Tricky question: obtain r2 from a sample of 10 observations...that are unknown.

#1
OK, I've been trying to figure this problem out for 2 whole days... its tough, at least to me, and its driving me crazy! Any help would be GREATLY appreciated.

From a sample of 10 observations, the following results were obtained:
sum(Yi)=1110
sum(Xi)=1700
sum(XiYi)=205500
sum(Xi^2)=322000
sum(Yi^2)=132100

The r^2 = 0.9758. But, on rechecking these calculations it was found that two pairs of observations were accidentally recorded, Y 90 X 120 and Y 140 X 220 -- instead of -- Y 80 X 110 and Y150 X 210.

Obtain the correct r^2.

...so I can tell that the new Ybar is the same, 111. and the new Xbar will be 168 instead of 170. The original sum(Yi^2) has to be wrong as well as the sum(XiYi) and sum(Xi^2).

How the heck do you do this?! (Not looking for a solution, just some detailed hints if possible.)

Thanks very much for reading!
 

Dragan

Super Moderator
#2
From a sample of 10 observations, the following results were obtained:
sum(Yi)=1110
sum(Xi)=1700
sum(XiYi)=205500
sum(Xi^2)=322000
sum(Yi^2)=132100

The r^2 = 0.9758.

Are you sure that the numbers above you're reporting also yield the r^2 = 0.9758??
 
#3
I'm really not that sure. That's how the problem is stated and I think that most of my trouble is coming from confusion.

Using the original numbers, I calculated R to be .99640, R2 .99281

If the problem is just worded funnily, I could be making things more complicated than they are.

I think it would make sense that if the variation in Y using the corrected observations stayed the same, but the variation in X went up, the R would go up as well, right? More variation in X makes for a stronger regression? (if the corrected numbers were used for the values above rather than the wrong ones)

...But it wouldn't make sense to ask for anyone to interpret the syntax of this question.

Basically what I should be asking is... can the question be answered as I posted it above? If so, what is right in front of my nose that I'm missing.
 
Last edited: