Help Again

#1
If forgot, I had one more. I'm stuck on this equation too:

A quadratic regression model is fit to a set of sample data consisting of 6 pairs of data. Given that the sum of squares of residuals is 18.17 and that the y-values are 11, 14, 19, 22, 26, 27, find

R^2 = 1 - {The sum of (y - the predicted value of y)^2}
divided by:{The sum of y - the mean of y)^2}

So I tried to put the numbers in the equation:
R^2 = 1 - 18.17^2 divided by:
119 - 19.833

fyi: 18.17 = (the sum of squares of residuals); (119= the sum of y) and
(19.833 = the mean of y)

What am I doing wrong?
 

JohnM

TS Contributor
#2
In your equation:

R^2 = 1 - {The sum of (y - the predicted value of y)^2}
divided by:{The sum of y - the mean of y)^2}

Although I'm not completely sure, I think it should actually be:

1 - [ {sum of (y - the predicted value of y)^2} / {sum of y - the mean of y)^2} ]

In other words 1 - [ the fraction of everything else ]

= 1 - [ ( 18.17^2 / (119 - 19.833)^2 ) ]

= 1 - .0336 = .9664

With an r^2 value this high, the regression line should fit the points very closely - is that the case?

 
#3
John,

My question is this:

Did I put the numbers in correctly? (It's hard to write ot the question as it appears on the paper. So I have to substitute since there is no "mean" sign available.)

Was 18.17 in the correct place? I mean, according to the question is the sum of (y - the predicted value of y)^2 - is that where sum of squares of residuals is 18.17 is supposed to be?

I hope I'm not confusing you. Please help.

I tried to put the answer .966 in the homework model and it showed incorrect.
 

JohnM

TS Contributor
#5
I think I found the error-

this formula:

1 - [ {sum of (y - the predicted value of y)^2} / {sum of y - the mean of y)^2} ]

should actually be:

1 - [ {sum of (y - the predicted value of y)^2} / {sum of (y - the mean of y)^2} ]

which would give you:

1 - [ 18.17 / 206.833 ]

= 1 - .0878 = .9122