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I wanna know which test should I use to see if there's correlation between the number of risk factors for a disease (three groups: none, 1, 2 or more), and the presence of symptoms for this disease (two groups: yes or no).

I'm very confused about the hypothesis I want to test, but I think my question would be "As risk factors increase, do patients become more symptomatic?"

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I'd phrase this as a logistic regression model, where the model is $$ \log(\frac{p}{1-p}) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \epsilon_i, $$ where $x_1$ is 1 if there is 1 risk factor present, zero otherwise, and $x_2$ is 1 if there are 2 or more risk factors present, and zero otherwise.

Once the model has been fit (easy to do in R or Python), the coefficients can be interpreted as the difference in log odds between when the respective regressors are zero and one.

Note that $p$ is the likelihood of disease, and the expression $log(\frac{p}{1-p})$ is known as the log odds of the disease.

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