测量R中点之间对齐方式的最可靠方法

Question

Until now I used to use cor to measure the alignment between points. I am quite happy with the results, values between -1 and 0 always spot the lines I want. However, thanks to the answers and comments in here , I realised it's not the most robust approach because of the standard deviation being zero for flat lines, such as:

> cor(1:10, rep(10,10))
[1] NA
Warning message:
In cor(1:10, rep(10, 10)) : the standard deviation is zero

My aim is to define a function which gives 1 for points perfectly aligned (regardless the slope) and values closer to 0 for points not in line. Would you suggest a more robust approach than mine?

EDIT:

following the suggestion of @Hong Ooi I got

data1 <- data.frame(date = c(13636, 13636, 14403, 14761, 15201, 15741),
                    value = c(865310, 999989, 999989, 2, 999989, 26))

data2 <- data.frame(date = c(12667, 12745, 13106, 13276, 13461, 13626),
                    value = c(1904, 2055, 2740, 3376, 3567, 4099))

m <- cbind(data1$date, data1$value)
sdev <- prcomp(m)$sdev
sdev[1]/sum(sdev)
# 0.9986399

m <- cbind(data2$date, data2$value)
sdev <- prcomp(m)$sdev
sdev[1]/sum(sdev)
# 0.961

However, I was expecting the a very low value for data1

Answer 1

You could use principal components , or more specifically, the proportion of total variance explained by the first principal component. This is equivalent to fitting the line that minimises the sum of squares of the orthogonal distances of points to the line, as opposed to vertical distances (which is what correlations do).

This can be done in R with either the prcomp or princomp function.

m <- cbind(1:10, rep(10, 10))
sdev <- prcomp(m)$sdev
sdev[1]/sum(sdev)

Answer 2

How about using the R-squared (or adjusted R-Squared) of a regression? After all, an R-squared is simply the square of the sample correlation coefficient.

reg.data1 <-lm(data1$value~data1$date)
summary(reg.data1)$adj.r.squared
#[1] 0.1844582

reg.data2 <-lm(data2$value~data2$date)
summary(reg.data2)$adj.r.squared
#[1] 0.9848801