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Deletion residuals

The $i^{th}$ deletion residual $e_{−i}$ is defined as $e_{−i}=y_{i}−X^{⊤}B_{−i}$ where $X^{⊤}$ is the $i^{th}$ row of the design matrix $X$ and $B_{−i}$ is a column vector of least square parameter estimates calculated without the $i^{th}$ observation. Write some annotated R code to calculate the deletion residuals when the linear model $y_{i}=B_{0}+B_{1}X_{i}+B_{2}X_{2i}+E_{i}$ is fitted to the data in the file quadratic.txt. By drawing suitable plot, comment on the distribution of these deletion residuals.

should I write what the exactly distribution?

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marked as duplicate by Andy W, jbowman, whuber Dec 5 '12 at 1:51

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Please don't copy and paste homework assignments verbatim. Put some effort into it and show what you have done so far. As is the last sentence doesn't even make sense. – Andy W Dec 4 '12 at 23:52

1 Answer 1

Agree with Andy W.

There's no way of learning R without practice...

To make your life easier:

$$ e_{(i)}=\frac{e_i}{1-h_{ii}} $$

where $e_i = y_i - \hat{y_i}$ and $h_{ii}$ is the $i^{th}$ element of the diagonal of the matrix $H = X(X^tX)^{-1}X^t$

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how can I get vec command in R thanks – hhh Dec 5 '12 at 18:40

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