Automatically detecting outliers is tricky stuff.
You normally need fairly precise information regarding your data as well as the model that you are fitting to your data.
Here's a relatively simple technique that will work for many types of linear models. The methodology is based on a statistics called "Cook's Distance" that you can extract from regstats.
Cook's Distance for a given data point measures the extent to which a regression model would change if this data point were excluded from the regression. Cook's Distance is sometimes used to suggest whether a given data point might be an outlier.
Here's a simple example illustrating how this works
% Create a vector of X values
X = 1:100;
X = X';
% Create a noise vector
noise = randn(100,1);
% Create a second noise value where sigma is much larger
noise2 = 10*randn(100,1);
% Substitute noise2 for noise1 at obs# (11, 31, 51, 71, 91)
% Many of these points will have an undue influence on the model
noise(11:20:91) = noise2(11:20:91);
% Specify Y = F(X)
Y = 3*X + 2 + noise;
% Cook's Distance for a given data point measures the extent to
% which a regression model would change if this data point
% were excluded from the regression. Cook's Distance is
% sometimes used to suggest whether a given data point might be an outlier.
% Use regstats to calculate Cook's Distance
stats = regstats(Y,X,'linear');
% if Cook's Distance > n/4 is a typical treshold that is used to suggest
% the presence of an outlier
potential_outlier = stats.cookd > 4/length(X);
% Display the index of potential outliers and graph the results
X(potential_outlier)
scatter(X,Y, 'b.')
hold on
scatter(X(potential_outlier),Y(potential_outlier), 'r.')
