May I please use your stat advise on the following question.
There are 45 schools and each school has a different number of students. All 45 schools can be ranked accordingly to the number of students from the school with the lowest to the school with the highest number of students.
I'd like to perform a cross-sectional analysis of flu illness in all schools and my hypothesis is that the schools with higher number of students will have a higher rate of flu illnesses and average duration of illness. The rate is calculated as the number of cases of flu per total number of students in that school. The average duration of illness is in days.
I believe that there is a linear relationship between number of students and flu rate (as the number of students go up the flu rate will also go up) as well as there is a linear relationship between number of students and average duration of illness (as the number of students go up the average duration of illness will also go up).
My goal is to construct a linear graph as well as to perform some statistical analyses to show the correlation.
My question is which stat tests can use and which correlation test is the best fit for this problem?