I'm taking an online intro class on Statistics and right now we are covering a topic on Relationship between Quantitative Variables. One of the subtopics is Coefficient of Determination. Here is an excerpt from the book:

The coefficient of determination is very simple to calculate if you know the correlation coefficient, since it is just $r^2$. The coefficient of determination can be interpreted as the percentage of variation of the $Y$ variable that can be attributed to the relationship. In other words, a value of $r^2 = 0.63$ can be interpreted as “63% of the variation in $Y$ can be attributed to the variation in $X$.

Here are my questions:
 

1. Why the coefficient of determination can be interpreted as the percentage of $Y$ variable that can be attributed to the relationship? In other words how did the author come up with this interpretation?
    
2. What does the last sentence in the excerpt mean? What does it mean that 63% of the variation in $Y$ can be attributed to the variation in $X$?

Any help is appreciated.

I'm taking an online intro class on statistics and right now we are covering a topic on relationship between quantitative variables. One of the subtopics is coefficient of determination. Here is an excerpt from the book:

The coefficient of determination is very simple to calculate if you know the correlation coefficient, since it is just $r^2$. The coefficient of determination can be interpreted as the percentage of variation of the $Y$ variable that can be attributed to the relationship. In other words, a value of $r^2 = 0.63$ can be interpreted as “63% of the variation in $Y$ can be attributed to the variation in $X$.

Here are my questions:

1. Why the coefficient of determination can be interpreted as the percentage of $Y$ variable that can be attributed to the relationship? In other words how did the author come up with this interpretation?
2. What does the last sentence in the excerpt mean? What does it mean that 63% of the variation in $Y$ can be attributed to the variation in $X$?