y 与 x 相关的预测区间

[#1]

你好，

我有两个相关的变量，希望得到 y vs x 的预测区间为 9.9%。我可以对线性回归拟合执行此操作。我的问题是是否有其他技术可以实现这一点。我已将 y vs.x 附上回归线。特别是我想知道 x 变量的哪个范围在 99.9% 置信度下给出 (a,b) 之间的所有 y 变量。

谢谢

亚当

[#2]

通过 X 拟合 Y 平台，您可以绘制（或保存）拟合和/或单个预测的置信区间。允许要求 99.9% 的置信区间，尽管这是一个不寻常的选择。对于您的密切关联，拟合的 99.9% 置信区间可能会起作用，但如果您想要单独的预测区间，我相信 99.9% 的区间太宽而没有意义。

[#3]

嗨，戴尔，

非常感谢您的快速回复。 我得到了附件中显示的 999% 预测区间。 上预测区间在某些数据内。 x 和 y 都是高斯分布的。 在上预测区间之外有数据可以吗？

谢谢

亚当

[#4 · Accepted solution]

With this much data you should expect some points to lie outside the confidence interval (regardless of the %).  If it is a mean confidence interval, indeed most points would like outside the interval.  If they are individual predictions, then fewer should be outside the interval.  Since the model is not perfect (it is only a model), of course some points will randomly vary outside the interval. 

However, the graph you provide suggests something else is going on.  There is an entire section of points outside the interval - this strongly suggests a lurking variable (likely a nominal variable) that is giving two groups of responses.  So, conditional on x, y appears to fall into two distinct ranges.  Failure to identify this lurking grouping variable means that the resulting confidence interval is too wide - and also, that at least one group will systematically (not randomly) lie outside the interval.

[#5]

Thanks Dale. I was able to identify the groups with distinct values and get the prediction interval vs. various groups. 

Thanks again.

Regards,

Adam