[R Studio][12.9.7][DS12.2.5] 문제 풀이

 

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이공학도를 위한 확률과 통계 3판 한글판

 

 

 

 

 

ds12.2.5-computer-system-management.txt

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 [ 문제 ]

 

DS 12.2.5 의 데이터를 이용하여 표본의 상관계수 r 를 구하고 표본상관계수로 표현되는 t 통계량 t = r√(𝑛 − 2)/√(1 − 𝑟^2)이 t 통계량 t = 𝛽̂ 1/s.e.(𝛽̂ 1)와 같음을 보여라.

 

 

 

> raw_datas <- read.table("ds12.2.5-computer-system-management.txt", header=T)
> cor.test(raw_datas$ActualTime, raw_datas$EstimatedTime)

	Pearson's product-moment correlation

data:  raw_datas$ActualTime and raw_datas$EstimatedTime
t = 5.7226, df = 30, p-value = 3.034e-06
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.4995797 0.8555920
sample estimates:
      cor 
0.7224266

표준 상관 계수 = 0.7224266

t = 5.7226

 

 

 

 

> lm2 <- lm(ActualTime~EstimatedTime, data=raw_datas)
> summary(lm2)

Call:
lm(formula = ActualTime ~ EstimatedTime, data = raw_datas)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.2801 -1.8631 -0.3749  0.8751  8.9582 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)    -1.9112     1.7598  -1.086    0.286    
EstimatedTime   1.6191     0.2829   5.723 3.03e-06 ***
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.544 on 30 degrees of freedom
Multiple R-squared:  0.5219,	Adjusted R-squared:  0.506 
F-statistic: 32.75 on 1 and 30 DF,  p-value: 3.034e-06

T 통계량 5.723 으로 동일합니다.