Solving R^2 = 1- ((1-R^2)(N-1)/(N-K-1)) for R^2

[spaul]

Sorry if this is in the wrong place!!

I am struggling with an Econometrics formula: Adjusted R^2 = 1- ((1-R^2)(N-1)/(N-K-1))

Please can someone help me solve for R^2? I am struggling to achieve this.

Thanks

 

[stapel]

Adjusted R^2 = 1- ((1-R^2)(N-1)/(N-K-1))

Please can someone help me solve for R^2? I am struggling to achieve this.

Unfortunately, we cannot check work that we cannot see. Please reply with a clear listing of what you've tried so far.

FYI: One method of attacking this would be to multiply through by the denominator, multiply everything out on each side of the equation, simplify, and then get all terms containing R^2 on one side of the "equals" sign, leaving all the other terms on the other side. Then factor out the R^2, and divide through.

 

[Denis]

R^2 = 1- ((1-R^2)(N-1)/(N-K-1))
Please can someone help me solve for R^2? I am struggling to achieve this.

Keep it simpler: use R instead of R^2 and let U = N-1 :
R = 1 - U(1-R)/(U-K)

HOKAY?

 

[spaul]

Unfortunately, we cannot check work that we cannot see. Please reply with a clear listing of what you've tried so far.

FYI: One method of attacking this would be to multiply through by the denominator, multiply everything out on each side of the equation, simplify, and then get all terms containing R^2 on one side of the "equals" sign, leaving all the other terms on the other side. Then factor out the R^2, and divide through.

Hello, sorry - here's what i worked out but it is wrong because when i substitute the numbers in place for N,K & A it doesn't create the same answer.

 

[HallsofIvy]

Sorry if this is in the wrong place!!

I am struggling with an Econometrics formula: Adjusted R^2 = 1- ((1-R^2)(N-1)/(N-K-1))

Please can someone help me solve for R^2? I am struggling to achieve this.

Thanks

This is equivalent to x= 1- ((1- x)A) where x= R^2 and A= (N- 1)/(N- K- 1).

So x= 1- A+ Ax. x- Ax= 1- A, x(1- A)= 1- A so x= 1 as long as A is not 1. That is, R^2= 1 as long as K is not 0. If K= 0 any value of R^2 satisfies that equation since then it reduces to R^2= R^2.

 

[Denis]

Hello, sorry - here's what i worked out but it is wrong because when i substitute the numbers in place for N,K & A it doesn't create the same answer.
View attachment 10004

The equation in your attachment is NOT the same as the one you originally posted.
And the 1st step in your attachment is NOT correct:
as example, if a = 1 - b/c, then ac = 1 - b is NOT correct....

 

[spaul]

The equation in your attachment is NOT the same as the one you originally posted.
And the 1st step in your attachment is NOT correct:
as example, if a = 1 - b/c, then ac = 1 - b is NOT correct....

Hello, they are the same the R^2 is a figure of speech it's not actually a squared value. Is there anything else that is wrong?

can you explain what if a = 1-b/c what is ac? Thanks

 

[Denis]

can you explain what if a = 1 - b/c what is ac? Thanks

multiply equation by c:
ac = c - b

ac - c = -b ............ ac = c - b
c(a - 1) = -b
c = -b / (a - 1)

That's quite basic stuff.
Are you a student attending math classes?

 

[stapel]

can you explain what if a = 1-b/c what is ac?

You have given us this equation:

. . . . .\(\displaystyle a\, =\, 1\, -\, \dfrac{b}{c}\)

To find an expression for "ac", multiply through by "c":

. . . . .\(\displaystyle ac\, =\, c\, -\, b\)

The answer would have been different, of course, had you given us "a = (1 - b)/c":

. . . . .\(\displaystyle a\, =\, \dfrac{1\, -\, b}{c}\)

. . . . .\(\displaystyle ac\, =\, 1\, -\, b\)