Homework #1

Code

library(tidyverse)
library(dplyr)
library(readxl)
library (ggplot)

Error in library(ggplot): there is no package called 'ggplot'

Code

lungcap<- read_excel("LungCapData.xls") 

Error: `path` does not exist: 'LungCapData.xls'

Code

knitr::opts_chunk$set(echo = TRUE)

LungCapData

1a. What does the distribution of LungCap look like?

Code

ggplot(lungcap, aes(x=LungCap))+ geom_histogram()
``
This is not normally distributed as there are far more observations of lower lung capacity than higher suggesting the distribution is negatively skewed.
 
### 1b. Compare the probability distribution of the LungCap with respect to Males and Females? 

Error: attempt to use zero-length variable name

Code

lungcap %>%
group_by(Gender)%>%
summarise(mean(LungCap))

Error in group_by(., Gender): object 'lungcap' not found

The average lung capacity for females is 7.41, lower than the average for males at 8.31.

1c. Compare the mean lung capacities for smokers and non-smokers. Does it make sense?

Code

lungcap %>%
group_by(Smoke)%>%
summarise(mean(LungCap))

Error in group_by(., Smoke): object 'lungcap' not found

The mean lung capacity for non-smokers is 7.77, lower than the mean for smokers at 8.65. At first glance, this seems contradictory as one would guess smokers to have a lower lung capacity than non-smokers.The following grid displays non-smokers as having overall higher lung capacity, conflicting with the mean above.

Code

ggplot(lungcap, aes(x = LungCap)) +
facet_grid(Gender ~ Smoke)+
  geom_histogram()

Error in ggplot(lungcap, aes(x = LungCap)): object 'lungcap' not found

1d. Examine the relationship between Smoking and Lung Capacity within age groups: “less than or equal to 13”, “14 to 15”, “16 to 17”, and “greater than or equal to 18”.

1e. Compare the lung capacities for smokers and non-smokers within each age group.

Lung capacity for those under age 13 is 6.36 for non-smokers and 7.20 for smokers.

Code

lungcap %>%
+ filter(Age <= 13)%>%
+ group_by(Smoke)%>%
+ summarise(mean(LungCap))

Lung capacity for those between the age of 14 to 15
lungcap%>%
+ filter(Age=<15 & Age >=14)%>%
+ group_by(Smoke)%>%
+ summarise(mean(LungCap))

Lung capacity for those between the age of 16 to 17
lungcap%>%
+     filter(Age=<17>=16)%>%
+ group_by(Smoke)%>%
+ summarise(mean(LungCap))

Lung capacity for those 18 and older
lungcap%>%
+ filter(Age>=18)%>%
+ group_by(Smoke)%>%
+ summarise(mean(LungCap))

Error: <text>:6:6: unexpected symbol
5: 
6: Lung capacity
        ^

Is your answer different from the one in part c? What could possibly be going on here?

1f. Calculate the correlation and covariance between Lung Capacity and Age. (use the cov() and cor() functions in R). Interpret results.

Code

cov(lungcap$LungCap, lungcap$Age)

Error in is.data.frame(y): object 'lungcap' not found

Code

cor(lungcap$LungCap, lungcap$Age)

Error in is.data.frame(y): object 'lungcap' not found

The covariance between lung capacity and age is 8.74 suggesting a positive relationship in which both variables move in the same direction (i.e. for this data set an increase in lung capacity would suggest an increase in age as well).

The correlation between lung capacity and age is 0.82 suggesting a strong positive correlation (0.82 of a potential -1 to +1).

Inmate Data

Code

x<- c(0, 1, 2, 3, 4)
y<- c(128, 434, 160, 64, 24)
prison <-data.frame(x,y)
View(prison)

2a. What is the probability that a randomly selected inmate has exactly 2 prior convictions? 20% 2b. What is the probability that a randomly selected inmate has fewer than 2 prior convictions? 69% 2c. What is the probability that a randomly selected inmate has 2 or fewer prior convictions? 89% 2d. What is the probability that a randomly selected inmate has more than 2 prior convictions? 11% 2e. What is the expected value for the number of prior convictions? 84% 2f. Calculate the variance and the standard deviation for the Prior Convictions.

Code

var(prison, y= NULL)
sd(rnorm(810))
The standard deviation is 1.02.

Error: <text>:3:5: unexpected symbol
2: sd(rnorm(810))
3: The standard
       ^