HW2.2

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

names(stat500)

## [1] "midterm" "final"   "hw"      "total"

plot(stat500$"midterm", stat500$"final")

hist(stat500$hw)

library(lattice)

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

## 
## 載入套件：'lattice'

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

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

dta_scores <- stat500[, c("midterm","final","hw","total")]

pairs(dta_scores, pch = '.', upper.panel = panel.smooth, lower.panel = NULL, 
      col = 'gray')

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

## [1] 0.545

round(cor(dta_scores), 3)

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

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

## 
##  Pearson's product-moment correlation
## 
## data:  midterm and final
## 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(dta_scores), type="pearson")

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