1. ## Residual Analysis

I'm wondering if someone can give me a brief explanation of what residual analysis is and what it's used for. I know it can be used to test for normality, and for detecting outliers, but I'm not sure how. My book doesn't really help.

Any help would be greatly appreciated.

2. Are you using a statistical program when analyzing the residuals?

3. Yes. I'm using SAS.

I forgot to mention that it's multivariate data, instead of univariate.

4. I haven't used that, but for instance, with eViews, I can go to residual table, and it will show which values lie outside two standard deviations. Look for something like that.

5. When the residuals are graphed, if one residual is particularly farther away from the x-axis than others, then we can conclude that the corresponding y-value is most likely an outlier. Also, the residuals are used in finding the Root Mean Square Error (RMSE), and this determines how good a model is relative to a data set.

$\displaystyle \sum_{n=2}^{n} \frac{(z_i-x_i)^2}{n-2}$

Where z represents the model, x represents the data set. Notice that the upper part of the fraction is actually just the residuals squared. Sorry about the summation symbol, Latex was being uncooperative.

Where Y is an (nxm) matrix and B is an [(r+1)xn) matrix. Y can also be writen as $\displaystyle Y = [Y_1 | Y_2]$ where Y1 and Y2 are both n x 1 vectors.