[R Studio][12.9.8][DS12.2.6] 문제 풀이

 

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이공학도를 위한 확률과 통계 3판 한글판

 

 

 

 

 

ds12.2.6-vacuum-transducer-bobbin-resistances.txt

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 [ 문제 ]

 

DS 12.2.6 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("ds12.2.6-vacuum-transducer-bobbin-resistances.txt", header=T)
> cor.test(raw_datas$Resistance, raw_datas$Temperature, data=raw_datas)

	Pearson's product-moment correlation

data:  raw_datas$Resistance and raw_datas$Temperature
t = 12.527, df = 22, p-value = 1.735e-11
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.8567817 0.9725042
sample estimates:
      cor 
0.9365019 

표준 상관 계수 = 0.9365019

t = 12.527

 

 

 

 

> lm3 <- lm(Resistance~Temperature, data=raw_datas)
> summary(lm3)

Call:
lm(formula = Resistance ~ Temperature, data = raw_datas)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.9946 -1.3764  0.7285  1.4036  3.4551 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 12.86392    4.55461   2.824  0.00987 ** 
Temperature  0.80507    0.06427  12.527 1.74e-11 ***
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.995 on 22 degrees of freedom
Multiple R-squared:  0.877,	Adjusted R-squared:  0.8714 
F-statistic: 156.9 on 1 and 22 DF,  p-value: 1.735e-11

T 통계량은 12.527로 같습니다.