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I have a dataset with the following variables:
-Branch (Categorical: Toronto, Montreal, Seattle, etc.)
-Attrition (Binary: Stay, Churn)
-Promotion (Binary: Promoted, Not Promoted)
-Sales Plan (Continuous, this is how much an employee must sell in that month)

I am not sure how best to analyze this. I have done a Fisher Test on the two binary variables, and got a very low p-value. Results below:

Fisher's Exact Test for Count Data
data:  dat2
p-value < 2.2e-16
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
1.764765 2.538665
sample estimates:
odds ratio 
  2.114975 

But I am not sure how to read the results to say that promoted employees are less likely to leave than non-promoted employees.

Moreover, I'd also like to show that the higher the sales plan, the more likely an employee is to leave. I've been warned recently that I can't do simply corrs between continuous variables and binary variables. I would also like to see if region has any impact on attrition.

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You want some form of regression. Which form depends on how churn (the dependent variable) is measured. Given that it is binary, and assuming you have data on individuals (that is, each observation in your data set is one person) you should do logistic regression.

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