# What is the relationship between R-squared and MS(Res)?

My textbook (Applied Regression Analysis: A Research Tool by Rawlings, Pantula, and Dickey) asks me to "Show algebraically the relationship between R-squared and MS(Res)", but I don't even know what this relationship should look like.

Thanks for any help in advance.

• You should be able to figure out how they're related from equation 7.2. Alternatively start from $R^2=1-\frac{\text{SS(Res)}}{\text{SS(Tot)}}$ and derive it from the relationship between $\text{SS(Res)}$ and $\text{MS(Res)}$. However, it will also be in terms of some other quantity (SS(Tot), MS(Tot), SS(Reg) etc). I don't see it specified which they want in what I can see on Google books, though it's easy to move between them. You may be able to see something I can't – Glen_b Oct 18 '15 at 21:50
• Are you saying, that MS(Res) is equal to SS(Total) * ((1-R^2)/(n-p'))? – shmiggens Oct 18 '15 at 22:00
• There are several different ways you could write the relationship, and as I said, it's not 100% clear to me what is wanted (but I can't see the whole book). In the case of the formula you just gave it may make more sense to write SS(Total) to a multiple of MS(Total) so that both terms are mean squares. – Glen_b Oct 18 '15 at 22:04