Data_Analytics_Lab 01
2024-01-25
Question 9
library(ISLR2)
data("Auto")
auto <- Auto
auto <- na.omit(auto)
str(auto)## '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 : Factor w/ 304 levels "amc ambassador brougham",..: 49 36 231 14 161 141 54 223 241 2 ...
## - attr(*, "na.action")= 'omit' Named int [1:5] 33 127 331 337 355
## ..- attr(*, "names")= chr [1:5] "33" "127" "331" "337" ...- Quantitative: mpg,cylinders,displacement,horsepower, weight, acceleration, year.
- Qualitative: name, origin.
sapply(Auto[,1:7], range)## mpg cylinders displacement horsepower weight acceleration year
## [1,] 9.0 3 68 46 1613 8.0 70
## [2,] 46.6 8 455 230 5140 24.8 82sapply(auto[, -c(4, 9)], mean)## mpg cylinders displacement weight acceleration year
## 23.445918 5.471939 194.411990 2977.584184 15.541327 75.979592
## origin
## 1.576531sapply(auto[, -c(4, 9)], sd)## mpg cylinders displacement weight acceleration year
## 7.8050075 1.7057832 104.6440039 849.4025600 2.7588641 3.6837365
## origin
## 0.8055182subset <- auto[-c(10:85), -c(4,9)]
sapply(subset, range)## mpg cylinders displacement weight acceleration year origin
## [1,] 11.0 3 68 1649 8.5 70 1
## [2,] 46.6 8 455 4997 24.8 82 3sapply(subset, mean)## mpg cylinders displacement weight acceleration year
## 24.404430 5.373418 187.240506 2935.971519 15.726899 77.145570
## origin
## 1.601266sapply(subset, sd)## mpg cylinders displacement weight acceleration year
## 7.867283 1.654179 99.678367 811.300208 2.693721 3.106217
## origin
## 0.819910pairs(auto)
- From the plots we can understand that mpg of the car decreases with
the increase in displacement and cylinders of the car. - the new models
are having higher mpg than the older ones. this can be concluded by
observing the mpg and year graph.
auto$horsepower <- as.numeric(auto$horsepower)
cor(auto$weight, auto$horsepower)## [1] 0.8645377cor(auto$weight, auto$displacement)## [1] 0.9329944cor(auto$displacement, auto$horsepower)## [1] 0.897257- From the plots we can understand that cylinders, horsepower, year and origin can be used as predictors. the dis
Question 10
data("Boston")
Boston -> Boston
dim(Boston)## [1] 506 13nrow(Boston)## [1] 506ncol(Boston)## [1] 13str(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 ...pairs(~crim+nox+dis+tax+medv, data = Boston)
cor(Boston[-1],Boston$crim)## [,1]
## zn -0.20046922
## indus 0.40658341
## chas -0.05589158
## nox 0.42097171
## rm -0.21924670
## age 0.35273425
## dis -0.37967009
## rad 0.62550515
## tax 0.58276431
## ptratio 0.28994558
## lstat 0.45562148
## medv -0.38830461pairs(Boston[Boston$crim < 20, ])
## -Crim has negative linear relationship with medv, dis , chas. - crim
has positive linear relationship with indus ,nox , rad and tax
High.Crime = Boston[which(Boston$crim > mean(Boston$crim) + 2*sd(Boston$crim)),]
print(High.Crime)## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 379 23.6482 0 18.1 0 0.671 6.380 96.2 1.3861 24 666 20.2 23.69 13.1
## 381 88.9762 0 18.1 0 0.671 6.968 91.9 1.4165 24 666 20.2 17.21 10.4
## 387 24.3938 0 18.1 0 0.700 4.652 100.0 1.4672 24 666 20.2 28.28 10.5
## 388 22.5971 0 18.1 0 0.700 5.000 89.5 1.5184 24 666 20.2 31.99 7.4
## 399 38.3518 0 18.1 0 0.693 5.453 100.0 1.4896 24 666 20.2 30.59 5.0
## 401 25.0461 0 18.1 0 0.693 5.987 100.0 1.5888 24 666 20.2 26.77 5.6
## 404 24.8017 0 18.1 0 0.693 5.349 96.0 1.7028 24 666 20.2 19.77 8.3
## 405 41.5292 0 18.1 0 0.693 5.531 85.4 1.6074 24 666 20.2 27.38 8.5
## 406 67.9208 0 18.1 0 0.693 5.683 100.0 1.4254 24 666 20.2 22.98 5.0
## 411 51.1358 0 18.1 0 0.597 5.757 100.0 1.4130 24 666 20.2 10.11 15.0
## 414 28.6558 0 18.1 0 0.597 5.155 100.0 1.5894 24 666 20.2 20.08 16.3
## 415 45.7461 0 18.1 0 0.693 4.519 100.0 1.6582 24 666 20.2 36.98 7.0
## 418 25.9406 0 18.1 0 0.679 5.304 89.1 1.6475 24 666 20.2 26.64 10.4
## 419 73.5341 0 18.1 0 0.679 5.957 100.0 1.8026 24 666 20.2 20.62 8.8
## 428 37.6619 0 18.1 0 0.679 6.202 78.7 1.8629 24 666 20.2 14.52 10.9
## 441 22.0511 0 18.1 0 0.740 5.818 92.4 1.8662 24 666 20.2 22.11 10.5range(Boston$crim) ; mean(Boston$crim) ; sd(Boston$crim)## [1] 0.00632 88.97620## [1] 3.613524## [1] 8.601545nrow(High.Crime)## [1] 16-There are 16 suburbs with a crime rate higher than 95% of the other suburbs. -The range is very wide, it goes from a rate of near zero to 89.
High.Tax = Boston[which(Boston$tax > mean(Boston$tax) + 2*sd(Boston$tax)),]
nrow(High.Tax)## [1] 0range(Boston$tax)## [1] 187 711- There are no suburbs that are having high taxes.
High.PT = Boston[which(Boston$ptratio > mean(Boston$ptratio) + 2*sd(Boston$ptratio)),]
range(Boston$ptratio)## [1] 12.6 22.0nrow(High.PT)## [1] 0-No suburbs exhibit a high pupil-to-teacher ratio, which is a reasonable outcome considering that educational regulations impose limits on the number of teachers or students per class or school. -The range is relatively narrow, and all pupil-teacher ratios fall within 2 standard deviations of the mean. -There are instances where pupil-teacher ratios exceed 1 standard deviation.
sum(Boston$chas==1)## [1] 35- there are 35 suburbs bound the charles river
median(Boston$ptratio)## [1] 19.05median(Boston$ptratio)## [1] 19.05which(Boston$medv == min(Boston$medv))## [1] 399 406Boston[399,]## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 399 38.3518 0 18.1 0 0.693 5.453 100 1.4896 24 666 20.2 30.59 5range(Boston$lstat)## [1] 1.73 37.97range(Boston$ptratio)## [1] 12.6 22.0399 and 406 suburbs are having lowest median property values.
sum(Boston$rm > 7)## [1] 64sum(Boston$rm > 8)## [1] 13summary(Boston)## crim zn indus chas
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000
## 1st Qu.: 0.08205 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 lstat
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 1.73
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.: 6.95
## Median : 5.000 Median :330.0 Median :19.05 Median :11.36
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :12.65
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:16.95
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :37.97
## medv
## Min. : 5.00
## 1st Qu.:17.02
## Median :21.20
## Mean :22.53
## 3rd Qu.:25.00
## Max. :50.00summary(subset(Boston, rm > 8))## 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 lstat medv
## Min. : 2.000 Min. :224.0 Min. :13.00 Min. :2.47 Min. :21.9
## 1st Qu.: 5.000 1st Qu.:264.0 1st Qu.:14.70 1st Qu.:3.32 1st Qu.:41.7
## Median : 7.000 Median :307.0 Median :17.40 Median :4.14 Median :48.3
## Mean : 7.462 Mean :325.1 Mean :16.36 Mean :4.31 Mean :44.2
## 3rd Qu.: 8.000 3rd Qu.:307.0 3rd Qu.:17.40 3rd Qu.:5.12 3rd Qu.:50.0
## Max. :24.000 Max. :666.0 Max. :20.20 Max. :7.44 Max. :50.0