Data input

下述例題乃為當資料單位改變時,相關係數(correlation coefficient),回歸係數(regression coefficient)會有何影響

x <- c(173,164,180,152,170,168,162,175,170,158)
y <- c(66,52,78,45,62,63,51,72,60,48)
x1 <- 0.347*x
y1 <- y/0.454
data <- data.frame(x,y,x1,y1)
data
##      x  y     x1        y1
## 1  173 66 60.031 145.37445
## 2  164 52 56.908 114.53744
## 3  180 78 62.460 171.80617
## 4  152 45 52.744  99.11894
## 5  170 62 58.990 136.56388
## 6  168 63 58.296 138.76652
## 7  162 51 56.214 112.33480
## 8  175 72 60.725 158.59031
## 9  170 60 58.990 132.15859
## 10 158 48 54.826 105.72687

summarize

將資料做敘述統計

##        Mean       S.d
## x  167.2000  8.350649
## y   59.7000 10.698390
## x1  58.0184  2.897675
## y1 131.4978 23.564736

Comparison

比較兩筆資料跑出來的回歸模型

lm.1 <- lm(y~x,data = data)
lm.2 <- lm(y1~x1,data = data)
summary(lm.1)$coefficients
##                Estimate Std. Error   t value     Pr(>|t|)
## (Intercept) -147.461759 19.2856388 -7.646195 6.038456e-05
## x              1.239006  0.1152155 10.753814 4.921301e-06
summary(lm.2)$coefficients
##                Estimate Std. Error   t value     Pr(>|t|)
## (Intercept) -324.805637 42.4793806 -7.646195 6.038456e-05
## x1             7.864806  0.7313504 10.753814 4.921301e-06
anova(lm.1)
## Analysis of Variance Table
## 
## Response: y
##           Df Sum Sq Mean Sq F value    Pr(>F)    
## x          1 963.45  963.45  115.64 4.921e-06 ***
## Residuals  8  66.65    8.33                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(lm.2)
## Analysis of Variance Table
## 
## Response: y1
##           Df Sum Sq Mean Sq F value    Pr(>F)    
## x1         1 4674.3  4674.3  115.64 4.921e-06 ***
## Residuals  8  323.4    40.4                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

由上述討論可以發現 1.單位改變後兩變數的判定係數()不變