Homework1

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Code

library(readxl)
library(dplyr)

Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

Code

library(tidyverse)

── Attaching packages
───────────────────────────────────────
tidyverse 1.3.2 ──

✔ ggplot2 3.4.0     ✔ purrr   0.3.5
✔ tibble  3.1.8     ✔ stringr 1.5.0
✔ tidyr   1.2.1     ✔ forcats 0.5.2
✔ readr   2.1.3     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()

Code

library(ggplot2)

  lung_data <- read_excel("_data/LungCapData.xls")
view(lung_data)

1A:

Code

hist(lung_data$LungCap, freq = FALSE, main = "Histogram", xlab = "Values", ylab = "Density")

B:

Code

boxplot(LungCap ~ Gender, data = lung_data)
title("lung capacity between male and female")

C:

Code

boxplot(LungCap ~ Smoke, data = lung_data)
title("Lung Capacity between Smokers and Non-Smokers")

D:

Code

lung2 <-lung %>%
  mutate(Age_Cat = case_when(
        Age >= 0 & Age <= 13 ~ "13 or less",
        Age >= 14 & Age <= 15 ~ "14 to 15" ,
        Age >= 16 & Age <= 17 ~ "16 to 17" ,
        Age >= 18 ~ "18 or more" ,
        ))

Error in mutate(., Age_Cat = case_when(Age >= 0 & Age <= 13 ~ "13 or less", : object 'lung' not found

Code

box_plot_crop2<-ggplot(data=lung2, aes(x=Smoke, y=LungCap, fill=Smoke)) 

Error in ggplot(data = lung2, aes(x = Smoke, y = LungCap, fill = Smoke)): object 'lung2' not found

Code

box_plot_crop2+ geom_boxplot() +
  theme(legend.position = "right") +
  theme (axis.text.x=element_blank(),
        axis.ticks.x=element_blank())+
  coord_cartesian(ylim =  c(0, 15))+
  labs(title="Box Plot - Lung Capacity",
        x ="Smoke", y = "Density")+
  facet_wrap(.~Age_Cat, scales= "free")

Error in eval(expr, envir, enclos): object 'box_plot_crop2' not found

E: Smoking has been found to have a negative correlation with lung capacity in three out of four groups studied. However, it is possible that another explanation exists. Older individuals tend to smoke more and also have higher lung capacity, so analyzing the relationship between smoking and lung capacity without factoring in age can lead to a misinterpretation of the true association.

2A:

Code

X <- c(0, 1, 2, 3, 4)
frequency <- c(128, 434, 160, 64, 24)

Code

prob_two <- frequency[3] / sum(frequency)
print(paste("the probability:", prob_two))

[1] "the probability: 0.197530864197531"

2B

Code

prob_two <- (frequency[1]+frequency[2]) / 810
print(paste("the probability:", prob_two))

[1] "the probability: 0.693827160493827"

2C:

Code

prob_two <- (frequency[1]+frequency[2]+frequency[3]) / 810
print(paste("the probability:", prob_two))

[1] "the probability: 0.891358024691358"

2D:

Code

prob_two <- (frequency[4]+frequency[5]) / 810
print(paste("the probability:", prob_two))

[1] "the probability: 0.108641975308642"

2E:

Code

probaility_fre<-c(128/810, 434/810, 160/810, 64/801, 24/810)
weigh_avg<-weighted.mean(X, probaility_fre)
print(paste("the expected value:", weigh_avg))

[1] "the expected value: 1.28793968456357"

2F:

Code

weigh_avgvariance <- sum((X-weigh_avg)^2*probaility_fre)
print(paste("the variance:", weigh_avgvariance))

[1] "the variance: 0.858839854536097"

Code

standad_deviation  <- sqrt(variance)

Error in eval(expr, envir, enclos): object 'variance' not found

Code

print(paste("the standad deviation:", standad_deviation))

Error in paste("the standad deviation:", standad_deviation): object 'standad_deviation' not found