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I'm a relative novice at statistics and would appreciate some help with a dataset I'm trying to crunch. I'm currently looking at factors that predict increasing utilization of healthcare resources following surgery in a set of 130+ patients. Some of the independent variables I'm looking at include age, BMI, Marital Status, Length of Stay after Surgery, Smoker Status (Y/N), etc. The dependent variables are number of ED visits, readmissions, post-op visits following surgery.

Initially, I was planning to run univariate linear regression on the data set, followed by multivariate regression. However, I tried running the analysis with age vs. ED visits on SPSS and got the following output after checking for assumptions of linearity and normality of residuals:

enter image description here

enter image description here

So based on this, I feel like linear regression is not the way to go and I have to consider analyzing the data via another method. Currently, the variables are coded as continuous variables (both age and ED_visits). What are your recommendations on how to run the data, or maybe recommendations to transform the data in some way to fix better meet assumptions of OLS? Other thoughts I've had include transforming the dependents into nominal variables and doing logistic regression or doing a Poisson regression, but honestly not sure if either of these would solve my problem. Thanks for the help!

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I would do some exploratory analysis before trying to fit a model. Plotting usually is a really good way to have a first hand on your problem.

What I would do in order:

  1. Plot your observed variables against your explanatory variables and see if there is any clear pattern.
  2. Try to aggregate some of the explanatory variables and see if the situation improves. Your dataset is not huge, maybe if you consider age groups (so age as a discrete variable) some sort of trend can appear.
  3. If you start with a linear model you can also build the correlation matrix to see which explanatory variables are better correlated with your observations.
  4. Start fitting a simple model and add the explanatory variables in rounds, checking how the goodness of fit measure compare. You can also plot the predicted values against the observed ones to have a direct feeling of how your model performs.
  5. Check the model's hypothesis.
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