rd Qu.:12925
## Max. :100.0 Max. :31643 Max. :21836.0 Max. :21700
## Room.Board Books Personal PhD
## Min. :1780 Min. : 96.0 Min. : 250 Min. : 8.00
## 1st Qu.:3597 1st Qu.: 470.0 1st Qu.: 850 1st Qu.: 62.00
## Median :4200 Median : 500.0 Median :1200 Median : 75.00
## Mean :4358 Mean : 549.4 Mean :1341 Mean : 72.66
## 3rd Qu.:5050 3rd Qu.: 600.0 3rd Qu.:1700 3rd Qu.: 85.00
## Max. :8124 Max. :2340.0 Max. :6800 Max. :103.00
## Terminal S.F.Ratio perc.alumni Expend
## Min. : 24.0 Min. : 2.50 Min. : 0.00 Min. : 3186
## 1st Qu.: 71.0 1st Qu.:11.50 1st Qu.:13.00 1st Qu.: 6751
## Median : 82.0 Median :13.60 Median :21.00 Median : 8377
## Mean : 79.7 Mean :14.09 Mean :22.74 Mean : 9660
## 3rd Qu.: 92.0 3rd Qu.:16.50 3rd Qu.:31.00 3rd Qu.:10830
## Max. :100.0 Max. :39.80 Max. :64.00 Max. :56233
## Grad.Rate Elite
## Min. : 10.00 No :699
## 1st Qu.: 53.00 Yes: 78
## Median : 65.00
## Mean : 65.46
## 3rd Qu.: 78.00
## Max. :118.00plot(Outstate ~ Elite, data = college_fixed_names)
There are 78 Elite universities
8cv.
par(mfrow = c(2, 2))
hist(college_fixed_names$Room.Board)
hist(college_fixed_names$Outstate)
hist(college_fixed_names$PhD)
hist(college_fixed_names$Grad.Rate)
hist(college_fixed_names$Room.Board, breaks = 20)
hist(college_fixed_names$Outstate, breaks = 30)
hist(college_fixed_names$PhD, breaks = 15)
hist(college_fixed_names$Grad.Rate, breaks = 25)
hist(college_fixed_names$Room.Board, breaks = 8)
hist(college_fixed_names$Outstate, breaks = 5)
hist(college_fixed_names$PhD, breaks = 4)
hist(college_fixed_names$Grad.Rate, breaks = 10)
8cvi. Summary/Additional findings: - The colleges appear to have a lower average enrollment rate when compared to their average acceptance and average applications values. - There is an outlier in the Private school data that claims to have a graduation rate of 118% which is impossible. (Casenovia College) - It also appears that many of the schools with high percentages of students who graduated in the top 10% of their high school and top 25% of their high school are prestigious/Ivy League schools. - The Harvey Mudd College appears to have the highest representation of top 10% and top 25% in their new student rankings - It also appears that private universities have a higher average graduation rate then public universities.
# Question: How many students in the Top 10 or 25% from their highs school were
#accepted to private schools?
summary(college_fixed_names$Accept)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 72 604 1110 2019 2424 26330summary(college_fixed_names$Apps)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 81 776 1558 3002 3624 48094summary(college_fixed_names$Enroll)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 35 242 434 780 902 6392range(college_fixed_names$Grad.Rate)## [1] 10 118range(college_fixed_names$Top10perc)## [1] 1 96range(college_fixed_names$Top25perc)## [1] 9 100Top10Following <- college_fixed_names[order(college_fixed_names$Top10perc, decreasing = TRUE), ][1:15, ]
View(Top10Following)
Top25Following <- college_fixed_names[order(college_fixed_names$Top25perc, decreasing = TRUE), ][1:15, ]
View(Top25Following)
GradRate <- college_fixed_names[order(college_fixed_names$Grad.Rate, decreasing = TRUE), ][1:50, ]
View(GradRate)
# Do private schools have a higher rate of graduation
plot(college_fixed_names$Private, college_fixed_names$Grad.Rate,
main = "Graduation Rate Public VS Graduation Rate Private",
xlab = "Is the university a private university?",
ylab = "Graduation rate")
Question 9
auto=read.csv("~/Grad School/Prediction Statistics/Module 2/Auto.csv", na.strings='?')
dim(auto)## [1] 397 9cleanAuto=na.omit(auto)
dim(cleanAuto)## [1] 392 9str(cleanAuto)## 'data.frame': 392 obs. of 9 variables:
## $ mpg : num 18 15 18 16 17 15 14 14 14 15 ...
## $ cylinders : int 8 8 8 8 8 8 8 8 8 8 ...
## $ displacement: num 307 350 318 304 302 429 454 440 455 390 ...
## $ horsepower : int 130 165 150 150 140 198 220 215 225 190 ...
## $ weight : int 3504 3693 3436 3433 3449 4341 4354 4312 4425 3850 ...
## $ acceleration: num 12 11.5 11 12 10.5 10 9 8.5 10 8.5 ...
## $ year : int 70 70 70 70 70 70 70 70 70 70 ...
## $ origin : int 1 1 1 1 1 1 1 1 1 1 ...
## $ name : chr "chevrolet chevelle malibu" "buick skylark 320" "plymouth satellite" "amc rebel sst" ...
## - attr(*, "na.action")= 'omit' Named int [1:5] 33 127 331 337 355
## ..- attr(*, "names")= chr [1:5] "33" "127" "331" "337" ...dataToPlayWith <- data.frame(cleanAuto)9a. After loading the data and removing all null values,initially MPG, Cylinders, Displacement, Horsepower, Weight, Acceleration, Year, and Origin are quantitative.
The only qualitative predictor is name.
I did decide to change ‘cylinders’, ‘year’, and ‘origin’ to factor types.
dataToPlayWith$cylinders <- as.factor(dataToPlayWith$cylinders)
dataToPlayWith$year <- as.factor(dataToPlayWith$year)
dataToPlayWith$origin <- as.factor(dataToPlayWith$origin)9b. Ranges
range(dataToPlayWith$mpg) ## [1] 9.0 46.6range(dataToPlayWith$displacement) ## [1] 68 455range(dataToPlayWith$horsepower) ## [1] 46 230range(dataToPlayWith$weight) ## [1] 1613 5140range(dataToPlayWith$acceleration) ## [1] 8.0 24.89c. Standard Deviations
sd(dataToPlayWith$mpg)## [1] 7.805007sd(dataToPlayWith$displacement)## [1] 104.644sd(dataToPlayWith$horsepower)## [1] 38.49116sd(dataToPlayWith$weight) ## [1] 849.4026sd(dataToPlayWith$acceleration)## [1] 2.758864Means
mean(dataToPlayWith$mpg)## [1] 23.44592mean(dataToPlayWith$displacement)## [1] 194.412mean(dataToPlayWith$horsepower)## [1] 104.4694mean(dataToPlayWith$weight) ## [1] 2977.584mean(dataToPlayWith$acceleration)## [1] 15.541339d.
View(dataToPlayWith)
dataToPlayWithDrop <- dataToPlayWith[-(10:84), ]
View(dataToPlayWithDrop)Means:
mean(dataToPlayWithDrop$mpg)## [1] 24.36845mean(dataToPlayWithDrop$displacement)## [1] 187.7539mean(dataToPlayWithDrop$horsepower)## [1] 100.9558mean(dataToPlayWithDrop$weight)## [1] 2939.644mean(dataToPlayWithDrop$acceleration)## [1] 15.7183Standard Deviations:
sd(dataToPlayWithDrop$mpg)## [1] 7.880898sd(dataToPlayWithDrop$displacement)## [1] 99.93949sd(dataToPlayWithDrop$horsepower)## [1] 35.89557sd(dataToPlayWithDrop$weight)## [1] 812.6496sd(dataToPlayWithDrop$acceleration)## [1] 2.693813Ranges:
range(dataToPlayWithDrop$mpg)## [1] 11.0 46.6range(dataToPlayWithDrop$displacement)## [1] 68 455range(dataToPlayWithDrop$horsepower)## [1] 46 230range(dataToPlayWithDrop$weight)## [1] 1649 4997range(dataToPlayWithDrop$acceleration)## [1] 8.5 24.89e. - In Figure 1, it appears that as horsepower increases, mpg decreases - In Figure 2, it appears that as horsepower increases, weight increases as well. - In Figure 3, it appears that as the cars become more recent, there is a decrease in the amount of horsepower the vehicles possess.
plot(dataToPlayWithDrop$horsepower, dataToPlayWithDrop$mpg,
main = "Figure 1",
xlab = "Horsepower",
ylab = "MPG")
plot(dataToPlayWithDrop$horsepower, dataToPlayWithDrop$weight,
main = "Figure 2",
xlab = "Horsepower",
ylab = "Weight")
plot(dataToPlayWithDrop$year, dataToPlayWithDrop$horsepower,
main = "Figure 3",
xlab = "Year Made",
ylab = "Horespower")
Yes, the plot showing the relationship between horsepower and mpg
(Figure 4) indicates that there is an inverse relationship. (As one
increases, the other decreases).
I made 2 additional plots (MPG vs. Year) & (MPG vs Cylinders).
Figure 5 shows that as the vehicles get newer, the MPG increases.
Figure 6 shows that vehicles with 4 & 5 cylinders, on average, have better MPGs then those vehicles with a different number of cylinders.
9f.
plot(dataToPlayWithDrop$horsepower, dataToPlayWithDrop$mpg,
main = "Figure 4",
xlab = "Horsepower",
ylab = "MPG")
plot(dataToPlayWithDrop$year, dataToPlayWithDrop$mpg,
main = "Figure 5",
xlab = "Year",
ylab = "MPG")
plot(dataToPlayWithDrop$cylinders, dataToPlayWithDrop$mpg,
main = "Figure 6",
xlab = "Cylinders",
ylab = "MPG")
Question 10 I installed the Boston data package.
install.packages("ISLR2")
Boston <- ISLR2::Boston
str(Boston)## 'data.frame': 506 obs. of 13 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 ...
## $ 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 ...There are 506 rows and 13 columns. Each row represents a census tract taken from a suburb in Boston. Each column represents a particular field that was recorded in the suburb (such as per capita crime rate by town and average number of rooms per dwelling.)
10b. - For 10B Fig 1, it can be assumed that as the proportion of non-retail business acres in a tract increases, so too does the concentration of nitrogen oxide. - For 10B Fig 2, the greatest concentration of high values for the proportions of residential land zoned for lots over 25,000 sq.ft.appears to occur for dwelling places with 6 to 7 rooms. - For 10B Fig 3, as the median value of owner-occupied homes decreases, the per capita crime rate increases.
firstTenBoston = Boston[,1:13]
pairs(firstTenBoston)
View(Boston)
plot(Boston$indus, Boston$nox,
xlab = "Proportion on non-retail business acres",
ylab = "Nitrogen oxides concentration",
main = "10B Fig 1")
plot(Boston$rm, Boston$zn,
xlab = "Average number of rooms per dwelling",
ylab = "proportion of residential land zoned for lots over 25000 sq. ft.",
main = "10B Fig 2")
plot(Boston$medv, Boston$crim,
xlab = "Median value of owner occupied homes",
ylab = "Per capita crime rate",
main = "10B Fig 3")
10c.
fit <- lm(crim~zn+indus+chas+nox+rm+age+dis+rad+tax+ptratio+lstat+medv, data=Boston)
summary(fit)##
## Call:
## lm(formula = crim ~ zn + indus + chas + nox + rm + age + dis +
## rad + tax + ptratio + lstat + medv, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.534 -2.248 -0.348 1.087 73.923
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.7783938 7.0818258 1.946 0.052271 .
## zn 0.0457100 0.0187903 2.433 0.015344 *
## indus -0.0583501 0.0836351 -0.698 0.485709
## chas -0.8253776 1.1833963 -0.697 0.485841
## nox -9.9575865 5.2898242 -1.882 0.060370 .
## rm 0.6289107 0.6070924 1.036 0.300738
## age -0.0008483 0.0179482 -0.047 0.962323
## dis -1.0122467 0.2824676 -3.584 0.000373 ***
## rad 0.6124653 0.0875358 6.997 8.59e-12 ***
## tax -0.0037756 0.0051723 -0.730 0.465757
## ptratio -0.3040728 0.1863598 -1.632 0.103393
## lstat 0.1388006 0.0757213 1.833 0.067398 .
## medv -0.2200564 0.0598240 -3.678 0.000261 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.46 on 493 degrees of freedom
## Multiple R-squared: 0.4493, Adjusted R-squared: 0.4359
## F-statistic: 33.52 on 12 and 493 DF, p-value: < 2.2e-16From the table above, ‘zn’, ‘dis’, ‘rad’, and ‘medv’ are significant predictors of ‘crim’. \(crim = (zn)0.0457100 - 1.0122467(dis) + 0.6124653(rad) - 0.2200564(medv)\)
For every 1% increase for the value of ‘zn’, crim is expected to increase by 0.046 in per capita crime rate. For every increase by 1 for the value of ‘dis’, crim is expected to decrease by 1.012 in per capita crime rate. For every increase by 1 for the value of ‘rad’, crim is expected to increase by 0.612 in per capita crime rate. For every $1000 increase for the value of ‘medv’, crim is expected to decrease by 0.220 in per capita crime rate.
10d. I decided to pull the top 50 values for ‘crim’ in the data set.
The highest recorded value for ‘crim’ is 88.97620 for census tract 381.
Of the 506 records, only 54 appear to have values greater then 10.
88.97620 is still extremely high compared to the lowest value of 0.00632.
Boston[order(Boston$crim, decreasing = TRUE), ][1:50, ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 381 88.9762 0 18.1 0 0.671 6.968 91.9 1.4165 24 666 20.2 17.21 10.4
## 419 73.5341 0 18.1 0 0.679 5.957 100.0 1.8026 24 666 20.2 20.62 8.8
## 406 67.9208 0 18.1 0 0.693 5.683 100.0 1.4254 24 666 20.2 22.98 5.0
## 411 51.1358 0 18.1 0 0.597 5.757 100.0 1.4130 24 666 20.2 10.11 15.0
## 415 45.7461 0 18.1 0 0.693 4.519 100.0 1.6582 24 666 20.2 36.98 7.0
## 405 41.5292 0 18.1 0 0.693 5.531 85.4 1.6074 24 666 20.2 27.38 8.5
## 399 38.3518 0 18.1 0 0.693 5.453 100.0 1.4896 24 666 20.2 30.59 5.0
## 428 37.6619 0 18.1 0 0.679 6.202 78.7 1.8629 24 666 20.2 14.52 10.9
## 414 28.6558 0 18.1 0 0.597 5.155 100.0 1.5894 24 666 20.2 20.08 16.3
## 418 25.9406 0 18.1 0 0.679 5.304 89.1 1.6475 24 666 20.2 26.64 10.4
## 401 25.0461 0 18.1 0 0.693 5.987 100.0 1.5888 24 666 20.2 26.77 5.6
## 404 24.8017 0 18.1 0 0.693 5.349 96.0 1.7028 24 666 20.2 19.77 8.3
## 387 24.3938 0 18.1 0 0.700 4.652 100.0 1.4672 24 666 20.2 28.28 10.5
## 379 23.6482 0 18.1 0 0.671 6.380 96.2 1.3861 24 666 20.2 23.69 13.1
## 388 22.5971 0 18.1 0 0.700 5.000 89.5 1.5184 24 666 20.2 31.99 7.4
## 441 22.0511 0 18.1 0 0.740 5.818 92.4 1.8662 24 666 20.2 22.11 10.5
## 407 20.7162 0 18.1 0 0.659 4.138 100.0 1.1781 24 666 20.2 23.34 11.9
## 385 20.0849 0 18.1 0 0.700 4.368 91.2 1.4395 24 666 20.2 30.63 8.8
## 376 19.6091 0 18.1 0 0.671 7.313 97.9 1.3163 24 666 20.2 13.44 15.0
## 413 18.8110 0 18.1 0 0.597 4.628 100.0 1.5539 24 666 20.2 34.37 17.9
## 375 18.4982 0 18.1 0 0.668 4.138 100.0 1.1370 24 666 20.2 37.97 13.8
## 416 18.0846 0 18.1 0 0.679 6.434 100.0 1.8347 24 666 20.2 29.05 7.2
## 380 17.8667 0 18.1 0 0.671 6.223 100.0 1.3861 24 666 20.2 21.78 10.2
## 386 16.8118 0 18.1 0 0.700 5.277 98.1 1.4261 24 666 20.2 30.81 7.2
## 382 15.8744 0 18.1 0 0.671 6.545 99.1 1.5192 24 666 20.2 21.08 10.9
## 426 15.8603 0 18.1 0 0.679 5.896 95.4 1.9096 24 666 20.2 24.39 8.3
## 469 15.5757 0 18.1 0 0.580 5.926 71.0 2.9084 24 666 20.2 18.13 19.1
## 377 15.2880 0 18.1 0 0.671 6.649 93.3 1.3449 24 666 20.2 23.24 13.9
## 438 15.1772 0 18.1 0 0.740 6.152 100.0 1.9142 24 666 20.2 26.45 8.7
## 478 15.0234 0 18.1 0 0.614 5.304 97.3 2.1007 24 666 20.2 24.91 12.0
## 410 14.4383 0 18.1 0 0.597 6.852 100.0 1.4655 24 666 20.2 19.78 27.5
## 437 14.4208 0 18.1 0 0.740 6.461 93.3 2.0026 24 666 20.2 18.05 9.6
## 389 14.3337 0 18.1 0 0.700 4.880 100.0 1.5895 24 666 20.2 30.62 10.2
## 480 14.3337 0 18.1 0 0.614 6.229 88.0 1.9512 24 666 20.2 13.11 21.4
## 402 14.2362 0 18.1 0 0.693 6.343 100.0 1.5741 24 666 20.2 20.32 7.2
## 412 14.0507 0 18.1 0 0.597 6.657 100.0 1.5275 24 666 20.2 21.22 17.2
## 435 13.9134 0 18.1 0 0.713 6.208 95.0 2.2222 24 666 20.2 15.17 11.7
## 439 13.6781 0 18.1 0 0.740 5.935 87.9 1.8206 24 666 20.2 34.02 8.4
## 368 13.5222 0 18.1 0 0.631 3.863 100.0 1.5106 24 666 20.2 13.33 23.1
## 395 13.3598 0 18.1 0 0.693 5.887 94.7 1.7821 24 666 20.2 16.35 12.7
## 470 13.0751 0 18.1 0 0.580 5.713 56.7 2.8237 24 666 20.2 14.76 20.1
## 445 12.8023 0 18.1 0 0.740 5.854 96.6 1.8956 24 666 20.2 23.79 10.8
## 427 12.2472 0 18.1 0 0.584 5.837 59.7 1.9976 24 666 20.2 15.69 10.2
## 423 12.0482 0 18.1 0 0.614 5.648 87.6 1.9512 24 666 20.2 14.10 20.8
## 408 11.9511 0 18.1 0 0.659 5.608 100.0 1.2852 24 666 20.2 12.13 27.9
## 420 11.8123 0 18.1 0 0.718 6.824 76.5 1.7940 24 666 20.2 22.74 8.4
## 393 11.5779 0 18.1 0 0.700 5.036 97.0 1.7700 24 666 20.2 25.68 9.7
## 436 11.1604 0 18.1 0 0.740 6.629 94.6 2.1247 24 666 20.2 23.27 13.4
## 374 11.1081 0 18.1 0 0.668 4.906 100.0 1.1742 24 666 20.2 34.77 13.8
## 421 11.0874 0 18.1 0 0.718 6.411 100.0 1.8589 24 666 20.2 15.02 16.7range(Boston$crim)## [1] 0.00632 88.97620Boston[Boston$crim > 10, ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 368 13.5222 0 18.1 0 0.631 3.863 100.0 1.5106 24 666 20.2 13.33 23.1
## 374 11.1081 0 18.1 0 0.668 4.906 100.0 1.1742 24 666 20.2 34.77 13.8
## 375 18.4982 0 18.1 0 0.668 4.138 100.0 1.1370 24 666 20.2 37.97 13.8
## 376 19.6091 0 18.1 0 0.671 7.313 97.9 1.3163 24 666 20.2 13.44 15.0
## 377 15.2880 0 18.1 0 0.671 6.649 93.3 1.3449 24 666 20.2 23.24 13.9
## 379 23.6482 0 18.1 0 0.671 6.380 96.2 1.3861 24 666 20.2 23.69 13.1
## 380 17.8667 0 18.1 0 0.671 6.223 100.0 1.3861 24 666 20.2 21.78 10.2
## 381 88.9762 0 18.1 0 0.671 6.968 91.9 1.4165 24 666 20.2 17.21 10.4
## 382 15.8744 0 18.1 0 0.671 6.545 99.1 1.5192 24 666 20.2 21.08 10.9
## 385 20.0849 0 18.1 0 0.700 4.368 91.2 1.4395 24 666 20.2 30.63 8.8
## 386 16.8118 0 18.1 0 0.700 5.277 98.1 1.4261 24 666 20.2 30.81 7.2
## 387 24.3938 0 18.1 0 0.700 4.652 100.0 1.4672 24 666 20.2 28.28 10.5
## 388 22.5971 0 18.1 0 0.700 5.000 89.5 1.5184 24 666 20.2 31.99 7.4
## 389 14.3337 0 18.1 0 0.700 4.880 100.0 1.5895 24 666 20.2 30.62 10.2
## 393 11.5779 0 18.1 0 0.700 5.036 97.0 1.7700 24 666 20.2 25.68 9.7
## 395 13.3598 0 18.1 0 0.693 5.887 94.7 1.7821 24 666 20.2 16.35 12.7
## 399 38.3518 0 18.1 0 0.693 5.453 100.0 1.4896 24 666 20.2 30.59 5.0
## 401 25.0461 0 18.1 0 0.693 5.987 100.0 1.5888 24 666 20.2 26.77 5.6
## 402 14.2362 0 18.1 0 0.693 6.343 100.0 1.5741 24 666 20.2 20.32 7.2
## 404 24.8017 0 18.1 0 0.693 5.349 96.0 1.7028 24 666 20.2 19.77 8.3
## 405 41.5292 0 18.1 0 0.693 5.531 85.4 1.6074 24 666 20.2 27.38 8.5
## 406 67.9208 0 18.1 0 0.693 5.683 100.0 1.4254 24 666 20.2 22.98 5.0
## 407 20.7162 0 18.1 0 0.659 4.138 100.0 1.1781 24 666 20.2 23.34 11.9
## 408 11.9511 0 18.1 0 0.659 5.608 100.0 1.2852 24 666 20.2 12.13 27.9
## 410 14.4383 0 18.1 0 0.597 6.852 100.0 1.4655 24 666 20.2 19.78 27.5
## 411 51.1358 0 18.1 0 0.597 5.757 100.0 1.4130 24 666 20.2 10.11 15.0
## 412 14.0507 0 18.1 0 0.597 6.657 100.0 1.5275 24 666 20.2 21.22 17.2
## 413 18.8110 0 18.1 0 0.597 4.628 100.0 1.5539 24 666 20.2 34.37 17.9
## 414 28.6558 0 18.1 0 0.597 5.155 100.0 1.5894 24 666 20.2 20.08 16.3
## 415 45.7461 0 18.1 0 0.693 4.519 100.0 1.6582 24 666 20.2 36.98 7.0
## 416 18.0846 0 18.1 0 0.679 6.434 100.0 1.8347 24 666 20.2 29.05 7.2
## 417 10.8342 0 18.1 0 0.679 6.782 90.8 1.8195 24 666 20.2 25.79 7.5
## 418 25.9406 0 18.1 0 0.679 5.304 89.1 1.6475 24 666 20.2 26.64 10.4
## 419 73.5341 0 18.1 0 0.679 5.957 100.0 1.8026 24 666 20.2 20.62 8.8
## 420 11.8123 0 18.1 0 0.718 6.824 76.5 1.7940 24 666 20.2 22.74 8.4
## 421 11.0874 0 18.1 0 0.718 6.411 100.0 1.8589 24 666 20.2 15.02 16.7
## 423 12.0482 0 18.1 0 0.614 5.648 87.6 1.9512 24 666 20.2 14.10 20.8
## 426 15.8603 0 18.1 0 0.679 5.896 95.4 1.9096 24 666 20.2 24.39 8.3
## 427 12.2472 0 18.1 0 0.584 5.837 59.7 1.9976 24 666 20.2 15.69 10.2
## 428 37.6619 0 18.1 0 0.679 6.202 78.7 1.8629 24 666 20.2 14.52 10.9
## 432 10.0623 0 18.1 0 0.584 6.833 94.3 2.0882 24 666 20.2 19.69 14.1
## 435 13.9134 0 18.1 0 0.713 6.208 95.0 2.2222 24 666 20.2 15.17 11.7
## 436 11.1604 0 18.1 0 0.740 6.629 94.6 2.1247 24 666 20.2 23.27 13.4
## 437 14.4208 0 18.1 0 0.740 6.461 93.3 2.0026 24 666 20.2 18.05 9.6
## 438 15.1772 0 18.1 0 0.740 6.152 100.0 1.9142 24 666 20.2 26.45 8.7
## 439 13.6781 0 18.1 0 0.740 5.935 87.9 1.8206 24 666 20.2 34.02 8.4
## 441 22.0511 0 18.1 0 0.740 5.818 92.4 1.8662 24 666 20.2 22.11 10.5
## 445 12.8023 0 18.1 0 0.740 5.854 96.6 1.8956 24 666 20.2 23.79 10.8
## 446 10.6718 0 18.1 0 0.740 6.459 94.8 1.9879 24 666 20.2 23.98 11.8
## 469 15.5757 0 18.1 0 0.580 5.926 71.0 2.9084 24 666 20.2 18.13 19.1
## 470 13.0751 0 18.1 0 0.580 5.713 56.7 2.8237 24 666 20.2 14.76 20.1
## 478 15.0234 0 18.1 0 0.614 5.304 97.3 2.1007 24 666 20.2 24.91 12.0
## 479 10.2330 0 18.1 0 0.614 6.185 96.7 2.1705 24 666 20.2 18.03 14.6
## 480 14.3337 0 18.1 0 0.614 6.229 88.0 1.9512 24 666 20.2 13.11 21.4I decided to pull the top 50 values for ‘tax’ in the data set.
The highest recorded value for ‘tax’ is 711. This occurs in census tract 489, 490, 491, 492 & 493.
Of the 506 records, 344 records appear to have a tax rate over $300 per every $10000.
711 is at least 3x more expensive then the lowest tax rate value of 187.
Boston[order(Boston$tax, decreasing = TRUE), ][1:50, ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 489 0.15086 0 27.74 0 0.609 5.454 92.7 1.8209 4 711 20.1 18.06 15.2
## 490 0.18337 0 27.74 0 0.609 5.414 98.3 1.7554 4 711 20.1 23.97 7.0
## 491 0.20746 0 27.74 0 0.609 5.093 98.0 1.8226 4 711 20.1 29.68 8.1
## 492 0.10574 0 27.74 0 0.609 5.983 98.8 1.8681 4 711 20.1 18.07 13.6
## 493 0.11132 0 27.74 0 0.609 5.983 83.5 2.1099 4 711 20.1 13.35 20.1
## 357 8.98296 0 18.10 1 0.770 6.212 97.4 2.1222 24 666 20.2 17.60 17.8
## 358 3.84970 0 18.10 1 0.770 6.395 91.0 2.5052 24 666 20.2 13.27 21.7
## 359 5.20177 0 18.10 1 0.770 6.127 83.4 2.7227 24 666 20.2 11.48 22.7
## 360 4.26131 0 18.10 0 0.770 6.112 81.3 2.5091 24 666 20.2 12.67 22.6
## 361 4.54192 0 18.10 0 0.770 6.398 88.0 2.5182 24 666 20.2 7.79 25.0
## 362 3.83684 0 18.10 0 0.770 6.251 91.1 2.2955 24 666 20.2 14.19 19.9
## 363 3.67822 0 18.10 0 0.770 5.362 96.2 2.1036 24 666 20.2 10.19 20.8
## 364 4.22239 0 18.10 1 0.770 5.803 89.0 1.9047 24 666 20.2 14.64 16.8
## 365 3.47428 0 18.10 1 0.718 8.780 82.9 1.9047 24 666 20.2 5.29 21.9
## 366 4.55587 0 18.10 0 0.718 3.561 87.9 1.6132 24 666 20.2 7.12 27.5
## 367 3.69695 0 18.10 0 0.718 4.963 91.4 1.7523 24 666 20.2 14.00 21.9
## 368 13.52220 0 18.10 0 0.631 3.863 100.0 1.5106 24 666 20.2 13.33 23.1
## 369 4.89822 0 18.10 0 0.631 4.970 100.0 1.3325 24 666 20.2 3.26 50.0
## 370 5.66998 0 18.10 1 0.631 6.683 96.8 1.3567 24 666 20.2 3.73 50.0
## 371 6.53876 0 18.10 1 0.631 7.016 97.5 1.2024 24 666 20.2 2.96 50.0
## 372 9.23230 0 18.10 0 0.631 6.216 100.0 1.1691 24 666 20.2 9.53 50.0
## 373 8.26725 0 18.10 1 0.668 5.875 89.6 1.1296 24 666 20.2 8.88 50.0
## 374 11.10810 0 18.10 0 0.668 4.906 100.0 1.1742 24 666 20.2 34.77 13.8
## 375 18.49820 0 18.10 0 0.668 4.138 100.0 1.1370 24 666 20.2 37.97 13.8
## 376 19.60910 0 18.10 0 0.671 7.313 97.9 1.3163 24 666 20.2 13.44 15.0
## 377 15.28800 0 18.10 0 0.671 6.649 93.3 1.3449 24 666 20.2 23.24 13.9
## 378 9.82349 0 18.10 0 0.671 6.794 98.8 1.3580 24 666 20.2 21.24 13.3
## 379 23.64820 0 18.10 0 0.671 6.380 96.2 1.3861 24 666 20.2 23.69 13.1
## 380 17.86670 0 18.10 0 0.671 6.223 100.0 1.3861 24 666 20.2 21.78 10.2
## 381 88.97620 0 18.10 0 0.671 6.968 91.9 1.4165 24 666 20.2 17.21 10.4
## 382 15.87440 0 18.10 0 0.671 6.545 99.1 1.5192 24 666 20.2 21.08 10.9
## 383 9.18702 0 18.10 0 0.700 5.536 100.0 1.5804 24 666 20.2 23.60 11.3
## 384 7.99248 0 18.10 0 0.700 5.520 100.0 1.5331 24 666 20.2 24.56 12.3
## 385 20.08490 0 18.10 0 0.700 4.368 91.2 1.4395 24 666 20.2 30.63 8.8
## 386 16.81180 0 18.10 0 0.700 5.277 98.1 1.4261 24 666 20.2 30.81 7.2
## 387 24.39380 0 18.10 0 0.700 4.652 100.0 1.4672 24 666 20.2 28.28 10.5
## 388 22.59710 0 18.10 0 0.700 5.000 89.5 1.5184 24 666 20.2 31.99 7.4
## 389 14.33370 0 18.10 0 0.700 4.880 100.0 1.5895 24 666 20.2 30.62 10.2
## 390 8.15174 0 18.10 0 0.700 5.390 98.9 1.7281 24 666 20.2 20.85 11.5
## 391 6.96215 0 18.10 0 0.700 5.713 97.0 1.9265 24 666 20.2 17.11 15.1
## 392 5.29305 0 18.10 0 0.700 6.051 82.5 2.1678 24 666 20.2 18.76 23.2
## 393 11.57790 0 18.10 0 0.700 5.036 97.0 1.7700 24 666 20.2 25.68 9.7
## 394 8.64476 0 18.10 0 0.693 6.193 92.6 1.7912 24 666 20.2 15.17 13.8
## 395 13.35980 0 18.10 0 0.693 5.887 94.7 1.7821 24 666 20.2 16.35 12.7
## 396 8.71675 0 18.10 0 0.693 6.471 98.8 1.7257 24 666 20.2 17.12 13.1
## 397 5.87205 0 18.10 0 0.693 6.405 96.0 1.6768 24 666 20.2 19.37 12.5
## 398 7.67202 0 18.10 0 0.693 5.747 98.9 1.6334 24 666 20.2 19.92 8.5
## 399 38.35180 0 18.10 0 0.693 5.453 100.0 1.4896 24 666 20.2 30.59 5.0
## 400 9.91655 0 18.10 0 0.693 5.852 77.8 1.5004 24 666 20.2 29.97 6.3
## 401 25.04610 0 18.10 0 0.693 5.987 100.0 1.5888 24 666 20.2 26.77 5.6range(Boston$tax)## [1] 187 711Boston[Boston$tax == 711, ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 489 0.15086 0 27.74 0 0.609 5.454 92.7 1.8209 4 711 20.1 18.06 15.2
## 490 0.18337 0 27.74 0 0.609 5.414 98.3 1.7554 4 711 20.1 23.97 7.0
## 491 0.20746 0 27.74 0 0.609 5.093 98.0 1.8226 4 711 20.1 29.68 8.1
## 492 0.10574 0 27.74 0 0.609 5.983 98.8 1.8681 4 711 20.1 18.07 13.6
## 493 0.11132 0 27.74 0 0.609 5.983 83.5 2.1099 4 711 20.1 13.35 20.1Boston[Boston$tax > 300, ]## crim zn indus chas nox rm age dis rad tax ptratio lstat
## 7 0.08829 12.5 7.87 0 0.5240 6.012 66.6 5.5605 5 311 15.2 12.43
## 8 0.14455 12.5 7.87 0 0.5240 6.172 96.1 5.9505 5 311 15.2 19.15
## 9 0.21124 12.5 7.87 0 0.5240 5.631 100.0 6.0821 5 311 15.2 29.93
## 10 0.17004 12.5 7.87 0 0.5240 6.004 85.9 6.5921 5 311 15.2 17.10
## 11 0.22489 12.5 7.87 0 0.5240 6.377 94.3 6.3467 5 311 15.2 20.45
## 12 0.11747 12.5 7.87 0 0.5240 6.009 82.9 6.2267 5 311 15.2 13.27
## 13 0.09378 12.5 7.87 0 0.5240 5.889 39.0 5.4509 5 311 15.2 15.71
## 14 0.62976 0.0 8.14 0 0.5380 5.949 61.8 4.7075 4 307 21.0 8.26
## 15 0.63796 0.0 8.14 0 0.5380 6.096 84.5 4.4619 4 307 21.0 10.26
## 16 0.62739 0.0 8.14 0 0.5380 5.834 56.5 4.4986 4 307 21.0 8.47
## 17 1.05393 0.0 8.14 0 0.5380 5.935 29.3 4.4986 4 307 21.0 6.58
## 18 0.78420 0.0 8.14 0 0.5380 5.990 81.7 4.2579 4 307 21.0 14.67
## 19 0.80271 0.0 8.14 0 0.5380 5.456 36.6 3.7965 4 307 21.0 11.69
## 20 0.72580 0.0 8.14 0 0.5380 5.727 69.5 3.7965 4 307 21.0 11.28
## 21 1.25179 0.0 8.14 0 0.5380 5.570 98.1 3.7979 4 307 21.0 21.02
## 22 0.85204 0.0 8.14 0 0.5380 5.965 89.2 4.0123 4 307 21.0 13.83
## 23 1.23247 0.0 8.14 0 0.5380 6.142 91.7 3.9769 4 307 21.0 18.72
## 24 0.98843 0.0 8.14 0 0.5380 5.813 100.0 4.0952 4 307 21.0 19.88
## 25 0.75026 0.0 8.14 0 0.5380 5.924 94.1 4.3996 4 307 21.0 16.30
## 26 0.84054 0.0 8.14 0 0.5380 5.599 85.7 4.4546 4 307 21.0 16.51
## 27 0.67191 0.0 8.14 0 0.5380 5.813 90.3 4.6820 4 307 21.0 14.81
## 28 0.95577 0.0 8.14 0 0.5380 6.047 88.8 4.4534 4 307 21.0 17.28
## 29 0.77299 0.0 8.14 0 0.5380 6.495 94.4 4.4547 4 307 21.0 12.80
## 30 1.00245 0.0 8.14 0 0.5380 6.674 87.3 4.2390 4 307 21.0 11.98
## 31 1.13081 0.0 8.14 0 0.5380 5.713 94.1 4.2330 4 307 21.0 22.60
## 32 1.35472 0.0 8.14 0 0.5380 6.072 100.0 4.1750 4 307 21.0 13.04
## 33 1.38799 0.0 8.14 0 0.5380 5.950 82.0 3.9900 4 307 21.0 27.71
## 34 1.15172 0.0 8.14 0 0.5380 5.701 95.0 3.7872 4 307 21.0 18.35
## 35 1.61282 0.0 8.14 0 0.5380 6.096 96.9 3.7598 4 307 21.0 20.34
## 55 0.01360 75.0 4.00 0 0.4100 5.888 47.6 7.3197 3 469 21.1 14.80
## 57 0.02055 85.0 0.74 0 0.4100 6.383 35.7 9.1876 2 313 17.3 5.77
## 66 0.03584 80.0 3.37 0 0.3980 6.290 17.8 6.6115 4 337 16.1 4.67
## 67 0.04379 80.0 3.37 0 0.3980 5.787 31.1 6.6115 4 337 16.1 10.24
## 68 0.05789 12.5 6.07 0 0.4090 5.878 21.4 6.4980 4 345 18.9 8.10
## 69 0.13554 12.5 6.07 0 0.4090 5.594 36.8 6.4980 4 345 18.9 13.09
## 70 0.12816 12.5 6.07 0 0.4090 5.885 33.0 6.4980 4 345 18.9 8.79
## 71 0.08826 0.0 10.81 0 0.4130 6.417 6.6 5.2873 4 305 19.2 6.72
## 72 0.15876 0.0 10.81 0 0.4130 5.961 17.5 5.2873 4 305 19.2 9.88
## 73 0.09164 0.0 10.81 0 0.4130 6.065 7.8 5.2873 4 305 19.2 5.52
## 74 0.19539 0.0 10.81 0 0.4130 6.245 6.2 5.2873 4 305 19.2 7.54
## 75 0.07896 0.0 12.83 0 0.4370 6.273 6.0 4.2515 5 398 18.7 6.78
## 76 0.09512 0.0 12.83 0 0.4370 6.286 45.0 4.5026 5 398 18.7 8.94
## 77 0.10153 0.0 12.83 0 0.4370 6.279 74.5 4.0522 5 398 18.7 11.97
## 78 0.08707 0.0 12.83 0 0.4370 6.140 45.8 4.0905 5 398 18.7 10.27
## 79 0.05646 0.0 12.83 0 0.4370 6.232 53.7 5.0141 5 398 18.7 12.34
## 80 0.08387 0.0 12.83 0 0.4370 5.874 36.6 4.5026 5 398 18.7 9.10
## 101 0.14866 0.0 8.56 0 0.5200 6.727 79.9 2.7778 5 384 20.9 9.42
## 102 0.11432 0.0 8.56 0 0.5200 6.781 71.3 2.8561 5 384 20.9 7.67
## 103 0.22876 0.0 8.56 0 0.5200 6.405 85.4 2.7147 5 384 20.9 10.63
## 104 0.21161 0.0 8.56 0 0.5200 6.137 87.4 2.7147 5 384 20.9 13.44
## 105 0.13960 0.0 8.56 0 0.5200 6.167 90.0 2.4210 5 384 20.9 12.33
## 106 0.13262 0.0 8.56 0 0.5200 5.851 96.7 2.1069 5 384 20.9 16.47
## 107 0.17120 0.0 8.56 0 0.5200 5.836 91.9 2.2110 5 384 20.9 18.66
## 108 0.13117 0.0 8.56 0 0.5200 6.127 85.2 2.1224 5 384 20.9 14.09
## 109 0.12802 0.0 8.56 0 0.5200 6.474 97.1 2.4329 5 384 20.9 12.27
## 110 0.26363 0.0 8.56 0 0.5200 6.229 91.2 2.5451 5 384 20.9 15.55
## 111 0.10793 0.0 8.56 0 0.5200 6.195 54.4 2.7778 5 384 20.9 13.00
## 112 0.10084 0.0 10.01 0 0.5470 6.715 81.6 2.6775 6 432 17.8 10.16
## 113 0.12329 0.0 10.01 0 0.5470 5.913 92.9 2.3534 6 432 17.8 16.21
## 114 0.22212 0.0 10.01 0 0.5470 6.092 95.4 2.5480 6 432 17.8 17.09
## 115 0.14231 0.0 10.01 0 0.5470 6.254 84.2 2.2565 6 432 17.8 10.45
## 116 0.17134 0.0 10.01 0 0.5470 5.928 88.2 2.4631 6 432 17.8 15.76
## 117 0.13158 0.0 10.01 0 0.5470 6.176 72.5 2.7301 6 432 17.8 12.04
## 118 0.15098 0.0 10.01 0 0.5470 6.021 82.6 2.7474 6 432 17.8 10.30
## 119 0.13058 0.0 10.01 0 0.5470 5.872 73.1 2.4775 6 432 17.8 15.37
## 120 0.14476 0.0 10.01 0 0.5470 5.731 65.2 2.7592 6 432 17.8 13.61
## 128 0.25915 0.0 21.89 0 0.6240 5.693 96.0 1.7883 4 437 21.2 17.19
## 129 0.32543 0.0 21.89 0 0.6240 6.431 98.8 1.8125 4 437 21.2 15.39
## 130 0.88125 0.0 21.89 0 0.6240 5.637 94.7 1.9799 4 437 21.2 18.34
## 131 0.34006 0.0 21.89 0 0.6240 6.458 98.9 2.1185 4 437 21.2 12.60
## 132 1.19294 0.0 21.89 0 0.6240 6.326 97.7 2.2710 4 437 21.2 12.26
## 133 0.59005 0.0 21.89 0 0.6240 6.372 97.9 2.3274 4 437 21.2 11.12
## 134 0.32982 0.0 21.89 0 0.6240 5.822 95.4 2.4699 4 437 21.2 15.03
## 135 0.97617 0.0 21.89 0 0.6240 5.757 98.4 2.3460 4 437 21.2 17.31
## 136 0.55778 0.0 21.89 0 0.6240 6.335 98.2 2.1107 4 437 21.2 16.96
## 137 0.32264 0.0 21.89 0 0.6240 5.942 93.5 1.9669 4 437 21.2 16.90
## 138 0.35233 0.0 21.89 0 0.6240 6.454 98.4 1.8498 4 437 21.2 14.59
## 139 0.24980 0.0 21.89 0 0.6240 5.857 98.2 1.6686 4 437 21.2 21.32
## 140 0.54452 0.0 21.89 0 0.6240 6.151 97.9 1.6687 4 437 21.2 18.46
## 141 0.29090 0.0 21.89 0 0.6240 6.174 93.6 1.6119 4 437 21.2 24.16
## 142 1.62864 0.0 21.89 0 0.6240 5.019 100.0 1.4394 4 437 21.2 34.41
## 143 3.32105 0.0 19.58 1 0.8710 5.403 100.0 1.3216 5 403 14.7 26.82
## 144 4.09740 0.0 19.58 0 0.8710 5.468 100.0 1.4118 5 403 14.7 26.42
## 145 2.77974 0.0 19.58 0 0.8710 4.903 97.8 1.3459 5 403 14.7 29.29
## 146 2.37934 0.0 19.58 0 0.8710 6.130 100.0 1.4191 5 403 14.7 27.80
## 147 2.15505 0.0 19.58 0 0.8710 5.628 100.0 1.5166 5 403 14.7 16.65
## 148 2.36862 0.0 19.58 0 0.8710 4.926 95.7 1.4608 5 403 14.7 29.53
## 149 2.33099 0.0 19.58 0 0.8710 5.186 93.8 1.5296 5 403 14.7 28.32
## 150 2.73397 0.0 19.58 0 0.8710 5.597 94.9 1.5257 5 403 14.7 21.45
## 151 1.65660 0.0 19.58 0 0.8710 6.122 97.3 1.6180 5 403 14.7 14.10
## 152 1.49632 0.0 19.58 0 0.8710 5.404 100.0 1.5916 5 403 14.7 13.28
## 153 1.12658 0.0 19.58 1 0.8710 5.012 88.0 1.6102 5 403 14.7 12.12
## 154 2.14918 0.0 19.58 0 0.8710 5.709 98.5 1.6232 5 403 14.7 15.79
## 155 1.41385 0.0 19.58 1 0.8710 6.129 96.0 1.7494 5 403 14.7 15.12
## 156 3.53501 0.0 19.58 1 0.8710 6.152 82.6 1.7455 5 403 14.7 15.02
## 157 2.44668 0.0 19.58 0 0.8710 5.272 94.0 1.7364 5 403 14.7 16.14
## 158 1.22358 0.0 19.58 0 0.6050 6.943 97.4 1.8773 5 403 14.7 4.59
## 159 1.34284 0.0 19.58 0 0.6050 6.066 100.0 1.7573 5 403 14.7 6.43
## 160 1.42502 0.0 19.58 0 0.8710 6.510 100.0 1.7659 5 403 14.7 7.39
## 161 1.27346 0.0 19.58 1 0.6050 6.250 92.6 1.7984 5 403 14.7 5.50
## 162 1.46336 0.0 19.58 0 0.6050 7.489 90.8 1.9709 5 403 14.7 1.73
## 163 1.83377 0.0 19.58 1 0.6050 7.802 98.2 2.0407 5 403 14.7 1.92
## 164 1.51902 0.0 19.58 1 0.6050 8.375 93.9 2.1620 5 403 14.7 3.32
## 165 2.24236 0.0 19.58 0 0.6050 5.854 91.8 2.4220 5 403 14.7 11.64
## 166 2.92400 0.0 19.58 0 0.6050 6.101 93.0 2.2834 5 403 14.7 9.81
## 167 2.01019 0.0 19.58 0 0.6050 7.929 96.2 2.0459 5 403 14.7 3.70
## 168 1.80028 0.0 19.58 0 0.6050 5.877 79.2 2.4259 5 403 14.7 12.14
## 169 2.30040 0.0 19.58 0 0.6050 6.319 96.1 2.1000 5 403 14.7 11.10
## 170 2.44953 0.0 19.58 0 0.6050 6.402 95.2 2.2625 5 403 14.7 11.32
## 171 1.20742 0.0 19.58 0 0.6050 5.875 94.6 2.4259 5 403 14.7 14.43
## 172 2.31390 0.0 19.58 0 0.6050 5.880 97.3 2.3887 5 403 14.7 12.03
## 188 0.07875 45.0 3.44 0 0.4370 6.782 41.1 3.7886 5 398 15.2 6.68
## 189 0.12579 45.0 3.44 0 0.4370 6.556 29.1 4.5667 5 398 15.2 4.56
## 190 0.08370 45.0 3.44 0 0.4370 7.185 38.9 4.5667 5 398 15.2 5.39
## 191 0.09068 45.0 3.44 0 0.4370 6.951 21.5 6.4798 5 398 15.2 5.10
## 192 0.06911 45.0 3.44 0 0.4370 6.739 30.8 6.4798 5 398 15.2 4.69
## 193 0.08664 45.0 3.44 0 0.4370 7.178 26.3 6.4798 5 398 15.2 2.87
## 197 0.04011 80.0 1.52 0 0.4040 7.287 34.1 7.3090 2 329 12.6 4.08
## 198 0.04666 80.0 1.52 0 0.4040 7.107 36.6 7.3090 2 329 12.6 8.61
## 199 0.03768 80.0 1.52 0 0.4040 7.274 38.3 7.3090 2 329 12.6 6.62
## 200 0.03150 95.0 1.47 0 0.4030 6.975 15.3 7.6534 3 402 17.0 4.56
## 201 0.01778 95.0 1.47 0 0.4030 7.135 13.9 7.6534 3 402 17.0 4.45
## 202 0.03445 82.5 2.03 0 0.4150 6.162 38.4 6.2700 2 348 14.7 7.43
## 203 0.02177 82.5 2.03 0 0.4150 7.610 15.7 6.2700 2 348 14.7 3.11
## 221 0.35809 0.0 6.20 1 0.5070 6.951 88.5 2.8617 8 307 17.4 9.71
## 222 0.40771 0.0 6.20 1 0.5070 6.164 91.3 3.0480 8 307 17.4 21.46
## 223 0.62356 0.0 6.20 1 0.5070 6.879 77.7 3.2721 8 307 17.4 9.93
## 224 0.61470 0.0 6.20 0 0.5070 6.618 80.8 3.2721 8 307 17.4 7.60
## 225 0.31533 0.0 6.20 0 0.5040 8.266 78.3 2.8944 8 307 17.4 4.14
## 226 0.52693 0.0 6.20 0 0.5040 8.725 83.0 2.8944 8 307 17.4 4.63
## 227 0.38214 0.0 6.20 0 0.5040 8.040 86.5 3.2157 8 307 17.4 3.13
## 228 0.41238 0.0 6.20 0 0.5040 7.163 79.9 3.2157 8 307 17.4 6.36
## 229 0.29819 0.0 6.20 0 0.5040 7.686 17.0 3.3751 8 307 17.4 3.92
## 230 0.44178 0.0 6.20 0 0.5040 6.552 21.4 3.3751 8 307 17.4 3.76
## 231 0.53700 0.0 6.20 0 0.5040 5.981 68.1 3.6715 8 307 17.4 11.65
## 232 0.46296 0.0 6.20 0 0.5040 7.412 76.9 3.6715 8 307 17.4 5.25
## 233 0.57529 0.0 6.20 0 0.5070 8.337 73.3 3.8384 8 307 17.4 2.47
## 234 0.33147 0.0 6.20 0 0.5070 8.247 70.4 3.6519 8 307 17.4 3.95
## 235 0.44791 0.0 6.20 1 0.5070 6.726 66.5 3.6519 8 307 17.4 8.05
## 236 0.33045 0.0 6.20 0 0.5070 6.086 61.5 3.6519 8 307 17.4 10.88
## 237 0.52058 0.0 6.20 1 0.5070 6.631 76.5 4.1480 8 307 17.4 9.54
## 238 0.51183 0.0 6.20 0 0.5070 7.358 71.6 4.1480 8 307 17.4 4.73
## 245 0.20608 22.0 5.86 0 0.4310 5.593 76.5 7.9549 7 330 19.1 12.50
## 246 0.19133 22.0 5.86 0 0.4310 5.605 70.2 7.9549 7 330 19.1 18.46
## 247 0.33983 22.0 5.86 0 0.4310 6.108 34.9 8.0555 7 330 19.1 9.16
## 248 0.19657 22.0 5.86 0 0.4310 6.226 79.2 8.0555 7 330 19.1 10.15
## 249 0.16439 22.0 5.86 0 0.4310 6.433 49.1 7.8265 7 330 19.1 9.52
## 250 0.19073 22.0 5.86 0 0.4310 6.718 17.5 7.8265 7 330 19.1 6.56
## 251 0.14030 22.0 5.86 0 0.4310 6.487 13.0 7.3967 7 330 19.1 5.90
## 252 0.21409 22.0 5.86 0 0.4310 6.438 8.9 7.3967 7 330 19.1 3.59
## 253 0.08221 22.0 5.86 0 0.4310 6.957 6.8 8.9067 7 330 19.1 3.53
## 254 0.36894 22.0 5.86 0 0.4310 8.259 8.4 8.9067 7 330 19.1 3.54
## 255 0.04819 80.0 3.64 0 0.3920 6.108 32.0 9.2203 1 315 16.4 6.57
## 256 0.03548 80.0 3.64 0 0.3920 5.876 19.1 9.2203 1 315 16.4 9.25
## 299 0.06466 70.0 2.24 0 0.4000 6.345 20.1 7.8278 5 358 14.8 4.97
## 300 0.05561 70.0 2.24 0 0.4000 7.041 10.0 7.8278 5 358 14.8 4.74
## 301 0.04417 70.0 2.24 0 0.4000 6.871 47.4 7.8278 5 358 14.8 6.07
## 302 0.03537 34.0 6.09 0 0.4330 6.590 40.4 5.4917 7 329 16.1 9.50
## 303 0.09266 34.0 6.09 0 0.4330 6.495 18.4 5.4917 7 329 16.1 8.67
## 304 0.10000 34.0 6.09 0 0.4330 6.982 17.7 5.4917 7 329 16.1 4.86
## 309 0.49298 0.0 9.90 0 0.5440 6.635 82.5 3.3175 4 304 18.4 4.54
## 310 0.34940 0.0 9.90 0 0.5440 5.972 76.7 3.1025 4 304 18.4 9.97
## 311 2.63548 0.0 9.90 0 0.5440 4.973 37.8 2.5194 4 304 18.4 12.64
## 312 0.79041 0.0 9.90 0 0.5440 6.122 52.8 2.6403 4 304 18.4 5.98
## 313 0.26169 0.0 9.90 0 0.5440 6.023 90.4 2.8340 4 304 18.4 11.72
## 314 0.26938 0.0 9.90 0 0.5440 6.266 82.8 3.2628 4 304 18.4 7.90
## 315 0.36920 0.0 9.90 0 0.5440 6.567 87.3 3.6023 4 304 18.4 9.28
## 316 0.25356 0.0 9.90 0 0.5440 5.705 77.7 3.9450 4 304 18.4 11.50
## 317 0.31827 0.0 9.90 0 0.5440 5.914 83.2 3.9986 4 304 18.4 18.33
## 318 0.24522 0.0 9.90 0 0.5440 5.782 71.7 4.0317 4 304 18.4 15.94
## 319 0.40202 0.0 9.90 0 0.5440 6.382 67.2 3.5325 4 304 18.4 10.36
## 320 0.47547 0.0 9.90 0 0.5440 6.113 58.8 4.0019 4 304 18.4 12.73
## 329 0.06617 0.0 3.24 0 0.4600 5.868 25.8 5.2146 4 430 16.9 9.97
## 330 0.06724 0.0 3.24 0 0.4600 6.333 17.2 5.2146 4 430 16.9 7.34
## 331 0.04544 0.0 3.24 0 0.4600 6.144 32.2 5.8736 4 430 16.9 9.09
## 332 0.05023 35.0 6.06 0 0.4379 5.706 28.4 6.6407 1 304 16.9 12.43
## 333 0.03466 35.0 6.06 0 0.4379 6.031 23.3 6.6407 1 304 16.9 7.83
## 343 0.02498 0.0 1.89 0 0.5180 6.540 59.7 6.2669 1 422 15.9 8.65
## 344 0.02543 55.0 3.78 0 0.4840 6.696 56.4 5.7321 5 370 17.6 7.18
## 345 0.03049 55.0 3.78 0 0.4840 6.874 28.1 6.4654 5 370 17.6 4.61
## 346 0.03113 0.0 4.39 0 0.4420 6.014 48.5 8.0136 3 352 18.8 10.53
## 347 0.06162 0.0 4.39 0 0.4420 5.898 52.3 8.0136 3 352 18.8 12.67
## 348 0.01870 85.0 4.15 0 0.4290 6.516 27.7 8.5353 4 351 17.9 6.36
## 350 0.02899 40.0 1.25 0 0.4290 6.939 34.5 8.7921 1 335 19.7 5.89
## 351 0.06211 40.0 1.25 0 0.4290 6.490 44.4 8.7921 1 335 19.7 5.98
## 352 0.07950 60.0 1.69 0 0.4110 6.579 35.9 10.7103 4 411 18.3 5.49
## 353 0.07244 60.0 1.69 0 0.4110 5.884 18.5 10.7103 4 411 18.3 7.79
## 355 0.04301 80.0 1.91 0 0.4130 5.663 21.9 10.5857 4 334 22.0 8.05
## 356 0.10659 80.0 1.91 0 0.4130 5.936 19.5 10.5857 4 334 22.0 5.57
## 357 8.98296 0.0 18.10 1 0.7700 6.212 97.4 2.1222 24 666 20.2 17.60
## 358 3.84970 0.0 18.10 1 0.7700 6.395 91.0 2.5052 24 666 20.2 13.27
## 359 5.20177 0.0 18.10 1 0.7700 6.127 83.4 2.7227 24 666 20.2 11.48
## 360 4.26131 0.0 18.10 0 0.7700 6.112 81.3 2.5091 24 666 20.2 12.67
## 361 4.54192 0.0 18.10 0 0.7700 6.398 88.0 2.5182 24 666 20.2 7.79
## 362 3.83684 0.0 18.10 0 0.7700 6.251 91.1 2.2955 24 666 20.2 14.19
## 363 3.67822 0.0 18.10 0 0.7700 5.362 96.2 2.1036 24 666 20.2 10.19
## 364 4.22239 0.0 18.10 1 0.7700 5.803 89.0 1.9047 24 666 20.2 14.64
## 365 3.47428 0.0 18.10 1 0.7180 8.780 82.9 1.9047 24 666 20.2 5.29
## 366 4.55587 0.0 18.10 0 0.7180 3.561 87.9 1.6132 24 666 20.2 7.12
## 367 3.69695 0.0 18.10 0 0.7180 4.963 91.4 1.7523 24 666 20.2 14.00
## 368 13.52220 0.0 18.10 0 0.6310 3.863 100.0 1.5106 24 666 20.2 13.33
## 369 4.89822 0.0 18.10 0 0.6310 4.970 100.0 1.3325 24 666 20.2 3.26
## 370 5.66998 0.0 18.10 1 0.6310 6.683 96.8 1.3567 24 666 20.2 3.73
## 371 6.53876 0.0 18.10 1 0.6310 7.016 97.5 1.2024 24 666 20.2 2.96
## 372 9.23230 0.0 18.10 0 0.6310 6.216 100.0 1.1691 24 666 20.2 9.53
## 373 8.26725 0.0 18.10 1 0.6680 5.875 89.6 1.1296 24 666 20.2 8.88
## 374 11.10810 0.0 18.10 0 0.6680 4.906 100.0 1.1742 24 666 20.2 34.77
## 375 18.49820 0.0 18.10 0 0.6680 4.138 100.0 1.1370 24 666 20.2 37.97
## 376 19.60910 0.0 18.10 0 0.6710 7.313 97.9 1.3163 24 666 20.2 13.44
## 377 15.28800 0.0 18.10 0 0.6710 6.649 93.3 1.3449 24 666 20.2 23.24
## 378 9.82349 0.0 18.10 0 0.6710 6.794 98.8 1.3580 24 666 20.2 21.24
## 379 23.64820 0.0 18.10 0 0.6710 6.380 96.2 1.3861 24 666 20.2 23.69
## 380 17.86670 0.0 18.10 0 0.6710 6.223 100.0 1.3861 24 666 20.2 21.78
## 381 88.97620 0.0 18.10 0 0.6710 6.968 91.9 1.4165 24 666 20.2 17.21
## 382 15.87440 0.0 18.10 0 0.6710 6.545 99.1 1.5192 24 666 20.2 21.08
## 383 9.18702 0.0 18.10 0 0.7000 5.536 100.0 1.5804 24 666 20.2 23.60
## 384 7.99248 0.0 18.10 0 0.7000 5.520 100.0 1.5331 24 666 20.2 24.56
## 385 20.08490 0.0 18.10 0 0.7000 4.368 91.2 1.4395 24 666 20.2 30.63
## 386 16.81180 0.0 18.10 0 0.7000 5.277 98.1 1.4261 24 666 20.2 30.81
## 387 24.39380 0.0 18.10 0 0.7000 4.652 100.0 1.4672 24 666 20.2 28.28
## 388 22.59710 0.0 18.10 0 0.7000 5.000 89.5 1.5184 24 666 20.2 31.99
## 389 14.33370 0.0 18.10 0 0.7000 4.880 100.0 1.5895 24 666 20.2 30.62
## 390 8.15174 0.0 18.10 0 0.7000 5.390 98.9 1.7281 24 666 20.2 20.85
## 391 6.96215 0.0 18.10 0 0.7000 5.713 97.0 1.9265 24 666 20.2 17.11
## 392 5.29305 0.0 18.10 0 0.7000 6.051 82.5 2.1678 24 666 20.2 18.76
## 393 11.57790 0.0 18.10 0 0.7000 5.036 97.0 1.7700 24 666 20.2 25.68
## 394 8.64476 0.0 18.10 0 0.6930 6.193 92.6 1.7912 24 666 20.2 15.17
## 395 13.35980 0.0 18.10 0 0.6930 5.887 94.7 1.7821 24 666 20.2 16.35
## 396 8.71675 0.0 18.10 0 0.6930 6.471 98.8 1.7257 24 666 20.2 17.12
## 397 5.87205 0.0 18.10 0 0.6930 6.405 96.0 1.6768 24 666 20.2 19.37
## 398 7.67202 0.0 18.10 0 0.6930 5.747 98.9 1.6334 24 666 20.2 19.92
## 399 38.35180 0.0 18.10 0 0.6930 5.453 100.0 1.4896 24 666 20.2 30.59
## 400 9.91655 0.0 18.10 0 0.6930 5.852 77.8 1.5004 24 666 20.2 29.97
## 401 25.04610 0.0 18.10 0 0.6930 5.987 100.0 1.5888 24 666 20.2 26.77
## 402 14.23620 0.0 18.10 0 0.6930 6.343 100.0 1.5741 24 666 20.2 20.32
## 403 9.59571 0.0 18.10 0 0.6930 6.404 100.0 1.6390 24 666 20.2 20.31
## 404 24.80170 0.0 18.10 0 0.6930 5.349 96.0 1.7028 24 666 20.2 19.77
## 405 41.52920 0.0 18.10 0 0.6930 5.531 85.4 1.6074 24 666 20.2 27.38
## 406 67.92080 0.0 18.10 0 0.6930 5.683 100.0 1.4254 24 666 20.2 22.98
## 407 20.71620 0.0 18.10 0 0.6590 4.138 100.0 1.1781 24 666 20.2 23.34
## 408 11.95110 0.0 18.10 0 0.6590 5.608 100.0 1.2852 24 666 20.2 12.13
## 409 7.40389 0.0 18.10 0 0.5970 5.617 97.9 1.4547 24 666 20.2 26.40
## 410 14.43830 0.0 18.10 0 0.5970 6.852 100.0 1.4655 24 666 20.2 19.78
## 411 51.13580 0.0 18.10 0 0.5970 5.757 100.0 1.4130 24 666 20.2 10.11
## 412 14.05070 0.0 18.10 0 0.5970 6.657 100.0 1.5275 24 666 20.2 21.22
## 413 18.81100 0.0 18.10 0 0.5970 4.628 100.0 1.5539 24 666 20.2 34.37
## 414 28.65580 0.0 18.10 0 0.5970 5.155 100.0 1.5894 24 666 20.2 20.08
## 415 45.74610 0.0 18.10 0 0.6930 4.519 100.0 1.6582 24 666 20.2 36.98
## 416 18.08460 0.0 18.10 0 0.6790 6.434 100.0 1.8347 24 666 20.2 29.05
## 417 10.83420 0.0 18.10 0 0.6790 6.782 90.8 1.8195 24 666 20.2 25.79
## 418 25.94060 0.0 18.10 0 0.6790 5.304 89.1 1.6475 24 666 20.2 26.64
## 419 73.53410 0.0 18.10 0 0.6790 5.957 100.0 1.8026 24 666 20.2 20.62
## 420 11.81230 0.0 18.10 0 0.7180 6.824 76.5 1.7940 24 666 20.2 22.74
## 421 11.08740 0.0 18.10 0 0.7180 6.411 100.0 1.8589 24 666 20.2 15.02
## 422 7.02259 0.0 18.10 0 0.7180 6.006 95.3 1.8746 24 666 20.2 15.70
## 423 12.04820 0.0 18.10 0 0.6140 5.648 87.6 1.9512 24 666 20.2 14.10
## 424 7.05042 0.0 18.10 0 0.6140 6.103 85.1 2.0218 24 666 20.2 23.29
## 425 8.79212 0.0 18.10 0 0.5840 5.565 70.6 2.0635 24 666 20.2 17.16
## 426 15.86030 0.0 18.10 0 0.6790 5.896 95.4 1.9096 24 666 20.2 24.39
## 427 12.24720 0.0 18.10 0 0.5840 5.837 59.7 1.9976 24 666 20.2 15.69
## 428 37.66190 0.0 18.10 0 0.6790 6.202 78.7 1.8629 24 666 20.2 14.52
## 429 7.36711 0.0 18.10 0 0.6790 6.193 78.1 1.9356 24 666 20.2 21.52
## 430 9.33889 0.0 18.10 0 0.6790 6.380 95.6 1.9682 24 666 20.2 24.08
## 431 8.49213 0.0 18.10 0 0.5840 6.348 86.1 2.0527 24 666 20.2 17.64
## 432 10.06230 0.0 18.10 0 0.5840 6.833 94.3 2.0882 24 666 20.2 19.69
## 433 6.44405 0.0 18.10 0 0.5840 6.425 74.8 2.2004 24 666 20.2 12.03
## 434 5.58107 0.0 18.10 0 0.7130 6.436 87.9 2.3158 24 666 20.2 16.22
## 435 13.91340 0.0 18.10 0 0.7130 6.208 95.0 2.2222 24 666 20.2 15.17
## 436 11.16040 0.0 18.10 0 0.7400 6.629 94.6 2.1247 24 666 20.2 23.27
## 437 14.42080 0.0 18.10 0 0.7400 6.461 93.3 2.0026 24 666 20.2 18.05
## 438 15.17720 0.0 18.10 0 0.7400 6.152 100.0 1.9142 24 666 20.2 26.45
## 439 13.67810 0.0 18.10 0 0.7400 5.935 87.9 1.8206 24 666 20.2 34.02
## 440 9.39063 0.0 18.10 0 0.7400 5.627 93.9 1.8172 24 666 20.2 22.88
## 441 22.05110 0.0 18.10 0 0.7400 5.818 92.4 1.8662 24 666 20.2 22.11
## 442 9.72418 0.0 18.10 0 0.7400 6.406 97.2 2.0651 24 666 20.2 19.52
## 443 5.66637 0.0 18.10 0 0.7400 6.219 100.0 2.0048 24 666 20.2 16.59
## 444 9.96654 0.0 18.10 0 0.7400 6.485 100.0 1.9784 24 666 20.2 18.85
## 445 12.80230 0.0 18.10 0 0.7400 5.854 96.6 1.8956 24 666 20.2 23.79
## 446 10.67180 0.0 18.10 0 0.7400 6.459 94.8 1.9879 24 666 20.2 23.98
## 447 6.28807 0.0 18.10 0 0.7400 6.341 96.4 2.0720 24 666 20.2 17.79
## 448 9.92485 0.0 18.10 0 0.7400 6.251 96.6 2.1980 24 666 20.2 16.44
## 449 9.32909 0.0 18.10 0 0.7130 6.185 98.7 2.2616 24 666 20.2 18.13
## 450 7.52601 0.0 18.10 0 0.7130 6.417 98.3 2.1850 24 666 20.2 19.31
## 451 6.71772 0.0 18.10 0 0.7130 6.749 92.6 2.3236 24 666 20.2 17.44
## 452 5.44114 0.0 18.10 0 0.7130 6.655 98.2 2.3552 24 666 20.2 17.73
## 453 5.09017 0.0 18.10 0 0.7130 6.297 91.8 2.3682 24 666 20.2 17.27
## 454 8.24809 0.0 18.10 0 0.7130 7.393 99.3 2.4527 24 666 20.2 16.74
## 455 9.51363 0.0 18.10 0 0.7130 6.728 94.1 2.4961 24 666 20.2 18.71
## 456 4.75237 0.0 18.10 0 0.7130 6.525 86.5 2.4358 24 666 20.2 18.13
## 457 4.66883 0.0 18.10 0 0.7130 5.976 87.9 2.5806 24 666 20.2 19.01
## 458 8.20058 0.0 18.10 0 0.7130 5.936 80.3 2.7792 24 666 20.2 16.94
## 459 7.75223 0.0 18.10 0 0.7130 6.301 83.7 2.7831 24 666 20.2 16.23
## 460 6.80117 0.0 18.10 0 0.7130 6.081 84.4 2.7175 24 666 20.2 14.70
## 461 4.81213 0.0 18.10 0 0.7130 6.701 90.0 2.5975 24 666 20.2 16.42
## 462 3.69311 0.0 18.10 0 0.7130 6.376 88.4 2.5671 24 666 20.2 14.65
## 463 6.65492 0.0 18.10 0 0.7130 6.317 83.0 2.7344 24 666 20.2 13.99
## 464 5.82115 0.0 18.10 0 0.7130 6.513 89.9 2.8016 24 666 20.2 10.29
## 465 7.83932 0.0 18.10 0 0.6550 6.209 65.4 2.9634 24 666 20.2 13.22
## 466 3.16360 0.0 18.10 0 0.6550 5.759 48.2 3.0665 24 666 20.2 14.13
## 467 3.77498 0.0 18.10 0 0.6550 5.952 84.7 2.8715 24 666 20.2 17.15
## 468 4.42228 0.0 18.10 0 0.5840 6.003 94.5 2.5403 24 666 20.2 21.32
## 469 15.57570 0.0 18.10 0 0.5800 5.926 71.0 2.9084 24 666 20.2 18.13
## 470 13.07510 0.0 18.10 0 0.5800 5.713 56.7 2.8237 24 666 20.2 14.76
## 471 4.34879 0.0 18.10 0 0.5800 6.167 84.0 3.0334 24 666 20.2 16.29
## 472 4.03841 0.0 18.10 0 0.5320 6.229 90.7 3.0993 24 666 20.2 12.87
## 473 3.56868 0.0 18.10 0 0.5800 6.437 75.0 2.8965 24 666 20.2 14.36
## 474 4.64689 0.0 18.10 0 0.6140 6.980 67.6 2.5329 24 666 20.2 11.66
## 475 8.05579 0.0 18.10 0 0.5840 5.427 95.4 2.4298 24 666 20.2 18.14
## 476 6.39312 0.0 18.10 0 0.5840 6.162 97.4 2.2060 24 666 20.2 24.10
## 477 4.87141 0.0 18.10 0 0.6140 6.484 93.6 2.3053 24 666 20.2 18.68
## 478 15.02340 0.0 18.10 0 0.6140 5.304 97.3 2.1007 24 666 20.2 24.91
## 479 10.23300 0.0 18.10 0 0.6140 6.185 96.7 2.1705 24 666 20.2 18.03
## 480 14.33370 0.0 18.10 0 0.6140 6.229 88.0 1.9512 24 666 20.2 13.11
## 481 5.82401 0.0 18.10 0 0.5320 6.242 64.7 3.4242 24 666 20.2 10.74
## 482 5.70818 0.0 18.10 0 0.5320 6.750 74.9 3.3317 24 666 20.2 7.74
## 483 5.73116 0.0 18.10 0 0.5320 7.061 77.0 3.4106 24 666 20.2 7.01
## 484 2.81838 0.0 18.10 0 0.5320 5.762 40.3 4.0983 24 666 20.2 10.42
## 485 2.37857 0.0 18.10 0 0.5830 5.871 41.9 3.7240 24 666 20.2 13.34
## 486 3.67367 0.0 18.10 0 0.5830 6.312 51.9 3.9917 24 666 20.2 10.58
## 487 5.69175 0.0 18.10 0 0.5830 6.114 79.8 3.5459 24 666 20.2 14.98
## 488 4.83567 0.0 18.10 0 0.5830 5.905 53.2 3.1523 24 666 20.2 11.45
## 489 0.15086 0.0 27.74 0 0.6090 5.454 92.7 1.8209 4 711 20.1 18.06
## 490 0.18337 0.0 27.74 0 0.6090 5.414 98.3 1.7554 4 711 20.1 23.97
## 491 0.20746 0.0 27.74 0 0.6090 5.093 98.0 1.8226 4 711 20.1 29.68
## 492 0.10574 0.0 27.74 0 0.6090 5.983 98.8 1.8681 4 711 20.1 18.07
## 493 0.11132 0.0 27.74 0 0.6090 5.983 83.5 2.1099 4 711 20.1 13.35
## 494 0.17331 0.0 9.69 0 0.5850 5.707 54.0 2.3817 6 391 19.2 12.01
## 495 0.27957 0.0 9.69 0 0.5850 5.926 42.6 2.3817 6 391 19.2 13.59
## 496 0.17899 0.0 9.69 0 0.5850 5.670 28.8 2.7986 6 391 19.2 17.60
## 497 0.28960 0.0 9.69 0 0.5850 5.390 72.9 2.7986 6 391 19.2 21.14
## 498 0.26838 0.0 9.69 0 0.5850 5.794 70.6 2.8927 6 391 19.2 14.10
## 499 0.23912 0.0 9.69 0 0.5850 6.019 65.3 2.4091 6 391 19.2 12.92
## 500 0.17783 0.0 9.69 0 0.5850 5.569 73.5 2.3999 6 391 19.2 15.10
## 501 0.22438 0.0 9.69 0 0.5850 6.027 79.7 2.4982 6 391 19.2 14.33
## medv
## 7 22.9
## 8 27.1
## 9 16.5
## 10 18.9
## 11 15.0
## 12 18.9
## 13 21.7
## 14 20.4
## 15 18.2
## 16 19.9
## 17 23.1
## 18 17.5
## 19 20.2
## 20 18.2
## 21 13.6
## 22 19.6
## 23 15.2
## 24 14.5
## 25 15.6
## 26 13.9
## 27 16.6
## 28 14.8
## 29 18.4
## 30 21.0
## 31 12.7
## 32 14.5
## 33 13.2
## 34 13.1
## 35 13.5
## 55 18.9
## 57 24.7
## 66 23.5
## 67 19.4
## 68 22.0
## 69 17.4
## 70 20.9
## 71 24.2
## 72 21.7
## 73 22.8
## 74 23.4
## 75 24.1
## 76 21.4
## 77 20.0
## 78 20.8
## 79 21.2
## 80 20.3
## 101 27.5
## 102 26.5
## 103 18.6
## 104 19.3
## 105 20.1
## 106 19.5
## 107 19.5
## 108 20.4
## 109 19.8
## 110 19.4
## 111 21.7
## 112 22.8
## 113 18.8
## 114 18.7
## 115 18.5
## 116 18.3
## 117 21.2
## 118 19.2
## 119 20.4
## 120 19.3
## 128 16.2
## 129 18.0
## 130 14.3
## 131 19.2
## 132 19.6
## 133 23.0
## 134 18.4
## 135 15.6
## 136 18.1
## 137 17.4
## 138 17.1
## 139 13.3
## 140 17.8
## 141 14.0
## 142 14.4
## 143 13.4
## 144 15.6
## 145 11.8
## 146 13.8
## 147 15.6
## 148 14.6
## 149 17.8
## 150 15.4
## 151 21.5
## 152 19.6
## 153 15.3
## 154 19.4
## 155 17.0
## 156 15.6
## 157 13.1
## 158 41.3
## 159 24.3
## 160 23.3
## 161 27.0
## 162 50.0
## 163 50.0
## 164 50.0
## 165 22.7
## 166 25.0
## 167 50.0
## 168 23.8
## 169 23.8
## 170 22.3
## 171 17.4
## 172 19.1
## 188 32.0
## 189 29.8
## 190 34.9
## 191 37.0
## 192 30.5
## 193 36.4
## 197 33.3
## 198 30.3
## 199 34.6
## 200 34.9
## 201 32.9
## 202 24.1
## 203 42.3
## 221 26.7
## 222 21.7
## 223 27.5
## 224 30.1
## 225 44.8
## 226 50.0
## 227 37.6
## 228 31.6
## 229 46.7
## 230 31.5
## 231 24.3
## 232 31.7
## 233 41.7
## 234 48.3
## 235 29.0
## 236 24.0
## 237 25.1
## 238 31.5
## 245 17.6
## 246 18.5
## 247 24.3
## 248 20.5
## 249 24.5
## 250 26.2
## 251 24.4
## 252 24.8
## 253 29.6
## 254 42.8
## 255 21.9
## 256 20.9
## 299 22.5
## 300 29.0
## 301 24.8
## 302 22.0
## 303 26.4
## 304 33.1
## 309 22.8
## 310 20.3
## 311 16.1
## 312 22.1
## 313 19.4
## 314 21.6
## 315 23.8
## 316 16.2
## 317 17.8
## 318 19.8
## 319 23.1
## 320 21.0
## 329 19.3
## 330 22.6
## 331 19.8
## 332 17.1
## 333 19.4
## 343 16.5
## 344 23.9
## 345 31.2
## 346 17.5
## 347 17.2
## 348 23.1
## 350 26.6
## 351 22.9
## 352 24.1
## 353 18.6
## 355 18.2
## 356 20.6
## 357 17.8
## 358 21.7
## 359 22.7
## 360 22.6
## 361 25.0
## 362 19.9
## 363 20.8
## 364 16.8
## 365 21.9
## 366 27.5
## 367 21.9
## 368 23.1
## 369 50.0
## 370 50.0
## 371 50.0
## 372 50.0
## 373 50.0
## 374 13.8
## 375 13.8
## 376 15.0
## 377 13.9
## 378 13.3
## 379 13.1
## 380 10.2
## 381 10.4
## 382 10.9
## 383 11.3
## 384 12.3
## 385 8.8
## 386 7.2
## 387 10.5
## 388 7.4
## 389 10.2
## 390 11.5
## 391 15.1
## 392 23.2
## 393 9.7
## 394 13.8
## 395 12.7
## 396 13.1
## 397 12.5
## 398 8.5
## 399 5.0
## 400 6.3
## 401 5.6
## 402 7.2
## 403 12.1
## 404 8.3
## 405 8.5
## 406 5.0
## 407 11.9
## 408 27.9
## 409 17.2
## 410 27.5
## 411 15.0
## 412 17.2
## 413 17.9
## 414 16.3
## 415 7.0
## 416 7.2
## 417 7.5
## 418 10.4
## 419 8.8
## 420 8.4
## 421 16.7
## 422 14.2
## 423 20.8
## 424 13.4
## 425 11.7
## 426 8.3
## 427 10.2
## 428 10.9
## 429 11.0
## 430 9.5
## 431 14.5
## 432 14.1
## 433 16.1
## 434 14.3
## 435 11.7
## 436 13.4
## 437 9.6
## 438 8.7
## 439 8.4
## 440 12.8
## 441 10.5
## 442 17.1
## 443 18.4
## 444 15.4
## 445 10.8
## 446 11.8
## 447 14.9
## 448 12.6
## 449 14.1
## 450 13.0
## 451 13.4
## 452 15.2
## 453 16.1
## 454 17.8
## 455 14.9
## 456 14.1
## 457 12.7
## 458 13.5
## 459 14.9
## 460 20.0
## 461 16.4
## 462 17.7
## 463 19.5
## 464 20.2
## 465 21.4
## 466 19.9
## 467 19.0
## 468 19.1
## 469 19.1
## 470 20.1
## 471 19.9
## 472 19.6
## 473 23.2
## 474 29.8
## 475 13.8
## 476 13.3
## 477 16.7
## 478 12.0
## 479 14.6
## 480 21.4
## 481 23.0
## 482 23.7
## 483 25.0
## 484 21.8
## 485 20.6
## 486 21.2
## 487 19.1
## 488 20.6
## 489 15.2
## 490 7.0
## 491 8.1
## 492 13.6
## 493 20.1
## 494 21.8
## 495 24.5
## 496 23.1
## 497 19.7
## 498 18.3
## 499 21.2
## 500 17.5
## 501 16.8I decided to pull the top 50 values for ‘ptratio’ in the data set.
The highest recorded value for ‘ptratio’ is 22.0. This occurs in census tract 355 & 356.
Of the 506 records, 201 records appear to have a pupil-teacher ratio of/over 20.0.
Concerning the rang values (12.6, 22.0), there does not seem to be a super noticeable distance in range among the values in the data set.
Boston[order(Boston$ptratio, decreasing = TRUE), ][1:50, ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 355 0.04301 80 1.91 0 0.413 5.663 21.9 10.5857 4 334 22.0 8.05 18.2
## 356 0.10659 80 1.91 0 0.413 5.936 19.5 10.5857 4 334 22.0 5.57 20.6
## 128 0.25915 0 21.89 0 0.624 5.693 96.0 1.7883 4 437 21.2 17.19 16.2
## 129 0.32543 0 21.89 0 0.624 6.431 98.8 1.8125 4 437 21.2 15.39 18.0
## 130 0.88125 0 21.89 0 0.624 5.637 94.7 1.9799 4 437 21.2 18.34 14.3
## 131 0.34006 0 21.89 0 0.624 6.458 98.9 2.1185 4 437 21.2 12.60 19.2
## 132 1.19294 0 21.89 0 0.624 6.326 97.7 2.2710 4 437 21.2 12.26 19.6
## 133 0.59005 0 21.89 0 0.624 6.372 97.9 2.3274 4 437 21.2 11.12 23.0
## 134 0.32982 0 21.89 0 0.624 5.822 95.4 2.4699 4 437 21.2 15.03 18.4
## 135 0.97617 0 21.89 0 0.624 5.757 98.4 2.3460 4 437 21.2 17.31 15.6
## 136 0.55778 0 21.89 0 0.624 6.335 98.2 2.1107 4 437 21.2 16.96 18.1
## 137 0.32264 0 21.89 0 0.624 5.942 93.5 1.9669 4 437 21.2 16.90 17.4
## 138 0.35233 0 21.89 0 0.624 6.454 98.4 1.8498 4 437 21.2 14.59 17.1
## 139 0.24980 0 21.89 0 0.624 5.857 98.2 1.6686 4 437 21.2 21.32 13.3
## 140 0.54452 0 21.89 0 0.624 6.151 97.9 1.6687 4 437 21.2 18.46 17.8
## 141 0.29090 0 21.89 0 0.624 6.174 93.6 1.6119 4 437 21.2 24.16 14.0
## 142 1.62864 0 21.89 0 0.624 5.019 100.0 1.4394 4 437 21.2 34.41 14.4
## 55 0.01360 75 4.00 0 0.410 5.888 47.6 7.3197 3 469 21.1 14.80 18.9
## 14 0.62976 0 8.14 0 0.538 5.949 61.8 4.7075 4 307 21.0 8.26 20.4
## 15 0.63796 0 8.14 0 0.538 6.096 84.5 4.4619 4 307 21.0 10.26 18.2
## 16 0.62739 0 8.14 0 0.538 5.834 56.5 4.4986 4 307 21.0 8.47 19.9
## 17 1.05393 0 8.14 0 0.538 5.935 29.3 4.4986 4 307 21.0 6.58 23.1
## 18 0.78420 0 8.14 0 0.538 5.990 81.7 4.2579 4 307 21.0 14.67 17.5
## 19 0.80271 0 8.14 0 0.538 5.456 36.6 3.7965 4 307 21.0 11.69 20.2
## 20 0.72580 0 8.14 0 0.538 5.727 69.5 3.7965 4 307 21.0 11.28 18.2
## 21 1.25179 0 8.14 0 0.538 5.570 98.1 3.7979 4 307 21.0 21.02 13.6
## 22 0.85204 0 8.14 0 0.538 5.965 89.2 4.0123 4 307 21.0 13.83 19.6
## 23 1.23247 0 8.14 0 0.538 6.142 91.7 3.9769 4 307 21.0 18.72 15.2
## 24 0.98843 0 8.14 0 0.538 5.813 100.0 4.0952 4 307 21.0 19.88 14.5
## 25 0.75026 0 8.14 0 0.538 5.924 94.1 4.3996 4 307 21.0 16.30 15.6
## 26 0.84054 0 8.14 0 0.538 5.599 85.7 4.4546 4 307 21.0 16.51 13.9
## 27 0.67191 0 8.14 0 0.538 5.813 90.3 4.6820 4 307 21.0 14.81 16.6
## 28 0.95577 0 8.14 0 0.538 6.047 88.8 4.4534 4 307 21.0 17.28 14.8
## 29 0.77299 0 8.14 0 0.538 6.495 94.4 4.4547 4 307 21.0 12.80 18.4
## 30 1.00245 0 8.14 0 0.538 6.674 87.3 4.2390 4 307 21.0 11.98 21.0
## 31 1.13081 0 8.14 0 0.538 5.713 94.1 4.2330 4 307 21.0 22.60 12.7
## 32 1.35472 0 8.14 0 0.538 6.072 100.0 4.1750 4 307 21.0 13.04 14.5
## 33 1.38799 0 8.14 0 0.538 5.950 82.0 3.9900 4 307 21.0 27.71 13.2
## 34 1.15172 0 8.14 0 0.538 5.701 95.0 3.7872 4 307 21.0 18.35 13.1
## 35 1.61282 0 8.14 0 0.538 6.096 96.9 3.7598 4 307 21.0 20.34 13.5
## 502 0.06263 0 11.93 0 0.573 6.593 69.1 2.4786 1 273 21.0 9.67 22.4
## 503 0.04527 0 11.93 0 0.573 6.120 76.7 2.2875 1 273 21.0 9.08 20.6
## 504 0.06076 0 11.93 0 0.573 6.976 91.0 2.1675 1 273 21.0 5.64 23.9
## 505 0.10959 0 11.93 0 0.573 6.794 89.3 2.3889 1 273 21.0 6.48 22.0
## 506 0.04741 0 11.93 0 0.573 6.030 80.8 2.5050 1 273 21.0 7.88 11.9
## 101 0.14866 0 8.56 0 0.520 6.727 79.9 2.7778 5 384 20.9 9.42 27.5
## 102 0.11432 0 8.56 0 0.520 6.781 71.3 2.8561 5 384 20.9 7.67 26.5
## 103 0.22876 0 8.56 0 0.520 6.405 85.4 2.7147 5 384 20.9 10.63 18.6
## 104 0.21161 0 8.56 0 0.520 6.137 87.4 2.7147 5 384 20.9 13.44 19.3
## 105 0.13960 0 8.56 0 0.520 6.167 90.0 2.4210 5 384 20.9 12.33 20.1range(Boston$ptratio)## [1] 12.6 22.0Boston[Boston$ptratio == 22.0, ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 355 0.04301 80 1.91 0 0.413 5.663 21.9 10.5857 4 334 22 8.05 18.2
## 356 0.10659 80 1.91 0 0.413 5.936 19.5 10.5857 4 334 22 5.57 20.6Boston[Boston$ptratio > 20.0, ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 14 0.62976 0 8.14 0 0.538 5.949 61.8 4.7075 4 307 21.0 8.26 20.4
## 15 0.63796 0 8.14 0 0.538 6.096 84.5 4.4619 4 307 21.0 10.26 18.2
## 16 0.62739 0 8.14 0 0.538 5.834 56.5 4.4986 4 307 21.0 8.47 19.9
## 17 1.05393 0 8.14 0 0.538 5.935 29.3 4.4986 4 307 21.0 6.58 23.1
## 18 0.78420 0 8.14 0 0.538 5.990 81.7 4.2579 4 307 21.0 14.67 17.5
## 19 0.80271 0 8.14 0 0.538 5.456 36.6 3.7965 4 307 21.0 11.69 20.2
## 20 0.72580 0 8.14 0 0.538 5.727 69.5 3.7965 4 307 21.0 11.28 18.2
## 21 1.25179 0 8.14 0 0.538 5.570 98.1 3.7979 4 307 21.0 21.02 13.6
## 22 0.85204 0 8.14 0 0.538 5.965 89.2 4.0123 4 307 21.0 13.83 19.6
## 23 1.23247 0 8.14 0 0.538 6.142 91.7 3.9769 4 307 21.0 18.72 15.2
## 24 0.98843 0 8.14 0 0.538 5.813 100.0 4.0952 4 307 21.0 19.88 14.5
## 25 0.75026 0 8.14 0 0.538 5.924 94.1 4.3996 4 307 21.0 16.30 15.6
## 26 0.84054 0 8.14 0 0.538 5.599 85.7 4.4546 4 307 21.0 16.51 13.9
## 27 0.67191 0 8.14 0 0.538 5.813 90.3 4.6820 4 307 21.0 14.81 16.6
## 28 0.95577 0 8.14 0 0.538 6.047 88.8 4.4534 4 307 21.0 17.28 14.8
## 29 0.77299 0 8.14 0 0.538 6.495 94.4 4.4547 4 307 21.0 12.80 18.4
## 30 1.00245 0 8.14 0 0.538 6.674 87.3 4.2390 4 307 21.0 11.98 21.0
## 31 1.13081 0 8.14 0 0.538 5.713 94.1 4.2330 4 307 21.0 22.60 12.7
## 32 1.35472 0 8.14 0 0.538 6.072 100.0 4.1750 4 307 21.0 13.04 14.5
## 33 1.38799 0 8.14 0 0.538 5.950 82.0 3.9900 4 307 21.0 27.71 13.2
## 34 1.15172 0 8.14 0 0.538 5.701 95.0 3.7872 4 307 21.0 18.35 13.1
## 35 1.61282 0 8.14 0 0.538 6.096 96.9 3.7598 4 307 21.0 20.34 13.5
## 55 0.01360 75 4.00 0 0.410 5.888 47.6 7.3197 3 469 21.1 14.80 18.9
## 101 0.14866 0 8.56 0 0.520 6.727 79.9 2.7778 5 384 20.9 9.42 27.5
## 102 0.11432 0 8.56 0 0.520 6.781 71.3 2.8561 5 384 20.9 7.67 26.5
## 103 0.22876 0 8.56 0 0.520 6.405 85.4 2.7147 5 384 20.9 10.63 18.6
## 104 0.21161 0 8.56 0 0.520 6.137 87.4 2.7147 5 384 20.9 13.44 19.3
## 105 0.13960 0 8.56 0 0.520 6.167 90.0 2.4210 5 384 20.9 12.33 20.1
## 106 0.13262 0 8.56 0 0.520 5.851 96.7 2.1069 5 384 20.9 16.47 19.5
## 107 0.17120 0 8.56 0 0.520 5.836 91.9 2.2110 5 384 20.9 18.66 19.5
## 108 0.13117 0 8.56 0 0.520 6.127 85.2 2.1224 5 384 20.9 14.09 20.4
## 109 0.12802 0 8.56 0 0.520 6.474 97.1 2.4329 5 384 20.9 12.27 19.8
## 110 0.26363 0 8.56 0 0.520 6.229 91.2 2.5451 5 384 20.9 15.55 19.4
## 111 0.10793 0 8.56 0 0.520 6.195 54.4 2.7778 5 384 20.9 13.00 21.7
## 128 0.25915 0 21.89 0 0.624 5.693 96.0 1.7883 4 437 21.2 17.19 16.2
## 129 0.32543 0 21.89 0 0.624 6.431 98.8 1.8125 4 437 21.2 15.39 18.0
## 130 0.88125 0 21.89 0 0.624 5.637 94.7 1.9799 4 437 21.2 18.34 14.3
## 131 0.34006 0 21.89 0 0.624 6.458 98.9 2.1185 4 437 21.2 12.60 19.2
## 132 1.19294 0 21.89 0 0.624 6.326 97.7 2.2710 4 437 21.2 12.26 19.6
## 133 0.59005 0 21.89 0 0.624 6.372 97.9 2.3274 4 437 21.2 11.12 23.0
## 134 0.32982 0 21.89 0 0.624 5.822 95.4 2.4699 4 437 21.2 15.03 18.4
## 135 0.97617 0 21.89 0 0.624 5.757 98.4 2.3460 4 437 21.2 17.31 15.6
## 136 0.55778 0 21.89 0 0.624 6.335 98.2 2.1107 4 437 21.2 16.96 18.1
## 137 0.32264 0 21.89 0 0.624 5.942 93.5 1.9669 4 437 21.2 16.90 17.4
## 138 0.35233 0 21.89 0 0.624 6.454 98.4 1.8498 4 437 21.2 14.59 17.1
## 139 0.24980 0 21.89 0 0.624 5.857 98.2 1.6686 4 437 21.2 21.32 13.3
## 140 0.54452 0 21.89 0 0.624 6.151 97.9 1.6687 4 437 21.2 18.46 17.8
## 141 0.29090 0 21.89 0 0.624 6.174 93.6 1.6119 4 437 21.2 24.16 14.0
## 142 1.62864 0 21.89 0 0.624 5.019 100.0 1.4394 4 437 21.2 34.41 14.4
## 334 0.05083 0 5.19 0 0.515 6.316 38.1 6.4584 5 224 20.2 5.68 22.2
## 335 0.03738 0 5.19 0 0.515 6.310 38.5 6.4584 5 224 20.2 6.75 20.7
## 336 0.03961 0 5.19 0 0.515 6.037 34.5 5.9853 5 224 20.2 8.01 21.1
## 337 0.03427 0 5.19 0 0.515 5.869 46.3 5.2311 5 224 20.2 9.80 19.5
## 338 0.03041 0 5.19 0 0.515 5.895 59.6 5.6150 5 224 20.2 10.56 18.5
## 339 0.03306 0 5.19 0 0.515 6.059 37.3 4.8122 5 224 20.2 8.51 20.6
## 340 0.05497 0 5.19 0 0.515 5.985 45.4 4.8122 5 224 20.2 9.74 19.0
## 341 0.06151 0 5.19 0 0.515 5.968 58.5 4.8122 5 224 20.2 9.29 18.7
## 355 0.04301 80 1.91 0 0.413 5.663 21.9 10.5857 4 334 22.0 8.05 18.2
## 356 0.10659 80 1.91 0 0.413 5.936 19.5 10.5857 4 334 22.0 5.57 20.6
## 357 8.98296 0 18.10 1 0.770 6.212 97.4 2.1222 24 666 20.2 17.60 17.8
## 358 3.84970 0 18.10 1 0.770 6.395 91.0 2.5052 24 666 20.2 13.27 21.7
## 359 5.20177 0 18.10 1 0.770 6.127 83.4 2.7227 24 666 20.2 11.48 22.7
## 360 4.26131 0 18.10 0 0.770 6.112 81.3 2.5091 24 666 20.2 12.67 22.6
## 361 4.54192 0 18.10 0 0.770 6.398 88.0 2.5182 24 666 20.2 7.79 25.0
## 362 3.83684 0 18.10 0 0.770 6.251 91.1 2.2955 24 666 20.2 14.19 19.9
## 363 3.67822 0 18.10 0 0.770 5.362 96.2 2.1036 24 666 20.2 10.19 20.8
## 364 4.22239 0 18.10 1 0.770 5.803 89.0 1.9047 24 666 20.2 14.64 16.8
## 365 3.47428 0 18.10 1 0.718 8.780 82.9 1.9047 24 666 20.2 5.29 21.9
## 366 4.55587 0 18.10 0 0.718 3.561 87.9 1.6132 24 666 20.2 7.12 27.5
## 367 3.69695 0 18.10 0 0.718 4.963 91.4 1.7523 24 666 20.2 14.00 21.9
## 368 13.52220 0 18.10 0 0.631 3.863 100.0 1.5106 24 666 20.2 13.33 23.1
## 369 4.89822 0 18.10 0 0.631 4.970 100.0 1.3325 24 666 20.2 3.26 50.0
## 370 5.66998 0 18.10 1 0.631 6.683 96.8 1.3567 24 666 20.2 3.73 50.0
## 371 6.53876 0 18.10 1 0.631 7.016 97.5 1.2024 24 666 20.2 2.96 50.0
## 372 9.23230 0 18.10 0 0.631 6.216 100.0 1.1691 24 666 20.2 9.53 50.0
## 373 8.26725 0 18.10 1 0.668 5.875 89.6 1.1296 24 666 20.2 8.88 50.0
## 374 11.10810 0 18.10 0 0.668 4.906 100.0 1.1742 24 666 20.2 34.77 13.8
## 375 18.49820 0 18.10 0 0.668 4.138 100.0 1.1370 24 666 20.2 37.97 13.8
## 376 19.60910 0 18.10 0 0.671 7.313 97.9 1.3163 24 666 20.2 13.44 15.0
## 377 15.28800 0 18.10 0 0.671 6.649 93.3 1.3449 24 666 20.2 23.24 13.9
## 378 9.82349 0 18.10 0 0.671 6.794 98.8 1.3580 24 666 20.2 21.24 13.3
## 379 23.64820 0 18.10 0 0.671 6.380 96.2 1.3861 24 666 20.2 23.69 13.1
## 380 17.86670 0 18.10 0 0.671 6.223 100.0 1.3861 24 666 20.2 21.78 10.2
## 381 88.97620 0 18.10 0 0.671 6.968 91.9 1.4165 24 666 20.2 17.21 10.4
## 382 15.87440 0 18.10 0 0.671 6.545 99.1 1.5192 24 666 20.2 21.08 10.9
## 383 9.18702 0 18.10 0 0.700 5.536 100.0 1.5804 24 666 20.2 23.60 11.3
## 384 7.99248 0 18.10 0 0.700 5.520 100.0 1.5331 24 666 20.2 24.56 12.3
## 385 20.08490 0 18.10 0 0.700 4.368 91.2 1.4395 24 666 20.2 30.63 8.8
## 386 16.81180 0 18.10 0 0.700 5.277 98.1 1.4261 24 666 20.2 30.81 7.2
## 387 24.39380 0 18.10 0 0.700 4.652 100.0 1.4672 24 666 20.2 28.28 10.5
## 388 22.59710 0 18.10 0 0.700 5.000 89.5 1.5184 24 666 20.2 31.99 7.4
## 389 14.33370 0 18.10 0 0.700 4.880 100.0 1.5895 24 666 20.2 30.62 10.2
## 390 8.15174 0 18.10 0 0.700 5.390 98.9 1.7281 24 666 20.2 20.85 11.5
## 391 6.96215 0 18.10 0 0.700 5.713 97.0 1.9265 24 666 20.2 17.11 15.1
## 392 5.29305 0 18.10 0 0.700 6.051 82.5 2.1678 24 666 20.2 18.76 23.2
## 393 11.57790 0 18.10 0 0.700 5.036 97.0 1.7700 24 666 20.2 25.68 9.7
## 394 8.64476 0 18.10 0 0.693 6.193 92.6 1.7912 24 666 20.2 15.17 13.8
## 395 13.35980 0 18.10 0 0.693 5.887 94.7 1.7821 24 666 20.2 16.35 12.7
## 396 8.71675 0 18.10 0 0.693 6.471 98.8 1.7257 24 666 20.2 17.12 13.1
## 397 5.87205 0 18.10 0 0.693 6.405 96.0 1.6768 24 666 20.2 19.37 12.5
## 398 7.67202 0 18.10 0 0.693 5.747 98.9 1.6334 24 666 20.2 19.92 8.5
## 399 38.35180 0 18.10 0 0.693 5.453 100.0 1.4896 24 666 20.2 30.59 5.0
## 400 9.91655 0 18.10 0 0.693 5.852 77.8 1.5004 24 666 20.2 29.97 6.3
## 401 25.04610 0 18.10 0 0.693 5.987 100.0 1.5888 24 666 20.2 26.77 5.6
## 402 14.23620 0 18.10 0 0.693 6.343 100.0 1.5741 24 666 20.2 20.32 7.2
## 403 9.59571 0 18.10 0 0.693 6.404 100.0 1.6390 24 666 20.2 20.31 12.1
## 404 24.80170 0 18.10 0 0.693 5.349 96.0 1.7028 24 666 20.2 19.77 8.3
## 405 41.52920 0 18.10 0 0.693 5.531 85.4 1.6074 24 666 20.2 27.38 8.5
## 406 67.92080 0 18.10 0 0.693 5.683 100.0 1.4254 24 666 20.2 22.98 5.0
## 407 20.71620 0 18.10 0 0.659 4.138 100.0 1.1781 24 666 20.2 23.34 11.9
## 408 11.95110 0 18.10 0 0.659 5.608 100.0 1.2852 24 666 20.2 12.13 27.9
## 409 7.40389 0 18.10 0 0.597 5.617 97.9 1.4547 24 666 20.2 26.40 17.2
## 410 14.43830 0 18.10 0 0.597 6.852 100.0 1.4655 24 666 20.2 19.78 27.5
## 411 51.13580 0 18.10 0 0.597 5.757 100.0 1.4130 24 666 20.2 10.11 15.0
## 412 14.05070 0 18.10 0 0.597 6.657 100.0 1.5275 24 666 20.2 21.22 17.2
## 413 18.81100 0 18.10 0 0.597 4.628 100.0 1.5539 24 666 20.2 34.37 17.9
## 414 28.65580 0 18.10 0 0.597 5.155 100.0 1.5894 24 666 20.2 20.08 16.3
## 415 45.74610 0 18.10 0 0.693 4.519 100.0 1.6582 24 666 20.2 36.98 7.0
## 416 18.08460 0 18.10 0 0.679 6.434 100.0 1.8347 24 666 20.2 29.05 7.2
## 417 10.83420 0 18.10 0 0.679 6.782 90.8 1.8195 24 666 20.2 25.79 7.5
## 418 25.94060 0 18.10 0 0.679 5.304 89.1 1.6475 24 666 20.2 26.64 10.4
## 419 73.53410 0 18.10 0 0.679 5.957 100.0 1.8026 24 666 20.2 20.62 8.8
## 420 11.81230 0 18.10 0 0.718 6.824 76.5 1.7940 24 666 20.2 22.74 8.4
## 421 11.08740 0 18.10 0 0.718 6.411 100.0 1.8589 24 666 20.2 15.02 16.7
## 422 7.02259 0 18.10 0 0.718 6.006 95.3 1.8746 24 666 20.2 15.70 14.2
## 423 12.04820 0 18.10 0 0.614 5.648 87.6 1.9512 24 666 20.2 14.10 20.8
## 424 7.05042 0 18.10 0 0.614 6.103 85.1 2.0218 24 666 20.2 23.29 13.4
## 425 8.79212 0 18.10 0 0.584 5.565 70.6 2.0635 24 666 20.2 17.16 11.7
## 426 15.86030 0 18.10 0 0.679 5.896 95.4 1.9096 24 666 20.2 24.39 8.3
## 427 12.24720 0 18.10 0 0.584 5.837 59.7 1.9976 24 666 20.2 15.69 10.2
## 428 37.66190 0 18.10 0 0.679 6.202 78.7 1.8629 24 666 20.2 14.52 10.9
## 429 7.36711 0 18.10 0 0.679 6.193 78.1 1.9356 24 666 20.2 21.52 11.0
## 430 9.33889 0 18.10 0 0.679 6.380 95.6 1.9682 24 666 20.2 24.08 9.5
## 431 8.49213 0 18.10 0 0.584 6.348 86.1 2.0527 24 666 20.2 17.64 14.5
## 432 10.06230 0 18.10 0 0.584 6.833 94.3 2.0882 24 666 20.2 19.69 14.1
## 433 6.44405 0 18.10 0 0.584 6.425 74.8 2.2004 24 666 20.2 12.03 16.1
## 434 5.58107 0 18.10 0 0.713 6.436 87.9 2.3158 24 666 20.2 16.22 14.3
## 435 13.91340 0 18.10 0 0.713 6.208 95.0 2.2222 24 666 20.2 15.17 11.7
## 436 11.16040 0 18.10 0 0.740 6.629 94.6 2.1247 24 666 20.2 23.27 13.4
## 437 14.42080 0 18.10 0 0.740 6.461 93.3 2.0026 24 666 20.2 18.05 9.6
## 438 15.17720 0 18.10 0 0.740 6.152 100.0 1.9142 24 666 20.2 26.45 8.7
## 439 13.67810 0 18.10 0 0.740 5.935 87.9 1.8206 24 666 20.2 34.02 8.4
## 440 9.39063 0 18.10 0 0.740 5.627 93.9 1.8172 24 666 20.2 22.88 12.8
## 441 22.05110 0 18.10 0 0.740 5.818 92.4 1.8662 24 666 20.2 22.11 10.5
## 442 9.72418 0 18.10 0 0.740 6.406 97.2 2.0651 24 666 20.2 19.52 17.1
## 443 5.66637 0 18.10 0 0.740 6.219 100.0 2.0048 24 666 20.2 16.59 18.4
## 444 9.96654 0 18.10 0 0.740 6.485 100.0 1.9784 24 666 20.2 18.85 15.4
## 445 12.80230 0 18.10 0 0.740 5.854 96.6 1.8956 24 666 20.2 23.79 10.8
## 446 10.67180 0 18.10 0 0.740 6.459 94.8 1.9879 24 666 20.2 23.98 11.8
## 447 6.28807 0 18.10 0 0.740 6.341 96.4 2.0720 24 666 20.2 17.79 14.9
## 448 9.92485 0 18.10 0 0.740 6.251 96.6 2.1980 24 666 20.2 16.44 12.6
## 449 9.32909 0 18.10 0 0.713 6.185 98.7 2.2616 24 666 20.2 18.13 14.1
## 450 7.52601 0 18.10 0 0.713 6.417 98.3 2.1850 24 666 20.2 19.31 13.0
## 451 6.71772 0 18.10 0 0.713 6.749 92.6 2.3236 24 666 20.2 17.44 13.4
## 452 5.44114 0 18.10 0 0.713 6.655 98.2 2.3552 24 666 20.2 17.73 15.2
## 453 5.09017 0 18.10 0 0.713 6.297 91.8 2.3682 24 666 20.2 17.27 16.1
## 454 8.24809 0 18.10 0 0.713 7.393 99.3 2.4527 24 666 20.2 16.74 17.8
## 455 9.51363 0 18.10 0 0.713 6.728 94.1 2.4961 24 666 20.2 18.71 14.9
## 456 4.75237 0 18.10 0 0.713 6.525 86.5 2.4358 24 666 20.2 18.13 14.1
## 457 4.66883 0 18.10 0 0.713 5.976 87.9 2.5806 24 666 20.2 19.01 12.7
## 458 8.20058 0 18.10 0 0.713 5.936 80.3 2.7792 24 666 20.2 16.94 13.5
## 459 7.75223 0 18.10 0 0.713 6.301 83.7 2.7831 24 666 20.2 16.23 14.9
## 460 6.80117 0 18.10 0 0.713 6.081 84.4 2.7175 24 666 20.2 14.70 20.0
## 461 4.81213 0 18.10 0 0.713 6.701 90.0 2.5975 24 666 20.2 16.42 16.4
## 462 3.69311 0 18.10 0 0.713 6.376 88.4 2.5671 24 666 20.2 14.65 17.7
## 463 6.65492 0 18.10 0 0.713 6.317 83.0 2.7344 24 666 20.2 13.99 19.5
## 464 5.82115 0 18.10 0 0.713 6.513 89.9 2.8016 24 666 20.2 10.29 20.2
## 465 7.83932 0 18.10 0 0.655 6.209 65.4 2.9634 24 666 20.2 13.22 21.4
## 466 3.16360 0 18.10 0 0.655 5.759 48.2 3.0665 24 666 20.2 14.13 19.9
## 467 3.77498 0 18.10 0 0.655 5.952 84.7 2.8715 24 666 20.2 17.15 19.0
## 468 4.42228 0 18.10 0 0.584 6.003 94.5 2.5403 24 666 20.2 21.32 19.1
## 469 15.57570 0 18.10 0 0.580 5.926 71.0 2.9084 24 666 20.2 18.13 19.1
## 470 13.07510 0 18.10 0 0.580 5.713 56.7 2.8237 24 666 20.2 14.76 20.1
## 471 4.34879 0 18.10 0 0.580 6.167 84.0 3.0334 24 666 20.2 16.29 19.9
## 472 4.03841 0 18.10 0 0.532 6.229 90.7 3.0993 24 666 20.2 12.87 19.6
## 473 3.56868 0 18.10 0 0.580 6.437 75.0 2.8965 24 666 20.2 14.36 23.2
## 474 4.64689 0 18.10 0 0.614 6.980 67.6 2.5329 24 666 20.2 11.66 29.8
## 475 8.05579 0 18.10 0 0.584 5.427 95.4 2.4298 24 666 20.2 18.14 13.8
## 476 6.39312 0 18.10 0 0.584 6.162 97.4 2.2060 24 666 20.2 24.10 13.3
## 477 4.87141 0 18.10 0 0.614 6.484 93.6 2.3053 24 666 20.2 18.68 16.7
## 478 15.02340 0 18.10 0 0.614 5.304 97.3 2.1007 24 666 20.2 24.91 12.0
## 479 10.23300 0 18.10 0 0.614 6.185 96.7 2.1705 24 666 20.2 18.03 14.6
## 480 14.33370 0 18.10 0 0.614 6.229 88.0 1.9512 24 666 20.2 13.11 21.4
## 481 5.82401 0 18.10 0 0.532 6.242 64.7 3.4242 24 666 20.2 10.74 23.0
## 482 5.70818 0 18.10 0 0.532 6.750 74.9 3.3317 24 666 20.2 7.74 23.7
## 483 5.73116 0 18.10 0 0.532 7.061 77.0 3.4106 24 666 20.2 7.01 25.0
## 484 2.81838 0 18.10 0 0.532 5.762 40.3 4.0983 24 666 20.2 10.42 21.8
## 485 2.37857 0 18.10 0 0.583 5.871 41.9 3.7240 24 666 20.2 13.34 20.6
## 486 3.67367 0 18.10 0 0.583 6.312 51.9 3.9917 24 666 20.2 10.58 21.2
## 487 5.69175 0 18.10 0 0.583 6.114 79.8 3.5459 24 666 20.2 14.98 19.1
## 488 4.83567 0 18.10 0 0.583 5.905 53.2 3.1523 24 666 20.2 11.45 20.6
## 489 0.15086 0 27.74 0 0.609 5.454 92.7 1.8209 4 711 20.1 18.06 15.2
## 490 0.18337 0 27.74 0 0.609 5.414 98.3 1.7554 4 711 20.1 23.97 7.0
## 491 0.20746 0 27.74 0 0.609 5.093 98.0 1.8226 4 711 20.1 29.68 8.1
## 492 0.10574 0 27.74 0 0.609 5.983 98.8 1.8681 4 711 20.1 18.07 13.6
## 493 0.11132 0 27.74 0 0.609 5.983 83.5 2.1099 4 711 20.1 13.35 20.1
## 502 0.06263 0 11.93 0 0.573 6.593 69.1 2.4786 1 273 21.0 9.67 22.4
## 503 0.04527 0 11.93 0 0.573 6.120 76.7 2.2875 1 273 21.0 9.08 20.6
## 504 0.06076 0 11.93 0 0.573 6.976 91.0 2.1675 1 273 21.0 5.64 23.9
## 505 0.10959 0 11.93 0 0.573 6.794 89.3 2.3889 1 273 21.0 6.48 22.0
## 506 0.04741 0 11.93 0 0.573 6.030 80.8 2.5050 1 273 21.0 7.88 11.9unique(Boston$ptratio)## [1] 15.3 17.8 18.7 15.2 21.0 19.2 18.3 17.9 16.8 21.1 17.3 15.1 19.7 18.6 16.1
## [16] 18.9 19.0 18.5 18.2 18.0 20.9 19.1 21.2 14.7 16.6 15.6 14.4 12.6 17.0 16.4
## [31] 17.4 15.9 13.0 17.6 14.9 13.6 16.0 14.8 18.4 19.6 16.9 20.2 15.5 18.8 22.0
## [46] 20.110e. There are 35 census tracts in this data set bound to the Charles River.
boundingRiver <- Boston[Boston$chas == 1, ]
boundingRiver## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 143 3.32105 0 19.58 1 0.8710 5.403 100.0 1.3216 5 403 14.7 26.82 13.4
## 153 1.12658 0 19.58 1 0.8710 5.012 88.0 1.6102 5 403 14.7 12.12 15.3
## 155 1.41385 0 19.58 1 0.8710 6.129 96.0 1.7494 5 403 14.7 15.12 17.0
## 156 3.53501 0 19.58 1 0.8710 6.152 82.6 1.7455 5 403 14.7 15.02 15.6
## 161 1.27346 0 19.58 1 0.6050 6.250 92.6 1.7984 5 403 14.7 5.50 27.0
## 163 1.83377 0 19.58 1 0.6050 7.802 98.2 2.0407 5 403 14.7 1.92 50.0
## 164 1.51902 0 19.58 1 0.6050 8.375 93.9 2.1620 5 403 14.7 3.32 50.0
## 209 0.13587 0 10.59 1 0.4890 6.064 59.1 4.2392 4 277 18.6 14.66 24.4
## 210 0.43571 0 10.59 1 0.4890 5.344 100.0 3.8750 4 277 18.6 23.09 20.0
## 211 0.17446 0 10.59 1 0.4890 5.960 92.1 3.8771 4 277 18.6 17.27 21.7
## 212 0.37578 0 10.59 1 0.4890 5.404 88.6 3.6650 4 277 18.6 23.98 19.3
## 213 0.21719 0 10.59 1 0.4890 5.807 53.8 3.6526 4 277 18.6 16.03 22.4
## 217 0.04560 0 13.89 1 0.5500 5.888 56.0 3.1121 5 276 16.4 13.51 23.3
## 219 0.11069 0 13.89 1 0.5500 5.951 93.8 2.8893 5 276 16.4 17.92 21.5
## 220 0.11425 0 13.89 1 0.5500 6.373 92.4 3.3633 5 276 16.4 10.50 23.0
## 221 0.35809 0 6.20 1 0.5070 6.951 88.5 2.8617 8 307 17.4 9.71 26.7
## 222 0.40771 0 6.20 1 0.5070 6.164 91.3 3.0480 8 307 17.4 21.46 21.7
## 223 0.62356 0 6.20 1 0.5070 6.879 77.7 3.2721 8 307 17.4 9.93 27.5
## 235 0.44791 0 6.20 1 0.5070 6.726 66.5 3.6519 8 307 17.4 8.05 29.0
## 237 0.52058 0 6.20 1 0.5070 6.631 76.5 4.1480 8 307 17.4 9.54 25.1
## 270 0.09065 20 6.96 1 0.4640 5.920 61.5 3.9175 3 223 18.6 13.65 20.7
## 274 0.22188 20 6.96 1 0.4640 7.691 51.8 4.3665 3 223 18.6 6.58 35.2
## 275 0.05644 40 6.41 1 0.4470 6.758 32.9 4.0776 4 254 17.6 3.53 32.4
## 277 0.10469 40 6.41 1 0.4470 7.267 49.0 4.7872 4 254 17.6 6.05 33.2
## 278 0.06127 40 6.41 1 0.4470 6.826 27.6 4.8628 4 254 17.6 4.16 33.1
## 283 0.06129 20 3.33 1 0.4429 7.645 49.7 5.2119 5 216 14.9 3.01 46.0
## 284 0.01501 90 1.21 1 0.4010 7.923 24.8 5.8850 1 198 13.6 3.16 50.0
## 357 8.98296 0 18.10 1 0.7700 6.212 97.4 2.1222 24 666 20.2 17.60 17.8
## 358 3.84970 0 18.10 1 0.7700 6.395 91.0 2.5052 24 666 20.2 13.27 21.7
## 359 5.20177 0 18.10 1 0.7700 6.127 83.4 2.7227 24 666 20.2 11.48 22.7
## 364 4.22239 0 18.10 1 0.7700 5.803 89.0 1.9047 24 666 20.2 14.64 16.8
## 365 3.47428 0 18.10 1 0.7180 8.780 82.9 1.9047 24 666 20.2 5.29 21.9
## 370 5.66998 0 18.10 1 0.6310 6.683 96.8 1.3567 24 666 20.2 3.73 50.0
## 371 6.53876 0 18.10 1 0.6310 7.016 97.5 1.2024 24 666 20.2 2.96 50.0
## 373 8.26725 0 18.10 1 0.6680 5.875 89.6 1.1296 24 666 20.2 8.88 50.010f. The median pupil-teacher ratio among the towns is 19.05.
median(Boston$ptratio)## [1] 19.0510g. The tract with lowest median value of owner occupied homes is tract 399.
The values for the other fields for the census tract are: - crim = 38.3518 - zin = 0 - indus = 18.1 - chas = 0 - nox = 0.693 - rm = 5.453 - age = 100 - dis = 1.4896 - rad = 24 - tax = 666 - ptratio = 20.2 - lstat = 30.59
The ‘crim’, ‘indus’, ‘nox’, ‘age’, ‘rad’, ‘tax’, ‘ptratio’ and ‘lstat’ values are above the median values recorded in the data set.
The ‘zn’ value is the lowest recorded value for that field in the data set.
The ‘chas’ value is more Boolean, then numerical, so there’s not much we can do other then assume that maybe not living near a river decreases the ‘medv’ value.
The census tract appears to be in a high tax bracket, is saturated proportionately with older units built before 1940, has a high crime rate (considering the data set), does not have any residential lots over 25,000ft, and a high rate of nitrogen oxide concentration.
It doesn’t sound like the best place to live, compared to others in the data set.
range(Boston$medv)## [1] 5 50Boston[which.min(Boston$medv), ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 399 38.3518 0 18.1 0 0.693 5.453 100 1.4896 24 666 20.2 30.59 5range(Boston$crim)## [1] 0.00632 88.97620range(Boston$zn)## [1] 0 100range(Boston$indus)## [1] 0.46 27.74range(Boston$chas)## [1] 0 1range(Boston$nox)## [1] 0.385 0.871range(Boston$rm)## [1] 3.561 8.780range(Boston$age)## [1] 2.9 100.0range(Boston$dis)## [1] 1.1296 12.1265range(Boston$rad) ## [1] 1 24range(Boston$tax)## [1] 187 711range(Boston$ptratio)## [1] 12.6 22.0range(Boston$lstat)## [1] 1.73 37.97median(Boston$crim)## [1] 0.25651median(Boston$zn)## [1] 0median(Boston$indus)## [1] 9.69median(Boston$chas)## [1] 0median(Boston$nox)## [1] 0.538median(Boston$rm)## [1] 6.2085median(Boston$age)## [1] 77.5median(Boston$dis)## [1] 3.20745median(Boston$rad) ## [1] 5median(Boston$tax)## [1] 330median(Boston$ptratio)## [1] 19.05median(Boston$lstat)## [1] 11.36- crim = 38.3518 +
- zin = 0
- indus = 18.1 +
- chas = 0
- nox = 0.693 +
- rm = 5.453 +
- age = 100 +
- dis = 1.4896 +
- rad = 24 +
- tax = 666 +
- ptratio = 20.2 +
- lstat = 30.59 +
10h. There are 64 census tracts that have an average of more than seven rooms per dwelling. There are 13 census tracts that have an average of more than eight rooms per dwelling.
Of the 13 census tracts with an average greater then 8 rooms per dwelling, only 2 are located near the river, census tract 365 has a value for ‘rad’ of 24 (which is the highest value observed in the data set), tend to be closer to 5 Boston employment centers, and tend to have lower tax rates (with 2 exceptions).
Boston[Boston$rm > 7, ]## crim zn indus chas nox rm age dis rad tax ptratio lstat
## 3 0.02729 0.0 7.07 0 0.4690 7.185 61.1 4.9671 2 242 17.8 4.03
## 5 0.06905 0.0 2.18 0 0.4580 7.147 54.2 6.0622 3 222 18.7 5.33
## 41 0.03359 75.0 2.95 0 0.4280 7.024 15.8 5.4011 3 252 18.3 1.98
## 56 0.01311 90.0 1.22 0 0.4030 7.249 21.9 8.6966 5 226 17.9 4.81
## 65 0.01951 17.5 1.38 0 0.4161 7.104 59.5 9.2229 3 216 18.6 8.05
## 89 0.05660 0.0 3.41 0 0.4890 7.007 86.3 3.4217 2 270 17.8 5.50
## 90 0.05302 0.0 3.41 0 0.4890 7.079 63.1 3.4145 2 270 17.8 5.70
## 98 0.12083 0.0 2.89 0 0.4450 8.069 76.0 3.4952 2 276 18.0 4.21
## 99 0.08187 0.0 2.89 0 0.4450 7.820 36.9 3.4952 2 276 18.0 3.57
## 100 0.06860 0.0 2.89 0 0.4450 7.416 62.5 3.4952 2 276 18.0 6.19
## 162 1.46336 0.0 19.58 0 0.6050 7.489 90.8 1.9709 5 403 14.7 1.73
## 163 1.83377 0.0 19.58 1 0.6050 7.802 98.2 2.0407 5 403 14.7 1.92
## 164 1.51902 0.0 19.58 1 0.6050 8.375 93.9 2.1620 5 403 14.7 3.32
## 167 2.01019 0.0 19.58 0 0.6050 7.929 96.2 2.0459 5 403 14.7 3.70
## 181 0.06588 0.0 2.46 0 0.4880 7.765 83.3 2.7410 3 193 17.8 7.56
## 183 0.09103 0.0 2.46 0 0.4880 7.155 92.2 2.7006 3 193 17.8 4.82
## 187 0.05602 0.0 2.46 0 0.4880 7.831 53.6 3.1992 3 193 17.8 4.45
## 190 0.08370 45.0 3.44 0 0.4370 7.185 38.9 4.5667 5 398 15.2 5.39
## 193 0.08664 45.0 3.44 0 0.4370 7.178 26.3 6.4798 5 398 15.2 2.87
## 196 0.01381 80.0 0.46 0 0.4220 7.875 32.0 5.6484 4 255 14.4 2.97
## 197 0.04011 80.0 1.52 0 0.4040 7.287 34.1 7.3090 2 329 12.6 4.08
## 198 0.04666 80.0 1.52 0 0.4040 7.107 36.6 7.3090 2 329 12.6 8.61
## 199 0.03768 80.0 1.52 0 0.4040 7.274 38.3 7.3090 2 329 12.6 6.62
## 201 0.01778 95.0 1.47 0 0.4030 7.135 13.9 7.6534 3 402 17.0 4.45
## 203 0.02177 82.5 2.03 0 0.4150 7.610 15.7 6.2700 2 348 14.7 3.11
## 204 0.03510 95.0 2.68 0 0.4161 7.853 33.2 5.1180 4 224 14.7 3.81
## 205 0.02009 95.0 2.68 0 0.4161 8.034 31.9 5.1180 4 224 14.7 2.88
## 225 0.31533 0.0 6.20 0 0.5040 8.266 78.3 2.8944 8 307 17.4 4.14
## 226 0.52693 0.0 6.20 0 0.5040 8.725 83.0 2.8944 8 307 17.4 4.63
## 227 0.38214 0.0 6.20 0 0.5040 8.040 86.5 3.2157 8 307 17.4 3.13
## 228 0.41238 0.0 6.20 0 0.5040 7.163 79.9 3.2157 8 307 17.4 6.36
## 229 0.29819 0.0 6.20 0 0.5040 7.686 17.0 3.3751 8 307 17.4 3.92
## 232 0.46296 0.0 6.20 0 0.5040 7.412 76.9 3.6715 8 307 17.4 5.25
## 233 0.57529 0.0 6.20 0 0.5070 8.337 73.3 3.8384 8 307 17.4 2.47
## 234 0.33147 0.0 6.20 0 0.5070 8.247 70.4 3.6519 8 307 17.4 3.95
## 238 0.51183 0.0 6.20 0 0.5070 7.358 71.6 4.1480 8 307 17.4 4.73
## 254 0.36894 22.0 5.86 0 0.4310 8.259 8.4 8.9067 7 330 19.1 3.54
## 257 0.01538 90.0 3.75 0 0.3940 7.454 34.2 6.3361 3 244 15.9 3.11
## 258 0.61154 20.0 3.97 0 0.6470 8.704 86.9 1.8010 5 264 13.0 5.12
## 259 0.66351 20.0 3.97 0 0.6470 7.333 100.0 1.8946 5 264 13.0 7.79
## 261 0.54011 20.0 3.97 0 0.6470 7.203 81.8 2.1121 5 264 13.0 9.59
## 262 0.53412 20.0 3.97 0 0.6470 7.520 89.4 2.1398 5 264 13.0 7.26
## 263 0.52014 20.0 3.97 0 0.6470 8.398 91.5 2.2885 5 264 13.0 5.91
## 264 0.82526 20.0 3.97 0 0.6470 7.327 94.5 2.0788 5 264 13.0 11.25
## 265 0.55007 20.0 3.97 0 0.6470 7.206 91.6 1.9301 5 264 13.0 8.10
## 267 0.78570 20.0 3.97 0 0.6470 7.014 84.6 2.1329 5 264 13.0 14.79
## 268 0.57834 20.0 3.97 0 0.5750 8.297 67.0 2.4216 5 264 13.0 7.44
## 269 0.54050 20.0 3.97 0 0.5750 7.470 52.6 2.8720 5 264 13.0 3.16
## 274 0.22188 20.0 6.96 1 0.4640 7.691 51.8 4.3665 3 223 18.6 6.58
## 277 0.10469 40.0 6.41 1 0.4470 7.267 49.0 4.7872 4 254 17.6 6.05
## 281 0.03578 20.0 3.33 0 0.4429 7.820 64.5 4.6947 5 216 14.9 3.76
## 283 0.06129 20.0 3.33 1 0.4429 7.645 49.7 5.2119 5 216 14.9 3.01
## 284 0.01501 90.0 1.21 1 0.4010 7.923 24.8 5.8850 1 198 13.6 3.16
## 285 0.00906 90.0 2.97 0 0.4000 7.088 20.8 7.3073 1 285 15.3 7.85
## 292 0.07886 80.0 4.95 0 0.4110 7.148 27.7 5.1167 4 245 19.2 3.56
## 300 0.05561 70.0 2.24 0 0.4000 7.041 10.0 7.8278 5 358 14.8 4.74
## 305 0.05515 33.0 2.18 0 0.4720 7.236 41.1 4.0220 7 222 18.4 6.93
## 307 0.07503 33.0 2.18 0 0.4720 7.420 71.9 3.0992 7 222 18.4 6.47
## 342 0.01301 35.0 1.52 0 0.4420 7.241 49.3 7.0379 1 284 15.5 5.49
## 365 3.47428 0.0 18.10 1 0.7180 8.780 82.9 1.9047 24 666 20.2 5.29
## 371 6.53876 0.0 18.10 1 0.6310 7.016 97.5 1.2024 24 666 20.2 2.96
## 376 19.60910 0.0 18.10 0 0.6710 7.313 97.9 1.3163 24 666 20.2 13.44
## 454 8.24809 0.0 18.10 0 0.7130 7.393 99.3 2.4527 24 666 20.2 16.74
## 483 5.73116 0.0 18.10 0 0.5320 7.061 77.0 3.4106 24 666 20.2 7.01
## medv
## 3 34.7
## 5 36.2
## 41 34.9
## 56 35.4
## 65 33.0
## 89 23.6
## 90 28.7
## 98 38.7
## 99 43.8
## 100 33.2
## 162 50.0
## 163 50.0
## 164 50.0
## 167 50.0
## 181 39.8
## 183 37.9
## 187 50.0
## 190 34.9
## 193 36.4
## 196 50.0
## 197 33.3
## 198 30.3
## 199 34.6
## 201 32.9
## 203 42.3
## 204 48.5
## 205 50.0
## 225 44.8
## 226 50.0
## 227 37.6
## 228 31.6
## 229 46.7
## 232 31.7
## 233 41.7
## 234 48.3
## 238 31.5
## 254 42.8
## 257 44.0
## 258 50.0
## 259 36.0
## 261 33.8
## 262 43.1
## 263 48.8
## 264 31.0
## 265 36.5
## 267 30.7
## 268 50.0
## 269 43.5
## 274 35.2
## 277 33.2
## 281 45.4
## 283 46.0
## 284 50.0
## 285 32.2
## 292 37.3
## 300 29.0
## 305 36.1
## 307 33.4
## 342 32.7
## 365 21.9
## 371 50.0
## 376 15.0
## 454 17.8
## 483 25.0Boston[Boston$rm > 8, ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 98 0.12083 0 2.89 0 0.4450 8.069 76.0 3.4952 2 276 18.0 4.21 38.7
## 164 1.51902 0 19.58 1 0.6050 8.375 93.9 2.1620 5 403 14.7 3.32 50.0
## 205 0.02009 95 2.68 0 0.4161 8.034 31.9 5.1180 4 224 14.7 2.88 50.0
## 225 0.31533 0 6.20 0 0.5040 8.266 78.3 2.8944 8 307 17.4 4.14 44.8
## 226 0.52693 0 6.20 0 0.5040 8.725 83.0 2.8944 8 307 17.4 4.63 50.0
## 227 0.38214 0 6.20 0 0.5040 8.040 86.5 3.2157 8 307 17.4 3.13 37.6
## 233 0.57529 0 6.20 0 0.5070 8.337 73.3 3.8384 8 307 17.4 2.47 41.7
## 234 0.33147 0 6.20 0 0.5070 8.247 70.4 3.6519 8 307 17.4 3.95 48.3
## 254 0.36894 22 5.86 0 0.4310 8.259 8.4 8.9067 7 330 19.1 3.54 42.8
## 258 0.61154 20 3.97 0 0.6470 8.704 86.9 1.8010 5 264 13.0 5.12 50.0
## 263 0.52014 20 3.97 0 0.6470 8.398 91.5 2.2885 5 264 13.0 5.91 48.8
## 268 0.57834 20 3.97 0 0.5750 8.297 67.0 2.4216 5 264 13.0 7.44 50.0
## 365 3.47428 0 18.10 1 0.7180 8.780 82.9 1.9047 24 666 20.2 5.29 21.9Boston[(Boston$rm > 8) & (Boston$chas == 1), ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 164 1.51902 0 19.58 1 0.605 8.375 93.9 2.1620 5 403 14.7 3.32 50.0
## 365 3.47428 0 18.10 1 0.718 8.780 82.9 1.9047 24 666 20.2 5.29 21.9Boston[(Boston$rm > 8) & (Boston$tax < 350), ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 98 0.12083 0 2.89 0 0.4450 8.069 76.0 3.4952 2 276 18.0 4.21 38.7
## 205 0.02009 95 2.68 0 0.4161 8.034 31.9 5.1180 4 224 14.7 2.88 50.0
## 225 0.31533 0 6.20 0 0.5040 8.266 78.3 2.8944 8 307 17.4 4.14 44.8
## 226 0.52693 0 6.20 0 0.5040 8.725 83.0 2.8944 8 307 17.4 4.63 50.0
## 227 0.38214 0 6.20 0 0.5040 8.040 86.5 3.2157 8 307 17.4 3.13 37.6
## 233 0.57529 0 6.20 0 0.5070 8.337 73.3 3.8384 8 307 17.4 2.47 41.7
## 234 0.33147 0 6.20 0 0.5070 8.247 70.4 3.6519 8 307 17.4 3.95 48.3
## 254 0.36894 22 5.86 0 0.4310 8.259 8.4 8.9067 7 330 19.1 3.54 42.8
## 258 0.61154 20 3.97 0 0.6470 8.704 86.9 1.8010 5 264 13.0 5.12 50.0
## 263 0.52014 20 3.97 0 0.6470 8.398 91.5 2.2885 5 264 13.0 5.91 48.8
## 268 0.57834 20 3.97 0 0.5750 8.297 67.0 2.4216 5 264 13.0 7.44 50.0Boston[(Boston$rm > 8) & (Boston$zn > 80), ]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 205 0.02009 95 2.68 0 0.4161 8.034 31.9 5.118 4 224 14.7 2.88 50range(Boston$dis)## [1] 1.1296 12.1265range(Boston$tax)## [1] 187 711