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EXAM 1 - Note Dr M's comments appear in this green typeface...

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Note: Dr. M's comments appear in this green typeface. Question 1 Compare the difference between Sum of Squares in one-factor 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 one-factor 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 One-Factor ANOVA and for Sum of Squares in regression are the same. Total SS = ∑( Ýi- Ŷ) 2 This equation is used in both One-factor 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 mean-grand 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 mean-grand 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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