Statistical point: the variance of forecast error for correctly specified simple regression problems is equal to:
Sigma^2(1 + 1/N + (x_o—x_mean)^2 / (Sigma ( x_i—x_mean) ^2))
So forecast error increases as x_o moves away from x_mean, especially when the variance of x is low by comparison.
Edit: Sub notation was apparently indenting things. I’m going to take a picture from my stats book tonight. Should be more readable.
Edit: Here’s a more readable link. http://i.imgur.com/pu8lg0Wh.jpg
(1) Imgur offers editing capabilities. (2) LW allows images.
The get the imagevar(f)=σ2(11N(x0−¯x)2∑(xi−¯x)2)use the following code in your comment:
See Comment formatting/Using LaTeX to render mathematics on the wiki for more details. I’ve used codecogs editor and fixed an issue in the URL manually; there are other options listed on the wiki. The LaTeX code for the codecogs editor is this:
\textit{var}(f) = \sigma ^ 2 \left ( 1+\frac{1}{N} + \frac{(x_0 - \bar{x})^2}{\sum (x_i-\bar{x})^2} \right )
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Statistical point: the variance of forecast error for correctly specified simple regression problems is equal to:
Sigma^2(1 + 1/N + (x_o—x_mean)^2 / (Sigma ( x_i—x_mean) ^2))
So forecast error increases as x_o moves away from x_mean, especially when the variance of x is low by comparison.
Edit: Sub notation was apparently indenting things. I’m going to take a picture from my stats book tonight. Should be more readable.
Edit: Here’s a more readable link. http://i.imgur.com/pu8lg0Wh.jpg
(1) Imgur offers editing capabilities. (2) LW allows images.
The get the image
var(f)=σ2(11N(x0−¯x)2∑(xi−¯x)2)
use the following code in your comment:
See Comment formatting/Using LaTeX to render mathematics on the wiki for more details. I’ve used codecogs editor and fixed an issue in the URL manually; there are other options listed on the wiki. The LaTeX code for the codecogs editor is this: