Pool samples from several individuals

I have a system that can predict that can predict the blood pressure for hospitalized patients from zero to 120 minutes into the future. So my samples are sort of paired. For example, at time 21:00 we predict the blood pressure for the time 01:00. Then we measure the actual blood pressure at time 01:00. Then we can compare the real with the predicted value. Now I want to see if my predictions are statistically significant. So I want to investigate how well my predictions correlate with the real value. I have twenty patients with varying amount of samples, due to different duration of the hospitalization. My problem is that I don't know if I should pool all samples across all the patients or should I only pool one patient's samples at a time. My intuition tells me that I shouldn't pool all samples since patients that have high values also tend to have high errors and patients with more samples will weight more than other patients.
My strategy has been the following so far: For each patient, I take his/her samples and use the Shapiro Wilks test to test for normality. The results tell me that they are not normally distributed. Then I use the Spearman Rho test, and this gives me a p-value and confidence intervals. All patient's except one is significant. So can I take the mean of the p-values, or? I am not confident in my approach. But is this a way to go?