So I am learning about Sigmoid Curves and in this article it says the formula is:$$\tag{1} \frac{1}{1+e^{-\beta_0-\beta_1x}} $$Then it gives an example problem: Let’s say you take $ \beta_0 = -15$ and $\beta_1 = 0.065$. Now, what will be the probability of diabetes for a patient with sugar level $220$?
And the answer is given as follows:
The probability of diabetes for a person with sugar level $x$ is given by $\mathrm{P}(\mathrm{Diabetes})=\frac{1}{1+e^{-\beta_0-\beta_1x}}$. Now, taking $\beta_0=−15$ and $\beta_1=0.065$, the probability of diabetes for a person with sugar level $220$ will be given by
$$\mathrm{P(Diabetes)}= \frac{1}{1+e^{15-0.065\cdot 220}}\approx 0.33$$
So the answer is $0.33$. But I am not sure how they reached this result. I know that $-15+ 0.065\cdot 220 = -0.7$, but I dont know how the whole equation computes to $0.33$
Can anyone help in understanding? My math knowledge is very poor so I appreciate any help!
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$\begingroup$I'll just go ahead and post this as an answer. In Excel, you can write:
=1/(1+EXP(-(-15+0.065*220)))which returns $\approx 0.3318$. Another way to evaluate the expression, in Wolfram Alpha, is here:
So the lesson to take home from this, is that in Excel you just need to use the EXP function to calculate the exponentiation. And remember to use proper parentheses.
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