Suitable regression method Linear, mixed or non linear I have the below data related to a clinical study. I would like to understand if there is a correlation in prescribing the prescription per Genral practioner. In the data there are 3 GP's handling 14 patients GP 1 handled 5 patients, GP 2 handled 4 patients and GP 3. I want to know if the patients have strong or weak correlation in terms of having similar number of prescriptions prescribed by their GP. To understand the correlation by group what is the suitable method I can apply? Thank you for your help.
GP_Id Pat_Id    Total_prescribed_prescriptions
1   a   1
1   b   2
1   c   4
1   d   1
1   e   2
2   f   7
2   g   2
2   h   1
2   i   7
3   j   8
3   k   9
3   l   4
3   m   6
3   n   4

 A: The dataset is quite small so anything we find here should be treated cautiously.
The first thing I would do here is to plot the data:
library(ggplot2)
GP <- c(1,1,1,1,1,2,2,2,2,3,3,3,3,3)
presc <- c(1,2,4,1,2,7,2,1,7,8,9,4,6,4)
dt <- data.frame(GP = as.factor(GP), presc)
ggplot(dt, aes(y = presc, x = GP, color = GP)) + geom_boxplot()


From this we can see there is clear evidence that GP3 issues more prescriptions that GP1. There is also some evidence that GP2 issues more prescriptions that GP1, and a little less evidence that GP3 issues more prescriptions than GP2
We could also fit a regression model. Since the data are counts, this would be a generalised linear model with a poisson family distribution.
> summary(glm(presc ~ GP, data = dt, family = poisson))

Coefficients:
            Estimate Std. Error z value Pr(>|z|)   
(Intercept)   0.6931     0.3162   2.192  0.02839 * 
GP2           0.7538     0.3985   1.891  0.05857 . 
GP3           1.1314     0.3637   3.111  0.00186 **

This concurs with our visual findings: There is strong evidence that GP3 issues more prescriptions that GP1, and moderate evidence that GP2 issues more prescriptions that GP1.
Again, I would recommend using caution with these findings due to the small sample size.
