For a factor X with d categories, the one-factor mean function is where Uj is a dummy variable equal to 1 for the jth level of the factor and 0 otherwise. Show that the residual sum of squares can...

For a factor X with d categories, the one-factor mean function is

where Uj is a dummy variable equal to 1 for the jth level of the factor and 0 otherwise.

Show that the residual sum of squares can be written

where SDj is the standard deviation of the responses for the jth level of X. What is the df for RSS?