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Linear Models Homework 1
patr1.
Expand
Current expenditure per pupil in average daily
attendance in public elementary and secondary
schools,1994-1995(in thousands of dollars)
ratio Average pupil/teacher ratio in public elementary and
secondary schools ,Fall 1994
salary
Estimated average annual salary of teachers in public
elementary and secondary schools,1994-1995(in thousands
of dollars)
takers Percentage of all eligible students taking the SAT,1994-
1995
verbal Average verbal SAT score,1994-1995
math Average math SAT score,1994-1995
total Average total score on the SAT,1994-1995
>sat_data=read.table("http://www.stat.nthu.edu.tw/~swcheng/Teaching/
stat5410/data/sat_data.txt")
> head(sat_data)
(1) 50 7 50
SAT SAT ( )
(2) takers verbal math
total
NTHU STAT 5410, 2019 Solution to Homework 1
made by 邱奕豪, 黃俊閔 助教
:
> summary(sat_data)
:
(1) takers SAT
(2) SAT (verbal math total)
(3)
:
> par(mfrow=c(2,4))
> for(i in 1:ncol(sat_data)){
+ boxplot(sat_data[,i],main=names(sat_data)[i])
+ abline(h=apply(sat_data,2,mean)[i],col="red")
+ }
NTHU STAT 5410, 2019 Solution to Homework 1
made by 邱奕豪, 黃俊閔 助教
> findoutlier = function(x){
+ row.names(sat_data)[x>quantile(x, probs=0.75) + 1.5*IQR(x) | x<qua
ntile(x, probs=0.25) - 1.5*IQR(x)]
+ }
> findoutlier(sat_data$expend)
[1] "Alaska" "Connecticut" "New_Jersey" "New_York"
> findoutlier(sat_data$ratio)
[1] "California" "Utah"
> findoutlier(sat_data$salary)
[1] "Connecticut"
:
(1) expand ratio salary
: , :
IQR : ( - )
[Q1-1.5 IQR , Q3+1.5 IQR]
expand Alaska Connecticut New_Jersey New_York
Ratio California Utah
Salary Connecticut
(2) expand ratio
(3) salary takers verbal math total
NTHU STAT 5410, 2019 Solution to Homework 1
made by 邱奕豪, 黃俊閔 助教
:
> for(i in 1:ncol(sat_data)){
+ hist(sat_data[,i],main=names(sat_data)[i],prob=T)
+ lines(density(sat_data[,i]))
+ }
:
(1) takers verbal math total
(2) expand ratio salary
NTHU STAT 5410, 2019 Solution to Homework 1
made by 邱奕豪, 黃俊閔 助教
( correlation) :
> pairs(sat_data)
> M=cor(sat_data)
> library(corrplot)
> corrplot(M, method = "shade")
NTHU STAT 5410, 2019 Solution to Homework 1
made by 邱奕豪, 黃俊閔 助教
:
(1) expand verbal math total expand
SAT ( )
(2) SAT
(3)
(4) SAT SAT
(5)
(6) ratio verbal math total 0.1
(7) verbal math total
verbal SAT math SAT SAT
total = math + verbal math verbal total
Math verbal
NTHU STAT 5410, 2019 Solution to Homework 1
made by 邱奕豪, 黃俊閔 助教
Part2
Data
> data=read.table("C:/Users/stat_pc/Desktop/linear model/wrinkle.txt
",header = T)
press durable press rating
HCHO formaldehyde concentration
catalyst catalyst ration
temp curing temperature
time curing time
press
HCHO {2,4,5,6,7,8,10} catalyst {1,4,7,10,13}
temp {100,120,140,160,180} time {1,3,5,7}
> par(mfrow=c(1,5))
> hist(data$press,main="press");barplot(table(data$HCHO),main="HCHO
");barplot(table(data$catalyst),main="catalyst")
> barplot(table(data$temp),main="temp");barplot(table(data$time),main
="time")
1. time 1 7
HCHO catalyst temp
NTHU STAT 5410, 2019 Solution to Homework 1
made by 邱奕豪, 黃俊閔 助教
2. press [4.5,5] press 4.5~5
> par(mfrow=c(1,5))
> boxplot(data$press,main="press");boxplot(data$HCHO,main="HCHO")
> boxplot(data$catalyst,main="catalyst");boxplot(data$temp,main="temp
");boxplot(data$time,main="time")
summary(data) boxplot
1. press 50% [4.5,4.9]
2. HCHO catalyst
3. temp 25% temp 180
4. time time
1 7
NTHU STAT 5410, 2019 Solution to Homework 1
made by 邱奕豪, 黃俊閔 助教
> pairs(data)
pairs(data) cor(data)
1. press time
time 1 7 press 2
press time
2. press HCHO temp
3. press catalyst 0.72
catalyst press
4. pairs(data) press
data HCHO catalyst temp time
experimental data
NTHU STAT 5410, 2019 Solution to Homework 1
made by 邱奕豪, 黃俊閔 助教