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Question 1
Compare the difference between Sum of Squares in onefactor ANOVA with the Sum of Squares in regression.
We'd need to be a little careful on the wording of the question to be clear that we are talking about ANOVA by Regression. Probably:
Compare the difference between Sums of Squares in onefactor ANOVA (Total, Groups, Error) with the Sums of Squares when ANOVA
is done by regression using dummy variables (Total, Regression, Residual).
Answer 1
Total Sum of Squares for an OneFactor ANOVA and for Sum of Squares in regression are the same.
Total SS = ∑( Ýi Ŷ)
2
This equation is used in both Onefactor ANOVA and ANOVA by Regression.
Ýi=each individual weight.
Ŷ=grand mean of the individual weight (the mean of all the groups).
Don't talk about "weights" unless the question refers to weights. I assume you're referring to the weights of the babies, which is the
example we use over and over. But remember, "weights" also has a mathematical / statistical meaning, as in a "weighted mean".
Technically, Total SS is not a SS of weights in the math sense, so the evil Dr. M. could take off points here. Instead of "individual
weight", you'd want to say "datum" or "data point". Total SS is a SS of data about their mean.
So the total Sum of Square for this is sum of the squared deviation of each individual weight, minus the grand mean of the individuals weight.
There's those weights again!
Group Sum of Squares vs. Regression Sum of Squares:
Group Sum of Squares:
Group SS=∑nj( Ýj Ý)
2
nj=# of people in the group.
Ýj=group men
Hmmm.
...group men? Should that be group mean?
Ý=grand mean
Group Sum or Squares is the (group meangrand mean)
2
and multiply by the number of data points in the group(nj)
Regression Sum of Squares:
Regression SS =∑( Ŷ j Ý)
2
Ŷ j=predicted mean of an individual(Y)
Be careful with your symbols. Above, the symbol Ŷ was the grand mean; now it's a group mean. This is okay because you've defined it 
but don't get yourself confused. And  it's a good idea not to get Dr. M. confused as he's grading your exam!! :)
Ý=grand mean
This may look almost the same as the Group SS but it is just slightly different but we get the same answer. We look at each group and take the
(group meangrand mean)
2
and we do this for each group that we are looking at. It is the same as just multiplying it by the number of individuals
you have.
Well, we haven't hit the really key point! Remember, the reason regression calculations using dummy variables produces the same
results as standard ANOVA calculations is because: "THE PREDICTED VALUE FOR EACH SUBJECT IN THE REGRESSION IS
THE MEAN OF THE SUBJECT'S GROUP." The only reason all of this works is because the predicted values are the group means.
That was a critical point in lecture, and I'd really be looking for it in this answer.
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This note was uploaded on 03/10/2008 for the course BIO 499 taught by Professor Moriarty during the Winter '08 term at Cal Poly Pomona.
 Winter '08
 Moriarty

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