# Rearranging an equation to solve for a variable

### Rearranging an equation to solve for a variable

In this problem, I need to rearrange the equation to solve for the variable of interest which is TSS.

I have been given the following values to use to solve the problem:

R2 = 0.78
However, when I try to rearrange the equation I think I am doing something wrong but I am not sure what exactly.

This is the equation: I am trying to rearrange:

$$R^2 = 1-\binom{RSS}{TSS}$$

I know the value of TSS should be ~ 1227.78, but I just cannot get this result when I try to rearrange the equation.

To see where I may be going wrong, please see the screenshot of my whiteboard below:

https://i.stack.imgur.com/VN9pD.png

Guest

### Re: Rearranging an equation to solve for a variable

Is $$\begin{pmatrix}a \\ b \end{pmatrix}$$ the binomial coefficient?
Guest

### Re: Rearranging an equation to solve for a variable

Ah, so it is just a fraction!
$$R_2= 1- \frac{RSS}{TSS}$$ and you want to solve for TSS.

Yes, "clear the fraction" by multiplying both sides by TSS- but you did that incorrectly!

$$R_2(TSS)= TSS- RSS$$. You didn't multiplty the "1" by TSS.
$$R_2(TSS)- TSS= (R_2- 1)TSS= -RSS$$

$$TSS= -\frac{RSS}{R_2- 1}$$

With $$R_2= 0.78$$ so that $$R_2- 1= -0.22$$ and $$RSS= 246.66$$
[tex]TSS= -\frac{246.66}{-0.22}= 1121.18
Guest