第4回統計的検定

Data Analysis and Experimental Design
第4回統計的検定
> cor(iris$Petal.Length,iris$Petal.Width)
[1] 0.9628654
> lsfit(cars$speed, cars$dist)
$coefficients
Intercept
X
-17.579095
3.932409
Data Analysis and Experimental Design
H0を棄却する
H0が真
H1が真
第Ⅰ種の誤り
α
1-α
1-β
第Ⅱ種の誤り
β
H0を棄却しない
H0：γ= 0
T=
r
1− r2
n−2
1
Data Analysis and Experimental Design
p = pl + pu = 0.05
pl = 0.025
-2.008
pu = 0.025
2.008
Data Analysis and Experimental Design
> r
> n
> T
> T
[1]
<- cor(iris$Petal.Length,iris$Petal.Width)
<- length(iris$Petal.Length) #標本数
<- r/(sqrt((1-r^2)/(n-2)))
43.38724
> qt(0.975,n-2) #qt(p,df):確率pのt値を与える
[1] 1.976122
> 1-pt(T,n-2) #pt(t,df)：t値の確率pを与える
[1] 0
2
Data Analysis and Experimental Design
> df <- lsfit(cars$speed, cars$dist)
> ls.print(df)
Residual Standard Error=15.3796
R-Square=0.6511
F-statistic (df=1, 48)=89.5671
p-value=0
Estimate Std.Err t-value Pr(>|t|)
Intercept -17.5791 6.7584 -2.6011
0.0123
X
3.9324 0.4155 9.4640
0.0000
3

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