통계에서 monotonic이란 표현의 의미는?

Monotonic relationship이란 두 변수(variable) 간의 관계가 

· One variable increases and the other increases.
· One variable decreases and the other decreases. 

인 경우를 뜻한다. 얼핏 보면 linear와 같은 게 아닌가 싶은데, 이에 대해서 아래와 같이 설명한 사이트가 있어 적어본다. 

https://www.statisticshowto.datasciencecentral.com/monotonic-relationship/

This increases (or decrease) doesn't have to happen at the same rate. For example, the data in the image b above is monotonic and linear. Linear relationships are monotonic (as shown in image b) and linear. Linear relationships are monotonic (as shown in image b), but not all monotonic relationships are linear (as shown in image a). 

· Monotonic variables increase (or decrease) in the same direction, but not always at the same rate.
· Linear variables increase (or decrease) in the same direction at the same rate.

If an increase in the independent variable causes a decrease in the dependent variable (image b), this is called a monotonic inverse relationship. An inverse relationship is the same thing as a negative correlation. A monotonic direct relationship is where an increase in the independent variable causes an increase in the dependent variable (image a). In other words, there's a positive correlation between the data.

즉 정리하면 linear은 monotonic과 다르다. monotonic은 한 변수가 증가할 때 다른 변수가 증가하는 것을 이야기 하는 것이고, 두 변수 간 양적 관계가 명확한 것은 아니다. linear은 두 변수간에 x가 1이 증가하면 y가 2가 증가하는 식으로 양적 관계가 명확하다. 
monotonic direct relationship은 positive correlation과 같은 뜻이고, monotonic inverse relationship은 negative correlation과 같은 뜻이다.