hw1
Author

Quinn He

Published

October 3, 2022

Code 
library(tidyverse)
library(readxl)

knitr::opts_chunk$set(echo = TRUE)

Reading in the data

Code 
LungCapData <- read_excel("_data/LungCapData.xls")

lungcap_prob_dense <- dnorm(LungCapData$LungCap, mean = 7.863, sd = 2.662)

1a

Code 
ggplot(LungCapData, mapping = aes(LungCap)) +
  geom_histogram(color = "black", fill = "grey")+
  geom_density()+
  labs(title = "Distribution of Lung Capacity", x = "Lung Capacity", y = "Count")
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Code 
plot(x = LungCapData$LungCap, y = lungcap_prob_dense)

With these two functions I can see the distribution is normal with both a histogram and regular graph. The second graph more clearly depicts a normal distribution with the probability density points laid throughout. ## 1b

Code 
ggplot(LungCapData, mapping = aes(x = Gender, y = LungCap)) +
  geom_boxplot()

It looks like men, on average, have a higher lung capacity than females, but only by a slim margin. Overall, lung capacity is relatively similar among genders. The real comparison will come with smokers and nonsmokers. ## 1c

Code 
LungCapData %>% 
  group_by(Smoke) %>% 
  summarise(lung_cap_mean = mean(LungCap))
# A tibble: 2 × 2
  Smoke lung_cap_mean
  <chr>         <dbl>
1 no             7.77
2 yes            8.65

Above is the lung capacity mean for smokers and nonsmokers. I’m actually a little surprised the mean lung capacity for nonsmokers is slightly higher than that of nonsmokers. I would think the opposite to be true, but I suspect because there is a range of ages under 18 and the body is not fully developed yet, I imagine a 6 year old nonsmoker will not have the same lung capacity as a 17 year old smoker.

1d

Below I created a bunch of variables to separate people into certain age groups. I imagine there would be an easier way to separate them.

Code 
#LungCapData %>% 
  #group_by(Age) %>% 
  #summarise(lungcap = mean(LungCap))
  
age13 <- LungCapData %>% 
  filter(Age <= 13) %>%
  group_by(Smoke) %>% 
  summarise(lung_cap_mean = mean(LungCap))

age1415 <- LungCapData %>% 
  filter(Age == 14 | Age == 15) %>%
  group_by(Smoke) %>% 
  summarise(lung_cap_mean = mean(LungCap))

age1617 <- LungCapData %>% 
  filter(Age == 16 | Age == 17) %>%
  group_by(Smoke) %>% 
  summarise(lung_cap_mean = mean(LungCap))

age18 <- LungCapData %>% 
  filter(Age >= 18) %>%
  group_by(Smoke) %>% 
  summarise(lung_cap_mean = mean(LungCap))

age13
# A tibble: 2 × 2
  Smoke lung_cap_mean
  <chr>         <dbl>
1 no             6.36
2 yes            7.20
Code 
age1415
# A tibble: 2 × 2
  Smoke lung_cap_mean
  <chr>         <dbl>
1 no             9.14
2 yes            8.39
Code 
age1617
# A tibble: 2 × 2
  Smoke lung_cap_mean
  <chr>         <dbl>
1 no            10.5 
2 yes            9.38
Code 
age18
# A tibble: 2 × 2
  Smoke lung_cap_mean
  <chr>         <dbl>
1 no             11.1
2 yes            10.5

1e

Based on the variables I created above, it appears the lung capacity for people under 13, and that smoke, is higher than people who do not smoke. As the age brackets increase, so does lung capacity overall, but it begins to show that those who do smoke, generally have a lower lung capacity than those who choose not to smoke. This is what I would expect to happen since a 13 year old still has plenty of growing to do, therefore the lung capacity will be much lower than a grown teenager.

1f

Code 
cor(LungCapData$LungCap, LungCapData$Age)
[1] 0.8196749

With a correlation of 0.81, lung capacity and age have a fairly strong positive relationship. This is what I figured would be the case. As people age, their lung capacities grow larger. A 17 year old will be more developed and most likely have a larger lung capacity than, say, a child the age of 8.

I created a table of the data frame in question 2

Code 
xx <- c(0:4)

freq <- c(128, 434, 160, 64, 24)

df <- tibble(xx, freq)

2a

Code 
160/810
[1] 0.1975309

The probability of selecting inmates with 2 prior convictions is 19.7%.

2b

Code 
562/810
[1] 0.6938272

The probability of selecting inmates with less than 2 prior convictions is 69%.

2c

Code 
722/810
[1] 0.891358

The probability of selecting inmates with 2 or less prior convictions is 89%.

2d

Code 
88/810
[1] 0.108642

The probability of selecting inmates with more than 2 prior convictions is 10.8%.

2e

The expected value for number of prior convictions is 291.4.

Code 
test <- c(128, 434, 160, 64, 24)

testprobs <- c(0.15, 0.54, 0.2, 0.08, 0.03)

sum(test*testprobs)
[1] 291.4

2f

use rep()

Code 
convictions <- c(rep(0,128), rep(1, 434), rep(2,160), rep(3,64), rep(4,24))

sd(convictions)
[1] 0.9259016
Code 
var(convictions)
[1] 0.8572937