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Plot logistic regression for categorical data / difference between LOWESS and logit

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I am trying to predict the probability for my regression model there are some issues. I tried the command which I learned in class but does not give me a single line but lots of them.
My dependend variable is categorical and can take values for 1, 2 and 3 and I guess it's because of that but I don't know what code to use.

I tried

logit Intention indexn1_
predict p
graph twoway line p Intention , ytitle(Propability)
xlabel(0(10)100) ylabel(0(0.2)1) sort


How do I plot the probability for categorical dependent variables?


Or - is there a crucial difference between LOWESS and the predict c and plot it command? I know that LOWESS gives me a local regression, not a logistic one but honestly, I just want to show the relation between the two variables and if LOWESS gives a very similar result to logit and then predict p, I could ommit the latter.



Thank you in advance.

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