(no subject)

[rivka]

In the years since high school, I've managed to completely forget how to do algebra.

No, scratch that. It's just been in the years since I took the GRE. I know I could do algebra when I took the GRE.

*sfx: tearing hair*

Comments

Re:

[redbird]

That's one equation in two unknowns; lacking a known value for y, it's a curve.

Re:

[rivka.livejournal.com]

Right. I was looking for a general equation in which to plug different values of y, to get x.

The specific y value I was working with was 0.246, but it doesn't really matter to the construction of the general equation.

(The values of y I have are odds ratios, which I want to convert to probabilities.)

Re:

[lerryn.livejournal.com]

My solution to that is to plug in the *insert obscenity here* y value of choice, then worry about solving for x. I seem to recall the real solution invoving taking the log of both sides, but that's just a pain.

Re:

[rivka.livejournal.com]

I had the y-value-of-choice, and I still couldn't solve the goddamned equation. And I did very well on the Math GRE! It's inexplicable.

Re:

[akicif.livejournal.com]

I cheated - rearranging the equation to give things like x = y + xy didn't really help, so I tried slotting in values of 0, ±1 and ±100 for x to get the general shape of the curve. When the absolute value of x is large y tends towards -1, when x is 0 y is 0 and there's a discontinuity at x = 1, where y effectively goes from plus to minus infinity.

This, of course, didn't help solve the beastie at all, so I tried sticking it in a spreadsheet and graphing it, then zooming in to give:



It is a cheat, and there's no doubt far better software for doing it with than Excel, but when the tool I've got's a hammer....

[wcg.livejournal.com]

Hey, it doesn't have to be that complicated, really!

To solve y = x/(1-x)

First, invert: 1/y = (1-x)/x
Now rewrite the right side of the equation as 1/x - x/x
Which is 1/x - 1

So now we know that 1/y = 1/x - 1
Or, 1/y + 1 = 1/x

From there just invert again, and you end up with:

x = y/(1+y)

[akicif.livejournal.com]

<FX="slaps head" /> Of course! Forgot I could invert .... it's not just algebra I'm losing, it's basic maths.

[rivka.livejournal.com]

I forgot that I could invert, too. Unless I never knew it in the first place. Yay for wcg.

[rivka.livejournal.com]

Misha solved it in about ten seconds without inverting anything, so now I feel even more abashed. I mean, even if I did forget that you can invert, I should have been able to find this solution:

y = x/(1-x)

x = y(1-x)

x = y-yx

yx+x = y <--(this is as far as I got)

x(y+1) = y

x = y/(y+1)