The partial regression plots can be used to examine an influential observation for a single parameter in multiple regression. However, it is often desirable to detect an influential observation for a subset of regression parameters when interest centers on a selected subset of independent variables. Cook and Weisberg (1980) suggest a statistic which can be used for this purpose.
In this paper, first, the partial regression is redefined to include more than a single parameter and its properties are discussed. Next, using the partial regression model, two statistics are suggested to detect an influential observation on a subset of regression parameters. An example is illustrated to compare the proposed statistics with the statistic of Cook and Weisberg.