Regression is commonly used in trend analysis for time$-$series data sets. An item in a time$-$series database is usually associated with properties in multidimensional space. For example, an electric power consumer may be associated with consumer location, category, and time of usage $($weekdays vs$.$ weekends$).$ In such a multidimensional space, it is often necessary to perform regression analysis in an OLAP manner $($i$.$e$.,$ drilling and rolling along any dimension combinations that a user desires$).$ What appropriate mechanism can be done so that regression analysis can be performed efficiently in multidimensional space?