R Notebook

clev=read.csv("ClevelandHeart.csv")
hist(clev$RestBP,xlab="blood pressure",ylab="number",main="Histogram of patients' resting blood pressure",breaks=20)

hist(clev$MaxHR,xlab="maximum heart rate",ylab="number",main="Histogram of patient maximum heart rates",breaks=20)

Q1 c

Total amount of patients is 303

dim(clev)

[1] 303  12

sum(clev$AHD=="Yes")

[1] 139

139/303

[1] 0.4587459

45.9% are diagnosed with heart disease

chestpain_table=table(clev$ChestPain, clev$AHD)
chestpain_table

              
                No Yes
  asymptomatic  39 105
  nonanginal    68  18
  nontypical    41   9
  typical       16   7

prop.table(chestpain_table, margin = 2)

              
                       No        Yes
  asymptomatic 0.23780488 0.75539568
  nonanginal   0.41463415 0.12949640
  nontypical   0.25000000 0.06474820
  typical      0.09756098 0.05035971

From the table, we can observe that patients with heart disease predominantly have asymptomatic chest pain whereas those who don’t have heart disease mostly have nonanginal, nontypical or asymptomatic chest pain. Typical chest pain is rare in both cases.

#Q1 d
heart_disease = subset(clev, AHD == "Yes")
hist(heart_disease$MaxHR,
     main = "Histogram of Maximum Heart Rate\n(Patients with Heart Disease)",
     xlab = "Maximum Heart Rate",
     col = "salmon",
     border = "black")

x = runif(10000)
hist(x)

vecthresh = function(x,threshold){
  output = numeric(length(threshold))
  for (i in seq_along(threshold)){
    output[i]=mean(x <= threshold[i])
  }
  return(output)
  }
  
x=runif(10000)
threshold=c(0.25, 0.5, 0.75, 1.0)
vecthresh(x,threshold)

[1] 0.2430 0.4895 0.7421 1.0000

genvec = function(m,n){
  output = numeric(n)
  for (i in 1:n){
    output[i]=mean(runif(m))
  }
  graph=hist(output)
  return(graph)
}
genvec(1000,1000)

$breaks
 [1] 0.475 0.480 0.485 0.490 0.495 0.500 0.505 0.510 0.515 0.520
[11] 0.525 0.530

$counts
 [1]  11  25  99 139 218 208 160  89  36  14   1

$density
 [1]  2.2  5.0 19.8 27.8 43.6 41.6 32.0 17.8  7.2  2.8  0.2

$mids
 [1] 0.4775 0.4825 0.4875 0.4925 0.4975 0.5025 0.5075 0.5125 0.5175
[10] 0.5225 0.5275

$xname
[1] "output"

$equidist
[1] TRUE

attr(,"class")
[1] "histogram"

genvec(100000,1000)

$breaks
 [1] 0.4970 0.4975 0.4980 0.4985 0.4990 0.4995 0.5000 0.5005 0.5010 0.5015 0.5020 0.5025 0.5030
[14] 0.5035

$counts
 [1]   6  10  43  81 166 204 200 152  84  33  16   2   3

$density
 [1]  12  20  86 162 332 408 400 304 168  66  32   4   6

$mids
 [1] 0.49725 0.49775 0.49825 0.49875 0.49925 0.49975 0.50025 0.50075 0.50125 0.50175 0.50225
[12] 0.50275 0.50325

$xname
[1] "output"

$equidist
[1] TRUE

attr(,"class")
[1] "histogram"

Observations, as m gets larger, the scale of the x axis gets smaller, meaning that all the numbers lie at a smaller range of values. This is because increasing the number of variables will decrease the variance.

#Q2 d
y = rexp(10000,rate=1)
hist(y)

#Q3 a
covid=read.csv("key-countries-pivoted.csv")
plot(covid$US,type="l",xlab="days since Jan 22, 2020",ylab = "cumulative
cases",main="Cumulative cases in US")

#Q3 b
new_cases=diff(covid$US)
plot(new_cases,type="l",xlab="days since Jan 22, 2020",ylab = "new cases",main="New daily cases in US")

#Q3 c
new_cases=diff(covid$China)
plot(new_cases,type="l",xlab="days since Jan 22, 2020",ylab = "new cases",main="New daily cases in China")

population <- c(
  China = 1412000000,
  US = 332000000,
  United_Kingdom = 67000000,
  Italy = 59000000,
  France = 68000000,
  Germany = 83000000,
  Spain = 47000000,
  Iran = 88000000
)

cases_apr16 <- covid[nrow(covid), names(population)]

results <- data.frame(
  Cases = cases_apr16,
  Fraction_of_total = cases_apr16 / sum(cases_apr16),
  Cases_per_capita = cases_apr16 / population
)

results

NA

Total Cases:

sum(x)

[1] 190085610