Ross Enlow - Problem Set 1
Directions
In this assignment you will get to practice your R coding skills a little more and also learn some more useful functions! This assignment should be done in R Markdown (don’t worry we will cover that in next week’s lecture 3A. In the meantime, you can start on the code and just save it as an R script.)
Problem 1: Auto Data
This exercise involves the Auto data set that we studied during lab. Make sure that the missing values have been removed from the data.
Auto=read.table("Auto.data")
library(tidyverse)## -- Attaching packages ---------------- tidyverse 1.2.1 --## v ggplot2 3.2.1 v purrr 0.3.2
## v tibble 2.1.3 v dplyr 0.8.3
## v tidyr 0.8.3 v stringr 1.4.0
## v readr 1.3.1 v forcats 0.4.0## -- Conflicts ------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()Auto=read.table("Auto.data",header=T,na.strings ="?")
dim(Auto)## [1] 397 9Auto=na.omit(Auto)
dim(Auto)## [1] 392 9A.) Which of the predictors are quantitative, and which are qualitative?
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 : num 130 165 150 150 140 198 220 215 225 190 ...
## $ weight : num 3504 3693 3436 3433 3449 ...
## $ 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 33 127 331 337 355
## ..- attr(*, "names")= chr "33" "127" "331" "337" ...Quantitative: MPG, Displacement, Horsepower, Weight, and Acceleration. Qualitative: Cylinders, Year, Origin.
B.) What is the range of each quantitative predictor?
range(Auto$mpg)## [1] 9.0 46.6range(Auto$displacement)## [1] 68 455range(Auto$horsepower)## [1] 46 230range(Auto$weight)## [1] 1613 5140range(Auto$acceleration)## [1] 8.0 24.8attach(Auto)## The following object is masked from package:ggplot2:
##
## mpgC.) What is the mean and standard deviation of each quantitative predictor?
mean(mpg)## [1] 23.44592mean(displacement)## [1] 194.412mean(horsepower)## [1] 104.4694mean(weight)## [1] 2977.584mean(acceleration)## [1] 15.54133sd(mpg)## [1] 7.805007sd(displacement)## [1] 104.644sd(horsepower)## [1] 38.49116sd(weight)## [1] 849.4026sd(acceleration)## [1] 2.758864D.) Now remove the 10th through 85th observations. What is the range, mean, and standard deviation of each predictor in the subset of the data that remains?
AutoSub<-Auto[-c(10:85),]
dim(AutoSub)## [1] 316 9range(AutoSub$mpg)## [1] 11.0 46.6range(AutoSub$displacement)## [1] 68 455range(AutoSub$horsepower)## [1] 46 230range(AutoSub$weight)## [1] 1649 4997range(AutoSub$acceleration)## [1] 8.5 24.8mean(AutoSub$mpg)## [1] 24.40443mean(AutoSub$displacement)## [1] 187.2405mean(AutoSub$horsepower)## [1] 100.7215mean(AutoSub$weight)## [1] 2935.972mean(AutoSub$acceleration)## [1] 15.7269sd(AutoSub$mpg)## [1] 7.867283sd(AutoSub$displacement)## [1] 99.67837sd(AutoSub$horsepower)## [1] 35.70885sd(AutoSub$weight)## [1] 811.3002sd(AutoSub$acceleration)## [1] 2.693721E.) Using the full data set, investigate the predictors graphically, using scatterplots and other tools of your choice. Create some plots (at least 3) highlighting the relationships among the predictors. Comment on your findings.
ggplot(data = Auto) +
geom_point(mapping = aes(x= horsepower, y= acceleration, color = cylinders))
cor(horsepower, acceleration)## [1] -0.6891955Here we see that there is a strong negative correlation between horsepower and acceleration in that at horsepower increases, acceleration decreases. The third variable of cylinders shows that typically cars with greater acceleration and lower horsepower have fewer cylinders, whereas when horsepower increases and acceleration decreases, the amount of cylinders typically appears to decreases.
ggplot(data = Auto) +
geom_smooth(mapping = aes(x= year, y= mpg))## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
cor(year, mpg)## [1] 0.580541Here we see a somewhat strong relationship between mpg and year, where as the vehicles are newer they get more miles per gallon.
ggplot(data = Auto, mapping = aes(x = weight, y = acceleration)) +
geom_point(mapping = aes(color = year)) +
geom_smooth()## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
cor(weight, acceleration)## [1] -0.4168392Here we see a negative medium to strong relationship between weight and acceleration in that as the weight increases, acceleration tends to decrease. We also see that the third variable of the year doesn’t seem to follow the trend of the relationship between weight and acceleration.
F.) Suppose that we wish to predict gas mileage (mpg) on the basis of the other variables. Do your plots suggest that any of the other variables might be useful in predicting mpg? Justify your answer
Yes. The second plot suggests that the year of the vehicle is a strong predictor of mpg. In statistical language, a correlation value of +0.58 suggests a strong relationship between variables, indicating that it is typical for the mpg to increase as the year increases. We can identify this trend quite easily when looking at the visual as well.
Problem 2: Working with vectors and matrices
Provide the code and output for each of the following tasks:
A.) Construct a matrix, where rows represent each movie. Name this matrix StarWars and output it
# Box office Star Wars (in millions!)
new_hope <- c(460.998, 314.4)
empire_strikes <- c(290.475, 247.900)
return_jedi <- c(309.306, 165.8)
# Vectors region and titles, used for naming
region <- c("US", "non-US")
titles <- c("A New Hope", "The Empire Strikes Back", "Return of
the Jedi")
starWars<-matrix(data= c(new_hope, empire_strikes, return_jedi), nrow = 3, ncol = 2, byrow = TRUE)
starWars## [,1] [,2]
## [1,] 460.998 314.4
## [2,] 290.475 247.9
## [3,] 309.306 165.8B.) Rename the rows and columns of the matrix you created in Part A with the vector region for columns and the vector titles for rows. Then print the matrix.
starWars<-matrix(data= c(new_hope, empire_strikes, return_jedi), nrow = 3, ncol = 2, byrow = TRUE)
rownames(starWars) <- c("A New Hope", "The Empire Strikes Back", "Return of the Jedi")
colnames(starWars) <- c("US", "non-US")
starWars## US non-US
## A New Hope 460.998 314.4
## The Empire Strikes Back 290.475 247.9
## Return of the Jedi 309.306 165.8C.) Calculate the worldwide box office figures for each movie using the rowSums() function. Name and output this vector.
WorldwideBoxOffice<-rowSums(starWars)
WorldwideBoxOffice## A New Hope The Empire Strikes Back Return of the Jedi
## 775.398 538.375 475.106D.) Now we want to add a column to our matrix for worldwide sales. You can do this by using the cbind() function. This function binds columns together.
US<- c(460.998, 290.475, 309.306)
nonUS<- c(314.4, 247.9, 165.8)
WorldWideSales<- c(775.398, 538.375, 475.106)
starWars<- cbind(US, nonUS, WorldWideSales)
starWars<-matrix(data= c(new_hope, empire_strikes, return_jedi), nrow = 3, ncol = 3, byrow = TRUE)
colnames(starWars) <- c("US", "non-US", "WorldWideSales")
rownames(starWars) <- c("A New Hope", "The Empire Strikes Back", "Return of the Jedi")
starWars## US non-US WorldWideSales
## A New Hope 460.998 314.400 290.475
## The Empire Strikes Back 247.900 309.306 165.800
## Return of the Jedi 460.998 314.400 290.475E.) Create another matrix for the prequels and name it starWars2. Don’t forget to name the rows and the columns (similar to above)
# Prequels
phantom_menace <- c(474.5, 552.5, 1027.0)
attack_clones <- c(310.7, 338.7, 649.4)
revenge_sith <- c(380.3, 468.5, 848.8)
titles2<-c("The Phantom Menace”, “Attack of the Clones”, “Revenge of the Sith")
starWars2<- matrix(data= c(phantom_menace, attack_clones, revenge_sith), nrow = 3, ncol = 3, byrow = TRUE)
rownames(starWars2)<- c("The Phantom Menace", "Attack of the Clones", "revenge of the Sith")
colnames(starWars2) <- c("US", "non-US", "WroldWideSalesPrequels")
starWars2## US non-US WroldWideSalesPrequels
## The Phantom Menace 474.5 552.5 1027.0
## Attack of the Clones 310.7 338.7 649.4
## revenge of the Sith 380.3 468.5 848.8F.) Make one big matrix that combines all the movies (from starWars and starWars2) using rbind(). This binds rows or in this case can be used to combine to matrices. Name this new matrix allStarWars.
allStarWars<-rbind(starWars, starWars2)
allStarWars## US non-US WorldWideSales
## A New Hope 460.998 314.400 290.475
## The Empire Strikes Back 247.900 309.306 165.800
## Return of the Jedi 460.998 314.400 290.475
## The Phantom Menace 474.500 552.500 1027.000
## Attack of the Clones 310.700 338.700 649.400
## revenge of the Sith 380.300 468.500 848.800G.) Find the total non-US revenue for all the movies using the colSums() function.
colSums(allStarWars)## US non-US WorldWideSales
## 2335.396 2297.806 3271.950Problem 3
College Data This uses the College.csv data set that can be found on the book’s website. It contains a number of variables for 777 different universities and colleges in the US. For information on the variables see page 54 in the textbook (Introduction to Statistical Learning).
A.) Use the read.csv() function to read the data into R. You can download the data from the book’s website (don’t forget to set the working directory) or you can use the URL.
college<-read.csv("College.csv", header = TRUE, na.strings = "?")B.)
View(college)
rownames(college) <- college[,1]
View(college)
College <- college[,-1]
View(college)C.)
Ca
summary(College)## Private Apps Accept Enroll Top10perc
## No :212 Min. : 81 Min. : 72 Min. : 35 Min. : 1.00
## Yes:565 1st Qu.: 776 1st Qu.: 604 1st Qu.: 242 1st Qu.:15.00
## Median : 1558 Median : 1110 Median : 434 Median :23.00
## Mean : 3002 Mean : 2019 Mean : 780 Mean :27.56
## 3rd Qu.: 3624 3rd Qu.: 2424 3rd Qu.: 902 3rd Qu.:35.00
## Max. :48094 Max. :26330 Max. :6392 Max. :96.00
## Top25perc F.Undergrad P.Undergrad Outstate
## Min. : 9.0 Min. : 139 Min. : 1.0 Min. : 2340
## 1st Qu.: 41.0 1st Qu.: 992 1st Qu.: 95.0 1st Qu.: 7320
## Median : 54.0 Median : 1707 Median : 353.0 Median : 9990
## Mean : 55.8 Mean : 3700 Mean : 855.3 Mean :10441
## 3rd Qu.: 69.0 3rd Qu.: 4005 3rd Qu.: 967.0 3rd Qu.:12925
## Max. :100.0 Max. :31643 Max. :21836.0 Max. :21700
## Room.Board Books Personal PhD
## Min. :1780 Min. : 96.0 Min. : 250 Min. : 8.00
## 1st Qu.:3597 1st Qu.: 470.0 1st Qu.: 850 1st Qu.: 62.00
## Median :4200 Median : 500.0 Median :1200 Median : 75.00
## Mean :4358 Mean : 549.4 Mean :1341 Mean : 72.66
## 3rd Qu.:5050 3rd Qu.: 600.0 3rd Qu.:1700 3rd Qu.: 85.00
## Max. :8124 Max. :2340.0 Max. :6800 Max. :103.00
## Terminal S.F.Ratio perc.alumni Expend
## Min. : 24.0 Min. : 2.50 Min. : 0.00 Min. : 3186
## 1st Qu.: 71.0 1st Qu.:11.50 1st Qu.:13.00 1st Qu.: 6751
## Median : 82.0 Median :13.60 Median :21.00 Median : 8377
## Mean : 79.7 Mean :14.09 Mean :22.74 Mean : 9660
## 3rd Qu.: 92.0 3rd Qu.:16.50 3rd Qu.:31.00 3rd Qu.:10830
## Max. :100.0 Max. :39.80 Max. :64.00 Max. :56233
## Grad.Rate
## Min. : 10.00
## 1st Qu.: 53.00
## Median : 65.00
## Mean : 65.46
## 3rd Qu.: 78.00
## Max. :118.00Cb
pairs(College[,1:10])
Cc
OvsP<- ggplot(data = College) +
geom_boxplot(mapping = aes(x = College$Private, y = College$Outstate))
OvsP<- OvsP + scale_x_discrete(name = "Private") +
scale_y_continuous(name = "OutState")
OvsP
Cd
Elite <- rep("No", nrow(College))
Elite[College$Top10perc > 50] = "Yes"
Elite <- as.factor(Elite)
College <- data.frame(College, Elite)
summary(College)## Private Apps Accept Enroll Top10perc
## No :212 Min. : 81 Min. : 72 Min. : 35 Min. : 1.00
## Yes:565 1st Qu.: 776 1st Qu.: 604 1st Qu.: 242 1st Qu.:15.00
## Median : 1558 Median : 1110 Median : 434 Median :23.00
## Mean : 3002 Mean : 2019 Mean : 780 Mean :27.56
## 3rd Qu.: 3624 3rd Qu.: 2424 3rd Qu.: 902 3rd Qu.:35.00
## Max. :48094 Max. :26330 Max. :6392 Max. :96.00
## Top25perc F.Undergrad P.Undergrad Outstate
## Min. : 9.0 Min. : 139 Min. : 1.0 Min. : 2340
## 1st Qu.: 41.0 1st Qu.: 992 1st Qu.: 95.0 1st Qu.: 7320
## Median : 54.0 Median : 1707 Median : 353.0 Median : 9990
## Mean : 55.8 Mean : 3700 Mean : 855.3 Mean :10441
## 3rd Qu.: 69.0 3rd Qu.: 4005 3rd Qu.: 967.0 3rd Qu.:12925
## Max. :100.0 Max. :31643 Max. :21836.0 Max. :21700
## Room.Board Books Personal PhD
## Min. :1780 Min. : 96.0 Min. : 250 Min. : 8.00
## 1st Qu.:3597 1st Qu.: 470.0 1st Qu.: 850 1st Qu.: 62.00
## Median :4200 Median : 500.0 Median :1200 Median : 75.00
## Mean :4358 Mean : 549.4 Mean :1341 Mean : 72.66
## 3rd Qu.:5050 3rd Qu.: 600.0 3rd Qu.:1700 3rd Qu.: 85.00
## Max. :8124 Max. :2340.0 Max. :6800 Max. :103.00
## Terminal S.F.Ratio perc.alumni Expend
## Min. : 24.0 Min. : 2.50 Min. : 0.00 Min. : 3186
## 1st Qu.: 71.0 1st Qu.:11.50 1st Qu.:13.00 1st Qu.: 6751
## Median : 82.0 Median :13.60 Median :21.00 Median : 8377
## Mean : 79.7 Mean :14.09 Mean :22.74 Mean : 9660
## 3rd Qu.: 92.0 3rd Qu.:16.50 3rd Qu.:31.00 3rd Qu.:10830
## Max. :100.0 Max. :39.80 Max. :64.00 Max. :56233
## Grad.Rate Elite
## Min. : 10.00 No :699
## 1st Qu.: 53.00 Yes: 78
## Median : 65.00
## Mean : 65.46
## 3rd Qu.: 78.00
## Max. :118.00OvsE<- ggplot(data = College) +
geom_boxplot(mapping = aes(x = College$Elite, y = College$Outstate))
OvsE<- OvsE + scale_x_discrete(name = "Elite") +
scale_y_continuous(name = "OutState")
OvsE