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안녕하세요! 이번에 Super Stat 강의를 듣게 된 학생입니다.
L10에서 "Some Facts about Regression"이라고 되어있는 첫번째 slide에 두번째 point가 "If you graph z-scores of y against z-scores of x, then the slope of the regression line would become precisely r, and intercept would be zero" 라고 되어있는데요
선생님 설명 중에 b= r* (Sy/Sx)이고 Sy/Sx가 standardized되면 1이 되기 때문에 상쇄되서 b=r이 된다는 부분은 이해했습니다만
graph z-scores of y against z-scores of x가 무슨 소리인지 이해가 안됩니다 ㅠㅠ 그리고 그것이 Sy/Sx가 standardized되는데 어떠한 영향을 미치는지도 이해가 안되구요 ...ㅠ 그래서 intercept가 0이 된다는 것은 무슨 의미인가요?
평소에 설명 너무 잘해주셔서 강의할 때 이해가 잘 되서 감사드려요!
Have a wonderful day :)
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Let's say we have 3 points in a scatterplot: (1, 1) (2,2) (3,3)
Then the plot will be a straight line through the origin.
Here, x-bar = y-bar = 2, and Sx = Sy = root(2/3)
so the z score version of the three data points would be: (-1/root(2/3), -1/root(2/3) ), (0,0), ( 1/root(2/3), 1/root(2/3) )
In fact, the point (x-bar, y-bar) would always become (0,0)
since the original data points will give you a regression line: y-hat = a + bX
and it ALWAYS passes through the point (x-bar, y-bar)
so the converted (Z-score versions) regression line will always pass through the origin. Hence the y-intercept, a, will be zero.
In this example the original data's regression line passed through the origin as well, but this is fortuitous; this will be true for any dataset.
Hope this helps :)
Jason.
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