I have the following question concerning ecological statistics in a scientific study I am performing. I have measured the amount of copepods (little invertebrates) at different locations and at different times of the year together with other parameters from the water. Thus:
I have one single responsible variable y (in this case the number of live copepods in $1m^3$ of water).
I have multiple predictor variables $x_1$ to $x_i$ (in this case temperature, acidity, salinity, amount of ammonium in the water, phosphate).
I have done this at five different locations and for ten different months of the year each time. For a total of 50 different y variables measured and 250 x variables measured.
My hypothesis is that the copepods do not react to any of these environmental factors and they thrive independently of temperature, acidity, etc.
I thus would like a test to demonstrate the lack of correlation or lack of prediction power of the x variables. But I'm not sure what to do. How would you proceed? How would you express the certainty that these x do not influence y?