HW5

匯入套件

匯入資料資料為主計處薪資及生產力統計資料，這裡只以服務業來進行分析

service <- read_csv("C:/Users/Daniel Chiang/Desktop/HW5/service.csv")

## Parsed with column specification:
## cols(
##   career = col_character(),
##   employee = col_integer(),
##   averagewage = col_integer(),
##   uaualwage = col_integer(),
##   unusualwage = col_integer(),
##   overtime = col_integer(),
##   averageworkhr = col_double(),
##   normalworkhr = col_double(),
##   overtimeworkhr = col_double(),
##   `in` = col_double(),
##   out = col_double(),
##   num = col_integer()
## )

進行相關性分析

require(reshape2)

## Loading required package: reshape2

require(scales)

## Loading required package: scales

## 
## Attaching package: 'scales'

## The following object is masked from 'package:readr':
## 
##     col_factor

serCor<-cor(service[,c(3,9:11)])
serMelt<-melt(serCor,varnames = c("x","y"),value.name = "Correlation")
serMelt<-serMelt[order(serMelt$Correlation),]
ggplot(serMelt,aes(x=x,y=y))+
  geom_tile(aes(fill=Correlation))+
  scale_fill_gradient2(low="black",mid="white",high="darkblue",guide=guide_colorbar(ticks=FALSE,barheight=10),limits=c(-1,1))+
  theme_minimal()+
  labs(x=NULL,y=NULL)

黑色表示負相關，藍色表示正相關，可以看出薪資和離職呈現負相關，而加班工時雖也和離職成正相關，新進部分，和薪資呈現負相關，但相關性較小；和加班工時成正相關，推估可能薪資較低希望可以有加班的機會。

進行t檢定

t.test(service$averagewage,alternative = "two.sided",mu=22000)

## 
##  One Sample t-test
## 
## data:  service$averagewage
## t = 5.1221, df = 11, p-value = 0.0003324
## alternative hypothesis: true mean is not equal to 22000
## 95 percent confidence interval:
##  37038.75 59701.75
## sample estimates:
## mean of x 
##  48370.25

randT<-rt(30000,df=NROW(service)-1)
serTTest<-t.test(service$averagewage,alternative = "two.sided",mu=22000)

ggplot(data.frame(x=randT))+
  geom_density(aes(x=x),fill="grey",color="grey")+
  geom_vline(xintercept = serTTest$statistic)+
  geom_vline(xintercept = mean(randT)+c(-2,2)*sd(randT),linetype=2)

假設薪資為22k進行預測，虛線為平均數左右兩個標準差，實現為t統計量，可以看到它離開分佈有一段距離，我們可知道平均值不等於22k，所以基本上在服務業可能起薪低於平均，但長期來看，薪資會再提高，平均不只22k。

ANOVA分析

services <- read_csv("C:/Users/Daniel Chiang/Desktop/HW5/services.csv")

## Parsed with column specification:
## cols(
##   year = col_integer(),
##   career = col_character(),
##   employee = col_integer(),
##   averagewage = col_integer(),
##   uaualwage = col_integer(),
##   unusualwage = col_integer(),
##   overtime = col_integer(),
##   averageworkhr = col_double(),
##   normalworkhr = col_double(),
##   overtimeworkhr = col_double(),
##   `in` = col_double(),
##   out = col_double()
## )

serAnova<-aov(averagewage~career-1 ,services)
summary(serAnova)

##           Df    Sum Sq   Mean Sq F value Pr(>F)    
## career    12 1.204e+11 1.004e+10    4219 <2e-16 ***
## Residuals 36 8.563e+07 2.379e+06                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

F value很大代表組跟組間差異大，但組內差異小，所以career中各行業別無明顯差異。

用找出薪資不同的行業來佐證

serout<-ddply(services,"career",summarise,
              averagewage.mean=mean(services$averagewage),
              averagewage.sd=sd(services$averagewage),
              Length=NROW(services$averagewage),
              tfrac=qt(p=0.90,df=Length-1),
              Lower=averagewage.mean-tfrac*averagewage.sd/sqrt(Length),
              Upper=averagewage.mean+tfrac*averagewage.sd/sqrt(Length))

ggplot(serout,aes(x=averagewage.mean,y=career))+geom_point()+
  geom_errorbarh(aes(xmin=Lower,xmax=Upper),height=0.3)

從圖表可看出不同職業別的平均值和信賴區間，個職業別間無非常明顯之差異，可佐證ANOVA分析。

HW5

b05702032