cor

install.packages("https://cran.rstudio.com/bin/windows/contrib/4.1/faraway_1.0.7.zip", repos = NULL)

## 將程式套件安載入 'C:/Users/user/Documents/R/win-library/4.1'
## (因為 'lib' 沒有被指定)

## package 'faraway' successfully unpacked and MD5 sums checked

library(faraway)

## Warning: 套件 'faraway' 是用 R 版本 4.1.2 來建造的

data(stat500)

str(stat500)

## 'data.frame':    55 obs. of  4 variables:
##  $ midterm: num  24.5 22.5 23.5 23.5 22.5 16 27.5 22.5 25 30 ...
##  $ final  : num  26 24.5 26.5 34.5 30.5 31 33.5 31 29.5 37.5 ...
##  $ hw     : num  28.5 28.2 28.3 29.2 27.3 27.5 29.7 29 27.3 27.2 ...
##  $ total  : num  79 75.2 78.3 87.2 80.3 74.5 90.7 82.5 81.8 94.7 ...

head(stat500)

##   midterm final   hw total
## 1    24.5  26.0 28.5  79.0
## 2    22.5  24.5 28.2  75.2
## 3    23.5  26.5 28.3  78.3
## 4    23.5  34.5 29.2  87.2
## 5    22.5  30.5 27.3  80.3
## 6    16.0  31.0 27.5  74.5

summary(stat500)

##     midterm          final             hw            total      
##  Min.   : 8.50   Min.   :13.00   Min.   : 9.20   Min.   :48.30  
##  1st Qu.:17.25   1st Qu.:23.00   1st Qu.:25.85   1st Qu.:68.15  
##  Median :20.50   Median :27.00   Median :27.50   Median :74.50  
##  Mean   :20.32   Mean   :26.49   Mean   :26.24   Mean   :73.05  
##  3rd Qu.:23.50   3rd Qu.:30.25   3rd Qu.:28.50   3rd Qu.:78.75  
##  Max.   :30.00   Max.   :37.50   Max.   :29.70   Max.   :94.70

plot(stat500$final, stat500$midterm)

hist(stat500$final)

library(lattice)

## 
## 載入套件：'lattice'

## 下列物件被遮斷自 'package:faraway':
## 
##     melanoma

histogram(~ final, data = stat500, xlab = '期末分數', ylab='機率',type = "density")

stat500_scores <- stat500[, c('final', 'midterm', 'hw', 'total')]

pairs(stat500_scores, pch = '.', upper.panel = panel.smooth, lower.panel = NULL, 
      col = 'orange')

round(cor(stat500$final,stat500$midterm), 3)

## [1] 0.545

round(cor(stat500_scores), 3)

##         final midterm    hw total
## final   1.000   0.545 0.087 0.779
## midterm 0.545   1.000 0.272 0.844
## hw      0.087   0.272 1.000 0.564
## total   0.779   0.844 0.564 1.000

cor.test( ~ final + midterm, data = stat500_scores)

## 
##  Pearson's product-moment correlation
## 
## data:  final and midterm
## t = 4.735, df = 53, p-value = 1.675e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3272692 0.7081001
## sample estimates:
##       cor 
## 0.5452277

library(Hmisc)

## Warning: 套件 'Hmisc' 是用 R 版本 4.1.2 來建造的

## 載入需要的套件：survival

## 
## 載入套件：'survival'

## 下列物件被遮斷自 'package:faraway':
## 
##     rats, solder

## 載入需要的套件：Formula

## Warning: 套件 'Formula' 是用 R 版本 4.1.1 來建造的

## 載入需要的套件：ggplot2

## Warning: 套件 'ggplot2' 是用 R 版本 4.1.2 來建造的

## 
## 載入套件：'Hmisc'

## 下列物件被遮斷自 'package:base':
## 
##     format.pval, units

rcorr(as.matrix(stat500_scores), type="pearson")

##         final midterm   hw total
## final    1.00    0.55 0.09  0.78
## midterm  0.55    1.00 0.27  0.84
## hw       0.09    0.27 1.00  0.56
## total    0.78    0.84 0.56  1.00
## 
## n= 55 
## 
## 
## P
##         final  midterm hw     total 
## final          0.0000  0.5260 0.0000
## midterm 0.0000         0.0445 0.0000
## hw      0.5260 0.0445         0.0000
## total   0.0000 0.0000  0.0000