We have the covariance of these two random variables.

我们有这两个随机变量的协方差。

And then we do the covariance between the vertical movements of wind and the concentration of gas.

然后我们计算风的垂直运动和气体浓度之间的协方差。

It's called an eddy covariance tower.

它被称为涡流协方差塔。

Now we don't know the entire covariance, we only have one sample here of this random variable.

现在我们不知道整个协方差，我们这里只有这个随机变量的一个样本。

Well, you could view this as the covariance of X with X. But we've actually already seen this.

好吧，您可以将其视为 X 与 X 的协方差。 但实际上我们已经看到了这一点。

The covariance of a random variable with itself is really just the variance of that random variable.

随机变量与其自身的协方差实际上只是该随机变量的方差。

And the degree to which they do it together will tell you the magnitude of the covariance.

他们一起做的程度会告诉你协方差的大小。

Hopefully that gives you a little bit of intuition about what the covariance is trying to tell us.

希望这能让您对协方差试图告诉我们的内容有一点直觉。

I want to connect to this definition of covariance to everything we've been doing with least squared regression.

我想将协方差的这个定义与我们用最小二乘回归所做的一切联系起来。

So this whole video, I'm just going to rewrite this definition of covariance right over here.

所以在整个视频中，我将在这里重写协方差的定义。

And if we kept doing this, let's say for the entire population this happened, then it would make sense that they have a negative covariance.

如果我们继续这样做，假设整个人口都发生了这种情况， 那么它们具有负协方差是有道理的。

And really it's just kind of a fun math thing to do to show you all of these connections, and where, really, the definition of covariance really becomes useful.

实际上，向您展示所有这些联系以及协方差的定义真正变得有用的地方确实是一件有趣的数学事情。

So we were installing what's called an " eddy covariance tower, " which is a series of instruments that measures the exchange of greenhouse gases, like carbon dioxide and methane, between the land and the atmosphere.

所以我们安装了一个被称为“涡度协方差塔”的装置，这种装置由多种仪器构成，用于测量地面与大气温室气体的交换，例如二氧化碳和甲烷。

Gosselin: So on the tower for eddy covariance, in principle, there's two main instruments: one instrument that measures the concentration of gas that we're interested in in the air and [another] that uses infrared.

Gosselin：原则上，在涡流协方差塔上有两种主要仪器：一种测量空气中我们感兴趣的气体浓度，[另一种]使用红外线。

Now, this right here-- so everything we've learned right now-- this right here is the covariance, or this is an estimate of the covariance of X and Y. Now what is this over here?

现在，这就是——所以我们现在学到的一切——这就是协方差，或者这是对 X 和 Y 的协方差的估计。 现在这里是什么？