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!
I'll just go ahead and post this as an answer. In Excel, you can write:
which returns $\approx 0.3318$. Another way to evaluate the expression, in Wolfram Alpha, is here: https://www.wolframalpha.com/input/?i=1%2F%281%2Be%5E%28-%28-15%2B0.065*220%29%29%29
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.