Limit theorems for change in linear regression

We consider some tests to detect a change-point in a multiple linear regression model. The tests are based on the maxima of the weighted cumulative sums processes. The limit distributions may be double exponential or maxima of Gaussian processes depending on the set where the maximum of the weighted cumulative sums of residuals is taken. The design-points can be fixed or random. We also give a few applications of our results.