计算直线和水平轴之间的角度

Question

考虑以下玩具数据集：

clear
input double(x y)
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end

现在考虑以下图表：

twoway line y x || scatteri 0 0 "Line A", msymbol(none) msymbol(none) /// 
mlabgap(0) mlabposition(0) mlabangle(60) legend(off)

显然，直线A相对于x-axis的角度是60度（手动指定）：

我试图按照我在similar post中找到的建议来计算这个角度：

summarize y
scalar y1 = r(min)
scalar y2 = r(max)

summarize x
scalar x1 = r(min)
scalar x2 = r(max)

scalar dy = y2 - y1
scalar dx = x2 - x1

display (180 / _pi) * atan2(dy, dx)
89.990983

为什么Stata会生成一个角度为60而不是90度的图形？

如果我将图形的纵横比设置为1，则角度似乎会更改为68，它仍然远不及计算值：

twoway line y x || scatteri 0 0 "Line A", msymbol(none) msymbol(none) /// 
mlabgap(0) mlabposition(0) mlabangle(68) legend(off) aspectratio(1)

如果给出尺度和纵横比的差异，我怎样才能始终如一地计算角度？

Answer 1

x和y轴在图中处于不同的比例，因此这不是1：1的纵横比，并且将绘制许多角度与具有相等轴比例的预期角度不同。这在几个图形包中是默认的，因为它通常更好地在图形中传播数据。