Applied Statistics-Homework 2 Solved

Exercise 1: Adding Variables to a Dataset
As a first step in analyzing the sb dataset, we’ll add a few variables to the dataset. We’ll analyze these variables throughout this assignment.

Note that for this assignment, because sb is already a copy of the original Seatbelts dataset from R, it is appropriate to adjust the sb dataset directly rather than creating a newly named dataframe, as discussed in lecture.

part a
The sb dataset contains the number of car drivers killed (DriversKilled) and the number of car drivers killed or seriously injured (drivers). Suppose that instead we are interested in the number of car drivers seriously injured.

Add new variable, DriversInjured, to the sb dataset for the number of car drivers seriously injured but not killed. You can calculate this variable using the two variables mentioned above.

# Use this code chunk to answer the question, by replacing this line or # adding a new line below it.

sb$DriversInjured = sb$drivers - sb$DriversKilled

part b
The sb dataset contains the number of rear-seat passengers killed or seriously injured in the rear variable. While there are often many seats available in the rear of a car, the driver and the front-seat passenger each refer to one specific location in the car. Therefore, create an AllFront variable that records the number of deaths or serious injuries for drivers and front-seat passengers, or in other words, all individuals sitting at the front of the car.

# Use this code chunk to answer the question, by replacing this line or # adding a new line below it.

sb$AllFront = sb$front + sb$drivers

part c
Confirm that your two variables have been correctly added to the dataframe. There are many ways this can be accomplished, so select one method and explain how you know that it worked.

# Use this code chunk to answer the question, by replacing this line or # adding a new line below it.

names(sb)

## [1] "DriversKilled" "drivers"                                         "front"                        "rear"

## [5] "kms"                                    "PetrolPrice"              "VanKilled"                "law"

## [9] "DriversInjured" "AllFront"

Exercise 2: Visualizing and Interpreting Two Variables
The Help file for the Seatbelts dataset indicates that the data were collected over a time when a compulsory seat belt law was introduced. We’ll analyze differences related to this law variable throughout this homework assignment.

Previous studies have shown that seat belts helped reduce driver death and serious injury. Does this safety feature have an affect on those in the front of the car, both drivers and passengers?

part a
As a first look at understanding this relationship, create a histogram of the AllFront deaths or serious injuries. Be sure to include coloring that indicates whether the deaths or serious injuries of the driver and front-seat passengers occurred during a month with and a month without the compulsory seat belt law. Make sure that your histogram is clear and easy to read.

# Use this code chunk to answer the question, by replacing this line or # adding a new line below it.

ggplot(sb, aes(x = AllFront, color = law, fill = law)) + geom_histogram()

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

 

part b
What do you notice from this graph?

part c
One theory is that any differences in deaths or serious injuries could be related to the amount of driving that is done in any given month. To visualize this relationship, create a scatterplot of distance driven (km) vs. deaths or serious injuries of drivers and front-seat passengers (AllFront). Include the variable law in the color and shape of the points based on whether the law was active at the time. Make sure your scatterplot is clear and easy to read.

# Use this code chunk to answer the question, by replacing this line or # adding a new line below it.

ggplot(sb, aes(x = kms, y = AllFront, color = law, shape = law)) +

geom_point()

 

part d
What do you notice from this graph? Discuss how your understanding has changed from part b, if at all.

 

Exercise 3: Logical Statements part a
How many months are included in this dataset? For how many months was the law in place?

## Use this code chunk to answer the question.

dim(sb)

## [1] 192 10

law_months = subset(sb, sb$law == 1) dim(law_months)

## [1] 23 10

 

part b
Define a deadly month for drivers to be a month where more than 100 drivers were killed. What proportion of months in this dataset would classify as a deadly month for drivers?

## Use this code chunk to answer the question.

deadly = subset(sb, sb$DriversKilled > 100) dim(deadly)/dim(sb)

## [1] 0.8177083 1.0000000

157/192

## [1] 0.8177083

 

part c
Define a deadly month for van drivers to be a month where more than 10 van drivers were killed. What proportion of months in this dataset would classify as a deadly month for van drivers?

## Use this code chunk to answer the question. deadly_van = subset(sb, sb$VanKilled > 10) dim(deadly_van)/dim(sb)

## [1] 0.359375 1.000000

69/192

## [1] 0.359375

 

 

part d
For what proportion of months in this dataset was it deadly for drivers, deadly for van drivers, or deadly for both drivers and van drivers? What proportion of months in this dataset was it deadly For both drivers and van drivers?

## Use this code chunk to answer the question.

deadly_either_or = subset(sb, sb$DriversKilled > 100 | sb$VanKilled > 10) dim(deadly_either_or)/dim(sb)

## [1] 0.8333333 1.0000000

160/192

## [1] 0.8333333

deadly_both = subset(sb, sb$DriversKilled > 100 & sb$VanKilled > 10) dim(deadly_both)/dim(sb)

## [1] 0.34375 1.00000

66/192

## [1] 0.34375

 

part e
Priya picked a different cutoff point for deciding a month was deadly. Priya decided that a month would be considered deadly for drivers if 90 or more drivers were killed. Determine how many additional months are considered deadly for drivers based on Priya’s cutoff compared to our original definition in part b.

## Use this code chunk to answer the question. priya_death = subset(sb, sb$DriversKilled > 90) dim(priya_death)-dim(deadly)

## [1] 20 0

 177 - 157

## [1] 20

 

Exercise 4: Subsetting Data
We’ll return to the idea of analyzing what the compulsory seat belt law accomplishes. To do this, it’ll be helpful to subset the data into two individual datasets.

part a
Create a withlaw dataset containing the observations for the months where the law was active, and a withoutlaw dataset that contains the observations for the months before the law was active.

## Use this code chunk to answer the questions.

withlaw = subset(sb, sb$law == 1) withoutlaw = subset(sb, sb$law == 0)
part b
Confirm that this separation worked. Do this using code along with reasoning based on interpreting your output. For this question, you should not print the entire dataset and check manually (by eye) that this separation worked.

## Use this code chunk to answer the question.

dim(sb)[1] == (dim(withlaw)[1] + dim(withoutlaw)[1])

## [1]

part c
Calculate summary statistics for the number of drivers seriously injured (DriversInjured) before the law was active and when the law was active. Describe what you see in these summary statistics (similarities & differences). If you were talking to a friend, would you suggest that there is a difference based on compulsory seat belt usage?

## Use this code chunk to answer the question summary(withlaw$DriversInjured)

##           Min. 1st Qu. Median              Mean 3rd Qu.      Max. ##              962        1087      1188              1221      1342      1609

summary(withoutlaw$DriversInjured)

##             Min. 1st Qu. Median              Mean 3rd Qu.          Max.

##         1197         1408         1530         1592         1785         2456

 

Exercise 5: Driver Recommendations part a
Create a scatterplot of the number of driver serious injuries vs. the number of driver deaths. Incorporate the law variable into this scatterplot, and make sure that the scatterplot has clear axes labels.

## Use this code chunk to answer the question.

ggplot(sb, aes(x = DriversInjured, y = DriversKilled, color = law, shape = law)) + geom_point() +

labs(title = "Number of Driver Seriously Injured vs. Number of Driver Deaths", x = "Number of Drivers Seriously Injured", y = "Number of Drivers Killed")
Number of Driver Seriously Injured vs. Number of Driver Deaths
 

part b
Interpret this scatterplot, and explain the real world significance of this graph. For example, what might you tell a driver about how using a seatbelt might affect the risk of serious injury and the risk of death?

 

Exercise 6: Line of Best Fit
Do gas prices affect driving decisions? We are interested in predicting the number of miles driven (km) from the price of gas (PetrolPrice). Generate a scatterplot for these two variables. Make sure that your scatterplot meets the following characteristics:

•      include clear axis labels & graph titles

•      include two lines summarizing the relationship between km and PetrolPrice, one for months before the seatbelt law was passed and one for months after it was passed

•      you may also include additional formatting, including colors and shapes, but these are not required.

## Use this code chunk to answer the question.

ggplot(sb, aes(x = PetrolPrice, y = kms, color = law, shape = law)) + geom_point() +

geom_smooth(method = 'lm', se = F, formula = 'y~x') + labs(title = "Number of Miles Driven vs. Price of Gas",
x = "Price of Gas", y = "Number of Miles Driven")

Number of Miles Driven vs. Price of Gas
 

Would you say that gas prices affect driving decisions? Explain.

 

Exercise 7: Asking Questions & Exploring Data
This exercise will be more open ended. Define and complete a new exploration of the seatbelts data in order to understand some aspect of the data. You may use graphs, numerical summaries, or some combination of the two in your exploration. You may return to your answer from Homework 1 Exercise 7 for additional inspiration. Be sure to write up your final findings in about 1-2 paragraphs. Make sure that your analysis is original analyses, not a recreation of something you have done in Homework 1 or Homework 2.

First, write your goal for your exploration below.

Goal: How the price of gas affects the number of Van driver deaths Then, complete the analyses.

## Use this code chunk to perform your data analysis.

ggplot(sb, aes(x = PetrolPrice, y = VanKilled, color = kms)) +

geom_point() +

geom_smooth(method = 'lm', se = F, formula = 'y~x' ) +

labs(title = "Relationship Between Gas Prices and Number of Van Drivers Killed", x = "Price of Gas",

y = "Number of Van Drivers Killed") +

theme_bw()
Relationship Between Gas Prices and Number of Van Drivers Killed
 

low_gas = subset(sb, sb$PetrolPrice < mean(sb$PetrolPrice)) high_gas = subset(sb, sb$PetrolPrice > mean(sb$PetrolPrice)) summary(low_gas$VanKilled)

## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 3.00 8.00 11.00 10.42 13.00 17.00

summary(high_gas$VanKilled)

## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 2.000 5.000 7.000 7.853 10.000 16.000

cor(sb$VanKilled,sb$PetrolPrice)

## [1] -0.2885584

cor(sb$VanKilled, sb$kms)

## [1] -0.4980356

cor(low_gas$VanKilled, low_gas$kms)

## [1] -0.3230645

cor(high_gas$VanKilled, high_gas$kms)

## [1] -0.4552476

Finally, write up your findings:

 

Exercise 8: Formatting
The last five points of the assignment will be earned for properly formatting your final document. Check that you have:

•      included your name in the document header

•      properly assigned pages to exercises on Gradescope

•      select page 1 (with your name) and this page for this exercise (Exercise 8)

•      all code is printed and readable for each question

•      generated a pdf file