This expression right here would be a surface, I guess you could view it as a surface in three dimensions, where for any m and b is going to be a point on that surface that represents the squared error for that line.

这个表达式可以看作一个表面，在三维空间中，对于任意的斜率m和b，会在这个表面上有一个点，代表该直线的平误差。

In the cost function, the squared error for the second example is also 0 squared.

在成本函数中，第二个示例的平误差也 0 平。

The fifth column is the F value. This is determined by dividing the mean square for the treatments by the mean square error. It is this value that determines if there are any significant differences between the treatment means.

第五列F值。这通过将处理的均除以均误差来确定的。正这个值决定了处理平均值之间在显着差异。

If the squared error of the line is huge, then that means there's a lot of error between the data points and the line.

如果直线的平误差很大，那就意味着数据点与直线之间的误差很多。

So if we find the m and the b values that satisfy the system of equations, we have minimized the squared error.

所以如果我们找到了满足程组的m和b值，我们就最小化了平误差。

And we want the squared errors between each of the points of the line.

我们希望得到线上每个点之间的平误差。

So this is the squared error of the line.

所以这就这条直线的平误差。

Our goal is to find the m and the b, which would define an actual line, that minimize the squared error.

我们的目标找到斜率m和b，它们定义了一条实际的直线， 使平误差最小。

So this whole expression, I'm just going to rewrite it, is the same thing as-- and remember this is just the squared error of the line.

所以这整个表达式，我只要重写它，一样的——记住这只直线的平误差。

You put it into this expression for the squared error of the line.

你把它代入这条线的平误差表达式中。

This is the squared error of the line axis.

这直线轴的平误差。

So are squared error versus our line, our total squared error, we just computed to be 2.74.

所以我们的平误差相对于这条线，总的平误差我们刚刚计算出来2.74。

So once again, this is just the squared error of that line with n points.

所以再一次，这只那条有 n 个点的直线的平误差。

Sometimes, it's called the squared error.

有时，它被称为平误差。

And so you can even visualize it the same way we visualized the squared error from the line.

你可以用同样的式来可视化它，就像我们可视化从回归线的平误差一样。

We have the squared error of the line.

我们有了这条线的平误差。

If the squared error of the line is really small what does that mean?

如果直线的平误差真的很小，那意味着什么？

The way that we do that, is we find a point where the partial derivative of the squared error with respect to m is 0, and the partial derivative with respect to b is also equal to 0.

我们实现这一点的法，找到一个点， 使得平误差对m的偏导数为0， 同时对b的偏导数也等于0。

If the squared error of the line is small, it tells us that the line is a good fit.

如果直线的平误差很小，就说明这条直线拟合得很好。

And so if the squared error of the line is large, this whole thing's going to be close to 1.

如果这条线的平误差很大，那么整个式子就会接近1。