I have data where for a specific threshold, I calculate what percentage of values meet a certain criteria. I want to calculate whether there is a statistically significant trend when I increase the threshold and there is a corresponding increase in the response variable. To give an example, I have the following data for one instance
x_threshold = [1,2,5,10,15,20,25,30,35,40] y_percentage = [47.90046656,53.894081,58.47457627,57.14285714,57.77777778, 57.89473684,59.375,63.15789474,68.75,69.23076923,72.72727273, 80]
At first, I tried the simple Linear Regression which did give a significant slope for this instance. However I am not convinced whether this is the right model to apply since the variables are not exactly continuous. Also note that at each threshold, the sample size n is different and % of n which is meeting a certain criteria is the response variable.
Can an appropriate model be suggested where this kind of data can be fit?