Section A
Exericse A.1
### Your code here:
2+2
## [1] 4
## [1] 4
##install.packages("ggplot2")
##install.packages()
library(ggplot2)
?"ggplot2"
## starting httpd help server ... done
Exericse A.2
### Your code here:
typeof(1.333)
## [1] "double"
## double
typeof(2)
## [1] "double"
## double
typeof("5.654")
## [1] "character"
## character
typeof(TRUE)
## [1] "logical"
## logical
typeof("Green is a pretty color")
## [1] "character"
## character
typeof(as.integer(4.5))
## [1] "integer"
## integer
typeof(FALSE)
## [1] "logical"
## logical
## "5.654"+"5.654"
## printed error
as.double("5.654")+ as.double("5.654")
## [1] 11.308
## 11.308
as.integer("5.654")+ as.integer("5.654")
## [1] 10
## 10
## as.double("TestTestTest")
## Warning message: NAs introduced by coercion, This warning message is expected because the characters in quotation marks cannot be converted into numbers.
Exericse A.3
### Your code here:
a <- 2.5
b <- 3.0
a+b
## [1] 5.5
## reassign values
a <- 10.0
a*b
## [1] 30
Exericse A.4
### Your code here:
v1 <- c(1,2,3,4,5)
v2 <- c(-1,-2,-3,-4,-5)
## adding the two vectors together
v1+v2
## [1] 0 0 0 0 0
## the result 0 0 0 0 0 is what I expected because the two vectors have the same dimension, and the corresponding values sum to 0.
v3 <- seq(from=1, to=5, by=+1)
v3
## [1] 1 2 3 4 5
s1 <- seq(from=-10, to=100,by=10)
c('a','b','c','d','e')[2]
## [1] "b"
## 'b'
c('a','b','c','d','e')[2:4]
## [1] "b" "c" "d"
## 'b' 'c' 'd'
p <- c(1,2,3,4,5)
p^2
## [1] 1 4 9 16 25
## 1 4 9 16 25
sqrt(p)
## [1] 1.000000 1.414214 1.732051 2.000000 2.236068
## 1.000000 1.414214 1.732051 2.000000 2.236068
exp(p)
## [1] 2.718282 7.389056 20.085537 54.598150 148.413159
## 2.718282 7.389056 20.085537 54.598150 148.413159
?exp
sum(p)
## [1] 15
## 15
mean(p)
## [1] 3
## 3
Exericse A.5
### Your code here:
data <- seq(from=1, to=10,by=+1)
data
## [1] 1 2 3 4 5 6 7 8 9 10
?matrix
d1 <- matrix(data=data,nrow=2,ncol=5)
d1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 3 5 7 9
## [2,] 2 4 6 8 10
d2 <- matrix(data=data,nrow=5,ncol=2)
d1%*%d2
## [,1] [,2]
## [1,] 95 220
## [2,] 110 260
## 95 220
## 110 260
d2%*%d1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 13 27 41 55 69
## [2,] 16 34 52 70 88
## [3,] 19 41 63 85 107
## [4,] 22 48 74 100 126
## [5,] 25 55 85 115 145
## 5*5 matrix
## the resulting matrix products are different because d1%*%d2 gives a 2*2 matrix and d2%*%d1 gives a 5*5 matrix
?data.frame()
d3 <- data.frame("col1"=data[1:5],"col2"=data[6:10])
colors_data <- c("green","blue","red","purple","yellow")
cbind(d3,colors_data)
## successfully add the colors_data as the third column
d3$colors <- colors_data
d3
## i got to decide what the new column name is called
##d3[colors] <- colors_data
## error message
d3["colors"] <- colors_data
## need to put a quotation mark around the column name
col2_data <-d3$col2
col2_data
## [1] 6 7 8 9 10
sum(col2_data)
## [1] 40
## 40
mean(col2_data)
## [1] 8
## 8
Exericse A.6
### Your code here:
## setwd("C:\OneDrive\桌面\Rice University\Spring 2025 -- In Progress\STAT 410\Lab 1")
vapor_df <- read.table(file="Vapor.txt", header=TRUE)
head(vapor_df)
vapor_df$Temp
## [1] 273 283 293 303 313 323 333 343 353 363 373
## [1] 273 283 293 303 313 323 333 343 353 363 373
vapor_df$vp
## [1] 4.6 9.2 17.5 31.8 55.3 92.5 149.4 233.7 355.1 525.8 760.0
## [1] 4.6 9.2 17.5 31.8 55.3 92.5 149.4 233.7 355.1 525.8 760.0
##setwd("C:\OneDrive\桌面\Rice University\Spring 2025 -- In Progress\STAT 410\Lab 1")
athlete_events_df <- read.csv(file="athlete_events.csv",header=TRUE)
View(athlete_events_df)
head(athlete_events_df)
Exericse A.7
### Your code here:
my_func <- function(x){
return(x**2-5*x+2)
}
my_func(2)
## [1] -4
## -4
my_nums <- seq(from=0, to=10, by=+1)
my_nums
## [1] 0 1 2 3 4 5 6 7 8 9 10
my_mean_func <- function(nums){
return(sum(nums)/length(nums))
}
my_mean_func(my_nums)
## [1] 5
## 5
mean(my_nums)
## [1] 5
## 5
## the results are the same because my function is defined correctly
Exericse A.8
### Your code here:
##setwd("C:\OneDrive\桌面\Rice University\Spring 2025 -- In Progress\STAT 410\Lab 1")
vapor_df <- read.table(file="Vapor.txt", header=TRUE, col.names=c("TEMP","VP"))
plot(vapor_df$TEMP,vapor_df$VP,type='b',xlab="Temperature",ylab="Vapor Pressure",col="blue",pch=7)
Section B
Exericse B.1.a
### Your code here:
##setwd("C:\OneDrive\桌面\Rice University\Spring 2025 -- In Progress\STAT 410\Lab 1")
vball <- read.csv(file="fallingballmars.csv", header=TRUE)
head(vball)
## the speedometer records "speed_mps"
plot(vball$time,vball$speed_mps,xlab="Time",ylab="Speed (m/s)")
## the data seems to show a strong negative linear relationship/correlation
Exericse B.1.b
### Your code here:
para_estimate <- function(x,y){
y_mean <- mean(y)
x_mean <- mean(x)
g_mars <- sum(y*(x-x_mean))/sum((x-x_mean)**2)
v_t0 <- y_mean - g_mars*x_mean
var <- sum((y-v_t0-g_mars*x)**2)/length(y)
para <- c(v_t0, g_mars,var)
return(para)
}
para <- para_estimate(vball$time,vball$speed_mps)
## v_t0 =15.224757
## g_mars = -3.750958
## variance = 10.029875
## the number seems reasonable
## according to google results, g_mars is 3.73m/s^2, so very reasonable
## the gravitation force on earth is 9.8
plot(vball$time,vball$speed_mps,xlab="Time",ylab="Speed (m/s)")
abline(a=para[1], b= para[2])
x <- para[1]/-para[2]
x
## [1] 4.058899
## expected time when speed = 0, expected time would be 4.05889s
Exericse B.1.c
### Your code here:
pred_speed <- para[1]+para[2]*vball$time
resi_error <- vball$speed_mps - pred_speed
plot(pred_speed,resi_error,xlab="Predicted Speed",ylab="Residuals")
abline(a=0,b=0)
## the graph doesn't have a distinct pattern or shape because it is not sqaured
sum(resi_error)
## [1] 3.608225e-14
## sum is 3.608225e-14
## theoretically, the value of sum of residuals should be 0
qqnorm(resi_error)
qqline(resi_error,col="blue")
calc_sig2 <- function(x,y){
y_mean <- mean(y)
x_mean <- mean(x)
g_mars <- sum(y*(x-x_mean))/sum((x-x_mean)**2)
v_t0 <- y_mean - g_mars*x_mean
var <- sum((y-v_t0-g_mars*x)**2)/length(y)
return(var)
}
calc_sig2(vball$time,vball$speed_mps)
## [1] 10.02987
## 10.02987