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I would like to rearrange the logistic function:

$$y=\frac1{1+\exp(-a+bx)}$$

To calculate $x=f(y)$

So I did the following:

$$\frac1{y}=1+\exp(-a+bx)$$ $$\ln\left(\frac1{y}-1\right)=-a+bx$$ $$\frac{\ln\left(\frac1{y}-1\right) +a}{b}=x$$

but when I try to plot this function, it appears that I have lost a '-' somewhere, i.e., I have calculated $-x=f(y)$

Where I have missed the negative sign?

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    Are you sure your original function is written correctly? Shouldn't $x$ have a negative coefficient?2011-04-19
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    @Qiaochu Do you mean $y=\frac{-1}{1+\text{exp}(-a+bx)}$?2011-04-20

2 Answers 2