Correlation between given day and mean of previous days

Hey guys, I would appreciate your help....

I need to find corr coef between daily mortality data and daily pollutant concentrations. I need to do it in 2 ways:

1. Correlation between given day of mortality and the same day of pollutant (e.g. mortality 03/01/2006-pollutant 03/01/2006),

2. Correlation between given day of mortality and mean concentration of pollutant on given day plus 2 days ago ( e.g. mortality 03/01/2006-pollutant 03/01/2006-02/01/2006-01/01/2006).

I am attaching an indicative .xlsx containing the necessary data. Could anyone help me on this?

PS. I'm on Matlab 2019a

[Scott MacKenzie]

It appears you are trying calculate the correlation between one point and another point. This isn't possible. Correlation is calculated between a range of values for one variable (e.g., mortality) and the corresponding values in another variable (e.g., concentration of a certain pollutant).

[Daphne PARLIARI]

What about this: what if I calculate movmean of each pollutant with 3-days window? Could I then calculate corrcoef between mortality on 01/01/2006 and moving average pollutant that corresponds to that day?

[Scott MacKenzie]

Sure, you can calculate the correlation between three points in one variable and three corresponding points in another variable. However, with only three points, the corresponding p-value will be high, which is to say, you can't put much faith in the computed correlation. For example, here's what you get using the first three days in your data set (mortality in column B vs. concentration of PM10_g_m3 in column G):

x = [12, 17, 21]; % B2:B4 
y = [33, 29, 58]; % G2:G4
[R, P] = corrcoef(x,y)

r =

1 0.75492

0.75492 1

p =

1 0.45535

0.45535 1

[Daphne PARLIARI]

Sorry, I didn't mean that...

I meant to first caclulate the movmean of the pollutant (e.g. concentration of PM10_g_m3 in column G) with a 3-day window, thus creating a new "column" with 4018 rows, and then find the corrcoef between the first item of this new "column" and the first item of mortality in column B .

[Scott MacKenzie]

You've just circled back to my original point:

find the corrcoef between the first item of ... and the first item of ...

[Daphne PARLIARI]

Yes right, but I want to see if there is a way I can do it without using movmean in case something is being calculated incorrectly.