# install.packages("ggplot2")
# install.packages("ISLR2")
library(ggplot2)

Conceptual

Question 2

Explain whether each scenario is a classification or regression problem, and indicate whether we are most interested in inference or prediction. Finally, provide n and p.

We collect a set of data on the top 500 firms in the US. For each firm we record profit, number of employees, industry and the CEO salary. We are interested in understanding which factors affect CEO salary.
- Number of Data Points (n): 500
- Number of Predictors (p): 3 (profit, number of employees, industry)
- Type of Problem: Regression
  - Reason: Response variable (CEO Salary) is a quantitative variable
- What are we most interested in: Inference
We are considering launching a new product and wish to know whether it will be a success or a failure. We collect data on 20 similar products that were previously launched. For each product we have recorded whether it was a success or failure, price charged for the product, marketing budget, competition price, and ten other variables.
- Number of Data Points (n): 20
- Number of Predictors (p): 13 (price charged for the product marketing budget, competition price, and ten other variables)
- Type of Problem: Classification
  - Reason: Response variable (If a new product will be a success of a failure) is a qualitative variable
- What are we most interested in: Prediction
We are interested in predicting the % change in the USD/Euro exchange rate in relation to the weekly changes in the world stock markets. Hence we collect weekly data for all of 2012. For each week we record the % change in the USD/Euro, the % change in the US market, the % change in the British market, and the % change in the German market.
- Number of Data Points (n): 52
- Number of Predictors (p): 3 (the % change in the US market, the % change in the British Market, the % change in the German market)
- Type of Problem: Regression
  - Reason: Response variable (the % change in the USD/Euro exchange rate in relation to the weekly changes in the world stock markets) is a quantitative variable
- What are we most interested in: Prediction

Question 5

What are the advantages and disadvantages of a very flexible (versus a less flexible) approach for regression or classification? Under what circumstances might a more flexible approach be preferred to a less flexible approach? When might a less flexible approach be preferred?

Flexible Approach
- Advantages: Can create models for predictors and response variables that do not have a linear relationship. Less chances of bias when finding a relationship between dependent and independent variables.
- Disadvantages: Hard to understand the relationship between the dependent and independent variable. Chance of overfitting
- Preferred circumstances: Models interested in only interested in prediction and the interpretability of the predictive model is simply not of interest
Less Flexible Approach
- Advantages: Easier to understand the relationship between the dependent and independent variables. Less of a chance of overfitting.
- Disadvantages: Higher chances of bias when finding a relationship between dependent and independent variables
- Preferred circumstances: Models focused on inference

Question 6

Describe the differences between a parametric and a non-parametric statistical learning approach. What are the advantages of a parametric approach to regression or classification (as opposed to a non-parametric approach)? What are its disadvantages?

Parametric Statistical Learning Approach
- Definition: A model that makes an assumption about the functional form/shape of f. After a model has been selected, it will then use training data to fit/train the model.
- Advantages: Reduces the problem of estimating f down to one of estimating a set of parameters.
- Disadvantages: The model chosen will usually not match the true unknown form of f
Non-parametric Statistical Learning Approach
- Definition: A model that does not make explicit assumptions about the functional form of f. Instead it takes an estimate of f that gets as close to the data points as possible without being too rough or wiggly.
- Advantages: This model have the potential to accurately fit a wider range of possible shapes for f.
- Disadvantages: Ths model requires a large number of observations to obtain an accurate estimate for f.

Applied

Question 8

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

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

Use the read.csv() function to read the data into R. Call the loaded data college. Make sure that you have the directory set to the correct location for the data.

college <- read.csv("College.csv", header = TRUE)

Look at the data using the View() function. You should notice that the first column is just the name of each university. We don’t really want R to treat this as data. However, it may be handy to have these names for later. Try the following commands:

rownames (college) <- college[, 1]
View(college)

rownames(college) <- college[,1]
# had to comment out view as R would not knit the file if it was included
# View(college)
head(college)

##                                                         X Private Apps Accept
## Abilene Christian University Abilene Christian University     Yes 1660   1232
## Adelphi University                     Adelphi University     Yes 2186   1924
## Adrian College                             Adrian College     Yes 1428   1097
## Agnes Scott College                   Agnes Scott College     Yes  417    349
## Alaska Pacific University       Alaska Pacific University     Yes  193    146
## Albertson College                       Albertson College     Yes  587    479
##                              Enroll Top10perc Top25perc F.Undergrad P.Undergrad
## Abilene Christian University    721        23        52        2885         537
## Adelphi University              512        16        29        2683        1227
## Adrian College                  336        22        50        1036          99
## Agnes Scott College             137        60        89         510          63
## Alaska Pacific University        55        16        44         249         869
## Albertson College               158        38        62         678          41
##                              Outstate Room.Board Books Personal PhD Terminal
## Abilene Christian University     7440       3300   450     2200  70       78
## Adelphi University              12280       6450   750     1500  29       30
## Adrian College                  11250       3750   400     1165  53       66
## Agnes Scott College             12960       5450   450      875  92       97
## Alaska Pacific University        7560       4120   800     1500  76       72
## Albertson College               13500       3335   500      675  67       73
##                              S.F.Ratio perc.alumni Expend Grad.Rate
## Abilene Christian University      18.1          12   7041        60
## Adelphi University                12.2          16  10527        56
## Adrian College                    12.9          30   8735        54
## Agnes Scott College                7.7          37  19016        59
## Alaska Pacific University         11.9           2  10922        15
## Albertson College                  9.4          11   9727        55

Use the summary() function to produce a numerical summary of the variables in the data set.

summary(college)

##       X               Private               Apps           Accept     
##  Length:777         Length:777         Min.   :   81   Min.   :   72  
##  Class :character   Class :character   1st Qu.:  776   1st Qu.:  604  
##  Mode  :character   Mode  :character   Median : 1558   Median : 1110  
##                                        Mean   : 3002   Mean   : 2019  
##                                        3rd Qu.: 3624   3rd Qu.: 2424  
##                                        Max.   :48094   Max.   :26330  
##      Enroll       Top10perc       Top25perc      F.Undergrad   
##  Min.   :  35   Min.   : 1.00   Min.   :  9.0   Min.   :  139  
##  1st Qu.: 242   1st Qu.:15.00   1st Qu.: 41.0   1st Qu.:  992  
##  Median : 434   Median :23.00   Median : 54.0   Median : 1707  
##  Mean   : 780   Mean   :27.56   Mean   : 55.8   Mean   : 3700  
##  3rd Qu.: 902   3rd Qu.:35.00   3rd Qu.: 69.0   3rd Qu.: 4005  
##  Max.   :6392   Max.   :96.00   Max.   :100.0   Max.   :31643  
##   P.Undergrad         Outstate       Room.Board       Books       
##  Min.   :    1.0   Min.   : 2340   Min.   :1780   Min.   :  96.0  
##  1st Qu.:   95.0   1st Qu.: 7320   1st Qu.:3597   1st Qu.: 470.0  
##  Median :  353.0   Median : 9990   Median :4200   Median : 500.0  
##  Mean   :  855.3   Mean   :10441   Mean   :4358   Mean   : 549.4  
##  3rd Qu.:  967.0   3rd Qu.:12925   3rd Qu.:5050   3rd Qu.: 600.0  
##  Max.   :21836.0   Max.   :21700   Max.   :8124   Max.   :2340.0  
##     Personal         PhD            Terminal       S.F.Ratio    
##  Min.   : 250   Min.   :  8.00   Min.   : 24.0   Min.   : 2.50  
##  1st Qu.: 850   1st Qu.: 62.00   1st Qu.: 71.0   1st Qu.:11.50  
##  Median :1200   Median : 75.00   Median : 82.0   Median :13.60  
##  Mean   :1341   Mean   : 72.66   Mean   : 79.7   Mean   :14.09  
##  3rd Qu.:1700   3rd Qu.: 85.00   3rd Qu.: 92.0   3rd Qu.:16.50  
##  Max.   :6800   Max.   :103.00   Max.   :100.0   Max.   :39.80  
##   perc.alumni        Expend        Grad.Rate     
##  Min.   : 0.00   Min.   : 3186   Min.   : 10.00  
##  1st Qu.:13.00   1st Qu.: 6751   1st Qu.: 53.00  
##  Median :21.00   Median : 8377   Median : 65.00  
##  Mean   :22.74   Mean   : 9660   Mean   : 65.46  
##  3rd Qu.:31.00   3rd Qu.:10830   3rd Qu.: 78.00  
##  Max.   :64.00   Max.   :56233   Max.   :118.00

Use the pairs() function to produce a scatterplot matrix of the first ten columns or variables of the data. Recall that you can reference the first ten columns of a matrix A using A[,1:10].

# used rows 3 through 12 for pair plot as columns 1 is college names
# columns 2 is private (Yes if a a college is private school, No if a college is a public school)
A <- college[,3:12]
pairs(A)

Use the plot() function to produce side-by-side boxplots of Outstate versus Private.

# converted Private column into a factor type 
college$Private <- as.factor(college$Private)
plot(college$Private, college$Outstate,
     xlab = "Private",
     ylab = "Outstate")

Create a new qualitative variable, called Elite, by binning the Top10perc variable. We are going to divide universities into two groups based on whether or not the proportion of students coming from the top 10 % of their high school classes exceeds 50 %.
- Elite <- rep(“No”, nrow(college))
- Elite[college$ Top10perc > 50] <- “Yes”
- Elite <- as.factor(Elite)
- college <- data.frame(college , Elite)
```
Elite <- rep("No", nrow(college))
Elite[college$ Top10perc > 50] <- "Yes"
Elite <- as.factor(Elite)
college <- data.frame(college , Elite)
```
Use the summary() function to see how many elite universities there are.
```
summary(college$Elite)
```
```
##  No Yes 
## 699  78
```
Now use the plot() function to produce side-by-side boxplots of Outstate versus Elite.
```
plot(college$Elite, college$Outstate,
     xlab = "Elite",
     ylab = "Outstate")
```
Use the hist() function to produce some histograms with differing numbers of bins for a few of the quantitative variables. You may find the command par(mfrow = c(2, 2)) useful: it will divide the print window into four regions so that four plots can be made simultaneously. Modifying the arguments to this function will divide the screen in other ways.

par(mfrow = c(2,2))
hist(college$Outstate)
hist(college$Apps)
hist(college$Enroll)
hist(college$Grad.Rate)

Continue exploring the data, and provide a brief summary of what you discover.

college |> 
  ggplot(
    aes(
      x = Outstate,
      y = Grad.Rate
  )) +
  geom_point() +
  geom_smooth(method = lm, color = "red")

## `geom_smooth()` using formula = 'y ~ x'

college |> 
  ggplot(
    aes(
      x = Apps,
      y = Accept
    )
  ) + geom_point() +
  geom_smooth(method = lm, color = "red")

## `geom_smooth()` using formula = 'y ~ x'

Based on the scatterplots above we can see that there is a positive correlation between students at outstate colleges and the graduation rate. We can also see that there is a positive correlation between the number of applications a college receives and the total number of students they accept. However, its important to note that majority of point are clustered on the lower left corner of the graph. This could be a problem when doing further analysis on the data.

Question 9

This exercise involves the Auto data set studied in the lab. Make sure that the missing values have been removed from the data.

# removing rows that have a ? listed for horsepower as it will affect other parts of the question.
auto <- read.csv("Auto.csv", header = TRUE, na.strings = "?")

Which of the predictors are quantitative, and which are qualitative?

Response variable: mpg The name column will not be included due to it not being a good predictor variable
- Quantitative:
  - displacement
  - weight
  - acceleration
  - horsepower
- Qualitative:
  - cylinders (number of cylinders are between 4 and 8)
  - year (Model Year)
  - origin (maker 1: American, 2: European, 3: Japanese)

What is the range of each quantitative predictor? You can answer this using the range() function.

# removed any NA values as the current data set was affecting the range of some variables. Because if a column has just one NA value 
# it will return NA for the whole function.

clean_auto <- na.omit(auto)
cat("displacement range:", range(clean_auto$displacement), "\n")
## displacement range: 68 455
cat("weight range:", range(clean_auto$weight), "\n")
## weight range: 1613 5140
cat("acceleration range:", range(clean_auto$acceleration), "\n")
## acceleration range: 8 24.8
cat("horsepower range:", range(clean_auto$horsepower), "\n")
## horsepower range: 46 230

Note that the horsepower range starts with ?. This is because there are 4 points in the dataset that have a ? listed as their horsepower.

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

# used cleaned data set from previous R chunk as the current data set was affecting the range of some variables. 
# Because if a column has just one NA value it will return NA for the whole function.

cat("displacement mean:", mean(clean_auto$displacement), "\n")
## displacement mean: 194.412
cat("displacement standard deviation:", sd(clean_auto$displacement), "\n")
## displacement standard deviation: 104.644
cat("weight mean:", mean(clean_auto$weight), "\n")
## weight mean: 2977.584
cat("weight standard deviation:", sd(clean_auto$weight), "\n")
## weight standard deviation: 849.4026
cat("acceleration mean:", mean(clean_auto$acceleration), "\n")
## acceleration mean: 15.54133
cat("acceleration standard deviation:", sd(clean_auto$acceleration), "\n")
## acceleration standard deviation: 2.758864
cat("horsepower mean:", mean(clean_auto$horsepower), "\n")
## horsepower mean: 104.4694
cat("horsepower standard deviation:", sd(clean_auto$horsepower), "\n")
## horsepower standard deviation: 38.49116

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?

# used cleaned data set from previous R chunk as the current data set was affecting the range of some variables. 
# Because if a column has just one NA value it will return NA for the whole function.
auto <- clean_auto[-c(10:85),]

cat("displacement range:", range(clean_auto$displacement), "\n")
## displacement range: 68 455
cat("displacement mean:", mean(clean_auto$displacement), "\n")
## displacement mean: 194.412
cat("displacement standard deviation:", sd(clean_auto$displacement), "\n")
## displacement standard deviation: 104.644
cat("weight range:", range(clean_auto$weight), "\n")
## weight range: 1613 5140
cat("weight mean:", mean(clean_auto$weight), "\n")
## weight mean: 2977.584
cat("weight standard deviation:", sd(clean_auto$weight), "\n")
## weight standard deviation: 849.4026
cat("acceleration range:", range(clean_auto$acceleration), "\n")
## acceleration range: 8 24.8
cat("acceleration mean:", mean(clean_auto$acceleration), "\n")
## acceleration mean: 15.54133
cat("acceleration standard deviation:", sd(clean_auto$acceleration), "\n")
## acceleration standard deviation: 2.758864
cat("horsepower range:", range(clean_auto$horsepower), "\n")
## horsepower range: 46 230
cat("horsepower mean:", mean(clean_auto$horsepower), "\n")
## horsepower mean: 104.4694
cat("horsepower standard deviation:", sd(clean_auto$horsepower), "\n")
## horsepower standard deviation: 38.49116

Using the full data set, investigate the predictors graphically, using scatterplots or other tools of your choice. Create some plots highlighting the relationships among the predictors. Comment on your findings.

auto_nums <- auto[1:8]
plot(auto_nums)

par(mfrow = c(1,2))
hist(auto$weight)
hist(auto$displacement)

Based on the pair plots above we can see that there is a negative correlation in the graph comparing mpg vs displacement and mpg vs weight. On the other hand for mpg vs year, we can see that the newer the car the more mpg a car has. Also, from the histograms we can see that the data is right skewed. For weight this means that majority of the cars in the data set are lighter in weight with a few points that are heavy. As for displacement, this means that majority of the cars in the data set have smaller engines. 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. Based on the previous plots, yes there are three main variables that to predict mpg would be weight, displacement, and horsepower. I believe these are the best options as we can see in the pair plots that they have the most correlation with each other. In the pair plots we can see that each has a negative correlation with mpg. While cylinder, year, and origin may be helpful in addition to the main three, I don’t think they provide enough information to a prediction model to accurately predict mpg.

Question 10

This exercise involves the Boston housing data set.

To begin, load in the Boston data set. The Boston data set is part of the ISLR2 library.

library(ISLR2)

Now the data set is contained in the object Boston

head(Boston, 20)

##       crim   zn indus chas   nox    rm   age    dis rad tax ptratio lstat medv
## 1  0.00632 18.0  2.31    0 0.538 6.575  65.2 4.0900   1 296    15.3  4.98 24.0
## 2  0.02731  0.0  7.07    0 0.469 6.421  78.9 4.9671   2 242    17.8  9.14 21.6
## 3  0.02729  0.0  7.07    0 0.469 7.185  61.1 4.9671   2 242    17.8  4.03 34.7
## 4  0.03237  0.0  2.18    0 0.458 6.998  45.8 6.0622   3 222    18.7  2.94 33.4
## 5  0.06905  0.0  2.18    0 0.458 7.147  54.2 6.0622   3 222    18.7  5.33 36.2
## 6  0.02985  0.0  2.18    0 0.458 6.430  58.7 6.0622   3 222    18.7  5.21 28.7
## 7  0.08829 12.5  7.87    0 0.524 6.012  66.6 5.5605   5 311    15.2 12.43 22.9
## 8  0.14455 12.5  7.87    0 0.524 6.172  96.1 5.9505   5 311    15.2 19.15 27.1
## 9  0.21124 12.5  7.87    0 0.524 5.631 100.0 6.0821   5 311    15.2 29.93 16.5
## 10 0.17004 12.5  7.87    0 0.524 6.004  85.9 6.5921   5 311    15.2 17.10 18.9
## 11 0.22489 12.5  7.87    0 0.524 6.377  94.3 6.3467   5 311    15.2 20.45 15.0
## 12 0.11747 12.5  7.87    0 0.524 6.009  82.9 6.2267   5 311    15.2 13.27 18.9
## 13 0.09378 12.5  7.87    0 0.524 5.889  39.0 5.4509   5 311    15.2 15.71 21.7
## 14 0.62976  0.0  8.14    0 0.538 5.949  61.8 4.7075   4 307    21.0  8.26 20.4
## 15 0.63796  0.0  8.14    0 0.538 6.096  84.5 4.4619   4 307    21.0 10.26 18.2
## 16 0.62739  0.0  8.14    0 0.538 5.834  56.5 4.4986   4 307    21.0  8.47 19.9
## 17 1.05393  0.0  8.14    0 0.538 5.935  29.3 4.4986   4 307    21.0  6.58 23.1
## 18 0.78420  0.0  8.14    0 0.538 5.990  81.7 4.2579   4 307    21.0 14.67 17.5
## 19 0.80271  0.0  8.14    0 0.538 5.456  36.6 3.7965   4 307    21.0 11.69 20.2
## 20 0.72580  0.0  8.14    0 0.538 5.727  69.5 3.7965   4 307    21.0 11.28 18.2

Read about the data set:

?Boston

How many rows are in this data set? How many columns? What do the rows and columns represent? - 506 rows - 13 columns The columns represents all the variables in a data set and the rows represents the values for 506 suburbs of Boston.

Make some pairwise scatterplots of the predictors (columns) in this data set. Describe your findings.

pairs(Boston[,1:4])

pairs(Boston[,c(1,5:9)])

pairs(Boston[,c(1,10:13)])

Based on the pairwise scatterplots, we can see that majority of the predictor variables against crime rate (crim) are not showing a clear pattern. We can see that in the data set that many of the points represent a low crime rate with a few high points.

Are any of the predictors associated with per capita crime rate? If so, explain the relationship. Based on the plot from the previous question, I would say rad and age could be associated with per capita crime rate. I say this because in the scatterplot we can see that when rad is 24, the per capita crime rate increases. Also, for age, we can see that the older a house is the higher the crime right. For both plots it seems as though the points are cluster together on the higher end of age and rad which the crime rate increases.
Do any of the census tracts of Boston appear to have particularly high crime rates? Tax rates? Pupil-teacher ratios? Comment on the range of each predictor.

cat("Crime Rate Range:", range(Boston$crim), "\n")
## Crime Rate Range: 0.00632 88.9762
cat("Tax Rates Range:", range(Boston$tax), "\n")
## Tax Rates Range: 187 711
cat("Pupil-teacher Ratios Range:", range(Boston$ptratio))
## Pupil-teacher Ratios Range: 12.6 22

We can see that the crime rate and tax rate ranges are large compare to the pupil teach ratio that has a small range.

hist(Boston$crim)

Based on the histogram, we can see that the data is right skewed meaning that my thought in the previous question was correct. The data set contains a high number of low crime rates in the data set.

How many of the census tracts in this data set bound the Charles river?

table(Boston$chas)

## 
##   0   1 
## 471  35

In this data set there are 35 census tracts that are bound to the Charles river. f. What is the median pupil-teacher ratio among the towns in this data set?

cat("Median Pupil-teacher Ratio:", median(Boston$ptratio))

## Median Pupil-teacher Ratio: 19.05

Which census tract of Boston has lowest median value of owner-occupied homes? What are the values of the other predictors for that census tract, and how do those values compare to the overall ranges for those predictors? Comment on your findings.

lowest_median <- which(Boston$medv == min(Boston$medv))
Boston[lowest_median,]

##        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    5
## 406 67.9208  0  18.1    0 0.693 5.683 100 1.4254  24 666    20.2 22.98    5

Using the which function along with minimum, we see there are two entries that have the lowest median value of owner-occupied homes; row 399 and row 406.

cat("zn Range:", range(Boston$zn), "\n")
## zn Range: 0 100
cat("indus Range:", range(Boston$indus), "\n")
## indus Range: 0.46 27.74
cat("chas Range:", range(Boston$chas), "\n")
## chas Range: 0 1
cat("nox Range:", range(Boston$nox), "\n")
## nox Range: 0.385 0.871
cat("rm Range:", range(Boston$rm), "\n")
## rm Range: 3.561 8.78
cat("age Range:", range(Boston$age), "\n")
## age Range: 2.9 100
cat("dis Range:", range(Boston$dis), "\n")
## dis Range: 1.1296 12.1265
cat("rad Range:", range(Boston$rad), "\n")
## rad Range: 1 24
cat("tax Range:", range(Boston$tax), "\n")
## tax Range: 187 711
cat("ptratio Range:", range(Boston$ptratio), "\n")
## ptratio Range: 12.6 22
cat("lstat Range:", range(Boston$lstat), "\n")
## lstat Range: 1.73 37.97
cat("medv Range:", range(Boston$medv))
## medv Range: 5 50

Based on the ranges, below is how rows 399 and 406 compare:

Row 399
- zn: 0
  - Lowest value of the range
- indus: 18.1
  - Towards the higher end of the range
- chas: 0
  - On the low end (the start) of the range. The house is not bound to the Charles River
- nox: 0.693
  - Near the middle of the range
- rm: 5.453
  - Near the middle of the range
- age: 100
  - Highest value of the range
- dis: 1.4896
  - Near the lower end of the range
- rad: 24
  - Highest value of the range
- tax: 666
  - Near the high end of the range
- ptratio: 20.2
  - Near the high end of the range
- lstat: 30.59
  - Near the high end of the range
- medv: 5
  - Lowest value of the range
Row 406
- zn: 0
  - Lowest value of the range
- indus: 18.1
  - Towards the higher end of the range
- chas: 0
  - On the low end (the start) of the range. The house is not bound to the Charles River
- nox: 0.693
  - Near the middle of the range
- rm: 5.683
  - Near the middle of the range
- age: 100
  - Highest value of the range
- dis: 1.4254
  - Near the lower end of the range
- rad: 24
  - Highest value of the range
- tax: 666
  - Near the high end of the range
- ptratio: 20.2
  - Near the high end of the range
- lstat: 22.98
  - Near the high end of the range
- medv: 5
  - Lowest value of the range

In this data set, how many of the census tracts average more than seven rooms per dwelling? More than eight rooms per dwelling? Comment on the census tracts that average more than eight rooms per dwelling.

plus_sev_rms <- which(Boston$rm > 7)
Boston[plus_sev_rms,]

##         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 25.0

In this data set there are 64 census tracts that average more than seven rooms per dwelling.

plus_eight_rms <- which(Boston$rm > 8)
Boston[plus_eight_rms,]

##        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 21.9

In this data set there are 13 census tracts that average more than eight rooms per dwelling.

Of the census tracts that average more than eight rooms per dwelling we can see:

The highest crime rate is 3.47, which compared to the range is on the low end.
The highest zn is 95, which compared to the range is near the high end
The highest indus is 19.58, which compared to the range is on the high end.
There are only 2 house that are bound to the Charles River.
The highest nox is 0.7180, which compared to the range is near the high end.
The highest average number of rooms is 8.780, which compared to the range is the max value of the range.
The highest age is 93, which compared to the range is near the high end.
The highest dis is 8.9067, which compared to the range is near the high end.
The highest rad is 24, which compared to the range is the max value of the range.
The highest tax is 666, which compared to the range is near the high end.
The highest ptratio is 20.2, which compared to the range is near the high end.
The highest lstat is 7.44, which compared to the range is near the low end.
The highest medv is 50.0, which compared to the range is the max value of the range.

Assignment 1

Briley Winge