I have two questions below:
Could a data point be an influential point if its cook distance is outstanding(greater than 4/(n-p-1)) while its standardised residual is less than 2? It looks like to me , to say a data point is an influential point, its Cook's distance has to be larger than 4/(n-p-1)) AND its standardised residual has to be greater than 2, am I correct?
Sometimes when we delete an influential point, the regression line does't change much then we leave the data point in the model. But why the influential point didn't change the regression line much? According to its large cook's distance, the data point is an influential point, being an influential point means the data point has to change the regression line very much if it is deleted,otherwise it shouldn't be called an influential point, isn't it?