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I'm working with some regression related stuff at the moment and i'd need some help with multiple variable prediction interval. Prediction interval for a single variable can be calculated using

[tex] PI = \hat{\beta_0}+\hat{\beta_1}x_i \pm t^* s_e \sqrt{1+\frac{1}{n} + \frac{(x_i-mean(x))^2}{S_{xx}}}[/tex]

where x can be thought as a 1 dimensional vector (or matrix/set) which holds the values x_0, x_1, x_2 and so on. Also, [itex]\hat{\beta_0}+\hat{\beta_1}x_i[/itex] is a linear regression line [itex]\hat{y}[/itex]. Finally, [itex]t^*[/itex] is the t-percentile, [itex]s_e[/itex] is standard deviation, [itex]n[/itex] is the amount of points in the sample and [itex]S_{xx} = \sum{(x_i-mean(x))^2}[/itex] from 1 --> n.

__Now what does the equation look like for multiple variable regression?__

I'd suppose [itex]\hat{\beta_0}+\hat{\beta_1}x_i[/itex] is easily changed to

[tex]\hat{\beta_0}+\hat{\beta_1}x_{0i}+\hat{\beta_2}x_{1i}+\hat{\beta_3}x_{2i}+...[/tex]

but what do i do with

[tex]\frac{(x_i-mean(x))^2}{S_{xx}}[/tex]

?